743.35/262.71	YES
743.35/262.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
743.35/262.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
743.35/262.73	
743.35/262.73	
743.35/262.73	Termination w.r.t. Q of the given QTRS could be proven:
743.35/262.73	
743.35/262.73	(0) QTRS
743.35/262.73	(1) DependencyPairsProof [EQUIVALENT, 551 ms]
743.35/262.73	(2) QDP
743.35/262.73	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	(4) AND
743.35/262.73	    (5) QDP
743.35/262.73	        (6) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (7) QDP
743.35/262.73	        (8) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (9) QDP
743.35/262.73	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (11) YES
743.35/262.73	    (12) QDP
743.35/262.73	        (13) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (14) QDP
743.35/262.73	        (15) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (16) QDP
743.35/262.73	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (18) YES
743.35/262.73	    (19) QDP
743.35/262.73	        (20) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (21) QDP
743.35/262.73	        (22) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (23) QDP
743.35/262.73	        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (25) YES
743.35/262.73	    (26) QDP
743.35/262.73	        (27) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (28) QDP
743.35/262.73	        (29) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (30) QDP
743.35/262.73	        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (32) YES
743.35/262.73	    (33) QDP
743.35/262.73	        (34) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (35) QDP
743.35/262.73	        (36) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (37) QDP
743.35/262.73	        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (39) YES
743.35/262.73	    (40) QDP
743.35/262.73	        (41) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (42) QDP
743.35/262.73	        (43) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (44) QDP
743.35/262.73	        (45) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (46) YES
743.35/262.73	    (47) QDP
743.35/262.73	        (48) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (49) QDP
743.35/262.73	        (50) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (51) QDP
743.35/262.73	        (52) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (53) YES
743.35/262.73	    (54) QDP
743.35/262.73	        (55) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (56) QDP
743.35/262.73	        (57) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (58) QDP
743.35/262.73	        (59) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (60) YES
743.35/262.73	    (61) QDP
743.35/262.73	        (62) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (63) QDP
743.35/262.73	        (64) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (65) QDP
743.35/262.73	        (66) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (67) YES
743.35/262.73	    (68) QDP
743.35/262.73	        (69) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (70) QDP
743.35/262.73	        (71) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (72) QDP
743.35/262.73	        (73) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (74) YES
743.35/262.73	    (75) QDP
743.35/262.73	        (76) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (77) QDP
743.35/262.73	        (78) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (79) QDP
743.35/262.73	        (80) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (81) YES
743.35/262.73	    (82) QDP
743.35/262.73	        (83) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (84) QDP
743.35/262.73	        (85) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (86) QDP
743.35/262.73	        (87) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (88) YES
743.35/262.73	    (89) QDP
743.35/262.73	        (90) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (91) QDP
743.35/262.73	        (92) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (93) QDP
743.35/262.73	        (94) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (95) YES
743.35/262.73	    (96) QDP
743.35/262.73	        (97) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (98) QDP
743.35/262.73	        (99) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (100) QDP
743.35/262.73	        (101) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (102) YES
743.35/262.73	    (103) QDP
743.35/262.73	        (104) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (105) QDP
743.35/262.73	        (106) QReductionProof [EQUIVALENT, 3 ms]
743.35/262.73	        (107) QDP
743.35/262.73	        (108) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (109) YES
743.35/262.73	    (110) QDP
743.35/262.73	        (111) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (112) QDP
743.35/262.73	        (113) QReductionProof [EQUIVALENT, 3 ms]
743.35/262.73	        (114) QDP
743.35/262.73	        (115) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (116) YES
743.35/262.73	    (117) QDP
743.35/262.73	        (118) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (119) QDP
743.35/262.73	        (120) QReductionProof [EQUIVALENT, 1 ms]
743.35/262.73	        (121) QDP
743.35/262.73	        (122) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (123) YES
743.35/262.73	    (124) QDP
743.35/262.73	        (125) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (126) QDP
743.35/262.73	        (127) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (128) QDP
743.35/262.73	        (129) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (130) YES
743.35/262.73	    (131) QDP
743.35/262.73	        (132) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (133) QDP
743.35/262.73	        (134) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (135) QDP
743.35/262.73	        (136) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (137) YES
743.35/262.73	    (138) QDP
743.35/262.73	        (139) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (140) QDP
743.35/262.73	        (141) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (142) QDP
743.35/262.73	        (143) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (144) YES
743.35/262.73	    (145) QDP
743.35/262.73	        (146) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (147) QDP
743.35/262.73	        (148) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (149) QDP
743.35/262.73	        (150) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (151) YES
743.35/262.73	    (152) QDP
743.35/262.73	        (153) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (154) QDP
743.35/262.73	        (155) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (156) QDP
743.35/262.73	        (157) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (158) YES
743.35/262.73	    (159) QDP
743.35/262.73	        (160) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (161) QDP
743.35/262.73	        (162) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (163) QDP
743.35/262.73	        (164) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (165) YES
743.35/262.73	    (166) QDP
743.35/262.73	        (167) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (168) QDP
743.35/262.73	        (169) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (170) QDP
743.35/262.73	        (171) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (172) YES
743.35/262.73	    (173) QDP
743.35/262.73	        (174) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (175) QDP
743.35/262.73	        (176) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (177) QDP
743.35/262.73	        (178) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (179) YES
743.35/262.73	    (180) QDP
743.35/262.73	        (181) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (182) QDP
743.35/262.73	        (183) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (184) QDP
743.35/262.73	        (185) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (186) YES
743.35/262.73	    (187) QDP
743.35/262.73	        (188) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (189) QDP
743.35/262.73	        (190) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (191) QDP
743.35/262.73	        (192) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (193) YES
743.35/262.73	    (194) QDP
743.35/262.73	        (195) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (196) QDP
743.35/262.73	        (197) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (198) QDP
743.35/262.73	        (199) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (200) YES
743.35/262.73	    (201) QDP
743.35/262.73	        (202) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (203) QDP
743.35/262.73	        (204) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (205) QDP
743.35/262.73	        (206) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (207) YES
743.35/262.73	    (208) QDP
743.35/262.73	        (209) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (210) QDP
743.35/262.73	        (211) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (212) QDP
743.35/262.73	        (213) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (214) YES
743.35/262.73	    (215) QDP
743.35/262.73	        (216) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (217) QDP
743.35/262.73	        (218) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (219) QDP
743.35/262.73	        (220) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (221) YES
743.35/262.73	    (222) QDP
743.35/262.73	        (223) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (224) QDP
743.35/262.73	        (225) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (226) QDP
743.35/262.73	        (227) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (228) YES
743.35/262.73	    (229) QDP
743.35/262.73	        (230) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (231) QDP
743.35/262.73	        (232) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (233) QDP
743.35/262.73	        (234) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (235) YES
743.35/262.73	    (236) QDP
743.35/262.73	        (237) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (238) QDP
743.35/262.73	        (239) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (240) QDP
743.35/262.73	        (241) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (242) YES
743.35/262.73	    (243) QDP
743.35/262.73	        (244) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (245) QDP
743.35/262.73	        (246) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (247) QDP
743.35/262.73	        (248) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (249) YES
743.35/262.73	    (250) QDP
743.35/262.73	        (251) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (252) QDP
743.35/262.73	        (253) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (254) QDP
743.35/262.73	        (255) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (256) YES
743.35/262.73	    (257) QDP
743.35/262.73	        (258) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (259) QDP
743.35/262.73	        (260) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (261) QDP
743.35/262.73	        (262) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (263) YES
743.35/262.73	    (264) QDP
743.35/262.73	        (265) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (266) QDP
743.35/262.73	        (267) QDPOrderProof [EQUIVALENT, 1854 ms]
743.35/262.73	        (268) QDP
743.35/262.73	        (269) QDPOrderProof [EQUIVALENT, 1512 ms]
743.35/262.73	        (270) QDP
743.35/262.73	        (271) QDPOrderProof [EQUIVALENT, 3906 ms]
743.35/262.73	        (272) QDP
743.35/262.73	        (273) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (274) QDP
743.35/262.73	        (275) QDPQMonotonicMRRProof [EQUIVALENT, 1601 ms]
743.35/262.73	        (276) QDP
743.35/262.73	        (277) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (278) QDP
743.35/262.73	        (279) QDPOrderProof [EQUIVALENT, 297 ms]
743.35/262.73	        (280) QDP
743.35/262.73	        (281) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (282) QDP
743.35/262.73	        (283) QDPOrderProof [EQUIVALENT, 1296 ms]
743.35/262.73	        (284) QDP
743.35/262.73	        (285) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (286) QDP
743.35/262.73	        (287) QDPOrderProof [EQUIVALENT, 527 ms]
743.35/262.73	        (288) QDP
743.35/262.73	        (289) QDPOrderProof [EQUIVALENT, 1124 ms]
743.35/262.73	        (290) QDP
743.35/262.73	        (291) QDPOrderProof [EQUIVALENT, 1065 ms]
743.35/262.73	        (292) QDP
743.35/262.73	        (293) QDPOrderProof [EQUIVALENT, 2534 ms]
743.35/262.73	        (294) QDP
743.35/262.73	        (295) QDPOrderProof [EQUIVALENT, 2498 ms]
743.35/262.73	        (296) QDP
743.35/262.73	        (297) QDPOrderProof [EQUIVALENT, 1173 ms]
743.35/262.73	        (298) QDP
743.35/262.73	        (299) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (300) QDP
743.35/262.73	        (301) QDPOrderProof [EQUIVALENT, 771 ms]
743.35/262.73	        (302) QDP
743.35/262.73	        (303) QDPOrderProof [EQUIVALENT, 2489 ms]
743.35/262.73	        (304) QDP
743.35/262.73	        (305) QDPOrderProof [EQUIVALENT, 2454 ms]
743.35/262.73	        (306) QDP
743.35/262.73	        (307) QDPOrderProof [EQUIVALENT, 2148 ms]
743.35/262.73	        (308) QDP
743.35/262.73	        (309) QDPOrderProof [EQUIVALENT, 1117 ms]
743.35/262.73	        (310) QDP
743.35/262.73	        (311) QDPOrderProof [EQUIVALENT, 1186 ms]
743.35/262.73	        (312) QDP
743.35/262.73	        (313) QDPOrderProof [EQUIVALENT, 2223 ms]
743.35/262.73	        (314) QDP
743.35/262.73	        (315) QDPOrderProof [EQUIVALENT, 2238 ms]
743.35/262.73	        (316) QDP
743.35/262.73	        (317) QDPOrderProof [EQUIVALENT, 2248 ms]
743.35/262.73	        (318) QDP
743.35/262.73	        (319) QDPOrderProof [EQUIVALENT, 2308 ms]
743.35/262.73	        (320) QDP
743.35/262.73	        (321) QDPOrderProof [EQUIVALENT, 2478 ms]
743.35/262.73	        (322) QDP
743.35/262.73	        (323) QDPOrderProof [EQUIVALENT, 2260 ms]
743.35/262.73	        (324) QDP
743.35/262.73	        (325) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (326) QDP
743.35/262.73	        (327) QDPOrderProof [EQUIVALENT, 1342 ms]
743.35/262.73	        (328) QDP
743.35/262.73	        (329) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (330) QDP
743.35/262.73	        (331) QDPOrderProof [EQUIVALENT, 1111 ms]
743.35/262.73	        (332) QDP
743.35/262.73	        (333) QDPOrderProof [EQUIVALENT, 2134 ms]
743.35/262.73	        (334) QDP
743.35/262.73	        (335) QDPOrderProof [EQUIVALENT, 1030 ms]
743.35/262.73	        (336) QDP
743.35/262.73	        (337) QDPOrderProof [EQUIVALENT, 938 ms]
743.35/262.73	        (338) QDP
743.35/262.73	        (339) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (340) QDP
743.35/262.73	        (341) QDPOrderProof [EQUIVALENT, 937 ms]
743.35/262.73	        (342) QDP
743.35/262.73	        (343) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (344) QDP
743.35/262.73	        (345) QDPOrderProof [EQUIVALENT, 2005 ms]
743.35/262.73	        (346) QDP
743.35/262.73	        (347) QDPOrderProof [EQUIVALENT, 2112 ms]
743.35/262.73	        (348) QDP
743.35/262.73	        (349) QDPOrderProof [EQUIVALENT, 2118 ms]
743.35/262.73	        (350) QDP
743.35/262.73	        (351) QDPQMonotonicMRRProof [EQUIVALENT, 725 ms]
743.35/262.73	        (352) QDP
743.35/262.73	        (353) QDPOrderProof [EQUIVALENT, 871 ms]
743.35/262.73	        (354) QDP
743.35/262.73	        (355) QDPOrderProof [EQUIVALENT, 2034 ms]
743.35/262.73	        (356) QDP
743.35/262.73	        (357) QDPQMonotonicMRRProof [EQUIVALENT, 762 ms]
743.35/262.73	        (358) QDP
743.35/262.73	        (359) QDPOrderProof [EQUIVALENT, 918 ms]
743.35/262.73	        (360) QDP
743.35/262.73	        (361) QDPOrderProof [EQUIVALENT, 1208 ms]
743.35/262.73	        (362) QDP
743.35/262.73	        (363) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (364) QDP
743.35/262.73	        (365) QDPOrderProof [EQUIVALENT, 885 ms]
743.35/262.73	        (366) QDP
743.35/262.73	        (367) QDPOrderProof [EQUIVALENT, 805 ms]
743.35/262.73	        (368) QDP
743.35/262.73	        (369) QDPOrderProof [EQUIVALENT, 1745 ms]
743.35/262.73	        (370) QDP
743.35/262.73	        (371) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (372) QDP
743.35/262.73	        (373) QDPOrderProof [EQUIVALENT, 930 ms]
743.35/262.73	        (374) QDP
743.35/262.73	        (375) QDPOrderProof [EQUIVALENT, 653 ms]
743.35/262.73	        (376) QDP
743.35/262.73	        (377) DependencyGraphProof [EQUIVALENT, 0 ms]
743.35/262.73	        (378) QDP
743.35/262.73	        (379) UsableRulesProof [EQUIVALENT, 0 ms]
743.35/262.73	        (380) QDP
743.35/262.73	        (381) QReductionProof [EQUIVALENT, 0 ms]
743.35/262.73	        (382) QDP
743.35/262.73	        (383) QDPSizeChangeProof [EQUIVALENT, 0 ms]
743.35/262.73	        (384) YES
743.35/262.73	
743.35/262.73	
743.35/262.73	----------------------------------------
743.35/262.73	
743.35/262.73	(0)
743.35/262.73	Obligation:
743.35/262.73	Q restricted rewrite system:
743.35/262.73	The TRS R consists of the following rules:
743.35/262.73	
743.35/262.73	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.73	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.73	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.73	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.73	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.73	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.73	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.73	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.73	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.73	   active(U16(tt)) -> mark(tt)
743.35/262.73	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.73	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.73	   active(U23(tt)) -> mark(tt)
743.35/262.73	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.73	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.73	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.73	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.73	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.73	   active(U36(tt)) -> mark(tt)
743.35/262.73	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.73	   active(U42(tt)) -> mark(tt)
743.35/262.73	   active(U51(tt)) -> mark(tt)
743.35/262.73	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.73	   active(U62(tt)) -> mark(tt)
743.35/262.73	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.73	   active(U72(tt, N)) -> mark(N)
743.35/262.73	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.73	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.73	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.73	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.73	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.73	   active(U92(tt)) -> mark(0)
743.35/262.73	   active(isNat(0)) -> mark(tt)
743.35/262.73	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.73	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.73	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.73	   active(isNatKind(0)) -> mark(tt)
743.35/262.73	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.73	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.73	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.73	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.73	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.73	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.73	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.73	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.73	   mark(tt) -> active(tt)
743.35/262.73	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.73	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.73	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.73	   mark(isNat(X)) -> active(isNat(X))
743.35/262.73	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.73	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.73	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.73	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.73	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.73	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.73	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.73	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.73	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.73	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.73	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.73	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.73	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.73	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.73	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.73	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.73	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.73	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.73	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.73	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.73	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.73	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.73	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.73	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.73	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.74	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.74	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.74	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.74	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.74	   mark(s(X)) -> active(s(mark(X)))
743.35/262.74	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.74	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.74	   mark(0) -> active(0)
743.35/262.74	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.74	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.74	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.74	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.74	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.74	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.74	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.74	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.74	   isNat(mark(X)) -> isNat(X)
743.35/262.74	   isNat(active(X)) -> isNat(X)
743.35/262.74	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.74	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.74	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.74	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.74	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.74	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.74	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.74	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.74	   x(active(X1), X2) -> x(X1, X2)
743.35/262.74	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.74	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.74	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.74	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.74	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.74	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.74	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.74	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.74	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.74	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.74	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.74	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.74	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.74	   U16(mark(X)) -> U16(X)
743.35/262.74	   U16(active(X)) -> U16(X)
743.35/262.74	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.74	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.74	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.74	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.74	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.74	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.74	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.74	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.74	   U23(mark(X)) -> U23(X)
743.35/262.74	   U23(active(X)) -> U23(X)
743.35/262.74	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.74	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.74	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.74	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.74	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.74	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.74	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.74	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.74	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.74	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.74	   U35(active(X1), X2) -> U35(X1, X2)
743.35/262.74	   U35(X1, active(X2)) -> U35(X1, X2)
743.35/262.74	   U36(mark(X)) -> U36(X)
743.35/262.74	   U36(active(X)) -> U36(X)
743.35/262.74	   U41(mark(X1), X2) -> U41(X1, X2)
743.35/262.74	   U41(X1, mark(X2)) -> U41(X1, X2)
743.35/262.74	   U41(active(X1), X2) -> U41(X1, X2)
743.35/262.74	   U41(X1, active(X2)) -> U41(X1, X2)
743.35/262.74	   U42(mark(X)) -> U42(X)
743.35/262.74	   U42(active(X)) -> U42(X)
743.35/262.74	   U51(mark(X)) -> U51(X)
743.35/262.74	   U51(active(X)) -> U51(X)
743.35/262.74	   U61(mark(X1), X2) -> U61(X1, X2)
743.35/262.74	   U61(X1, mark(X2)) -> U61(X1, X2)
743.35/262.74	   U61(active(X1), X2) -> U61(X1, X2)
743.35/262.74	   U61(X1, active(X2)) -> U61(X1, X2)
743.35/262.74	   U62(mark(X)) -> U62(X)
743.35/262.74	   U62(active(X)) -> U62(X)
743.35/262.74	   U71(mark(X1), X2) -> U71(X1, X2)
743.35/262.74	   U71(X1, mark(X2)) -> U71(X1, X2)
743.35/262.74	   U71(active(X1), X2) -> U71(X1, X2)
743.35/262.74	   U71(X1, active(X2)) -> U71(X1, X2)
743.35/262.74	   U72(mark(X1), X2) -> U72(X1, X2)
743.35/262.74	   U72(X1, mark(X2)) -> U72(X1, X2)
743.35/262.74	   U72(active(X1), X2) -> U72(X1, X2)
743.35/262.74	   U72(X1, active(X2)) -> U72(X1, X2)
743.35/262.74	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.35/262.74	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.35/262.74	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.35/262.74	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.35/262.74	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.35/262.74	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.35/262.74	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.35/262.74	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.35/262.74	   s(mark(X)) -> s(X)
743.35/262.74	   s(active(X)) -> s(X)
743.35/262.74	   U91(mark(X1), X2) -> U91(X1, X2)
743.35/262.74	   U91(X1, mark(X2)) -> U91(X1, X2)
743.35/262.74	   U91(active(X1), X2) -> U91(X1, X2)
743.35/262.74	   U91(X1, active(X2)) -> U91(X1, X2)
743.35/262.74	   U92(mark(X)) -> U92(X)
743.35/262.74	   U92(active(X)) -> U92(X)
743.35/262.74	
743.35/262.74	The set Q consists of the following terms:
743.35/262.74	
743.35/262.74	   active(U101(tt, x0, x1))
743.35/262.74	   active(U102(tt, x0, x1))
743.35/262.74	   active(U103(tt, x0, x1))
743.35/262.74	   active(U104(tt, x0, x1))
743.35/262.74	   active(U11(tt, x0, x1))
743.35/262.74	   active(U12(tt, x0, x1))
743.35/262.74	   active(U13(tt, x0, x1))
743.35/262.74	   active(U14(tt, x0, x1))
743.35/262.74	   active(U15(tt, x0))
743.35/262.74	   active(U16(tt))
743.35/262.74	   active(U21(tt, x0))
743.35/262.74	   active(U22(tt, x0))
743.35/262.74	   active(U23(tt))
743.35/262.74	   active(U31(tt, x0, x1))
743.35/262.74	   active(U32(tt, x0, x1))
743.35/262.74	   active(U33(tt, x0, x1))
743.35/262.74	   active(U34(tt, x0, x1))
743.35/262.74	   active(U35(tt, x0))
743.35/262.74	   active(U36(tt))
743.35/262.74	   active(U41(tt, x0))
743.35/262.74	   active(U42(tt))
743.35/262.74	   active(U51(tt))
743.35/262.74	   active(U61(tt, x0))
743.35/262.74	   active(U62(tt))
743.35/262.74	   active(U71(tt, x0))
743.35/262.74	   active(U72(tt, x0))
743.35/262.74	   active(U81(tt, x0, x1))
743.35/262.74	   active(U82(tt, x0, x1))
743.35/262.74	   active(U83(tt, x0, x1))
743.35/262.74	   active(U84(tt, x0, x1))
743.35/262.74	   active(U91(tt, x0))
743.35/262.74	   active(U92(tt))
743.35/262.74	   active(isNat(0))
743.35/262.74	   active(isNat(plus(x0, x1)))
743.35/262.74	   active(isNat(s(x0)))
743.35/262.74	   active(isNat(x(x0, x1)))
743.35/262.74	   active(isNatKind(0))
743.35/262.74	   active(isNatKind(plus(x0, x1)))
743.35/262.74	   active(isNatKind(s(x0)))
743.35/262.74	   active(isNatKind(x(x0, x1)))
743.35/262.74	   active(plus(x0, 0))
743.35/262.74	   active(plus(x0, s(x1)))
743.35/262.74	   active(x(x0, 0))
743.35/262.74	   active(x(x0, s(x1)))
743.35/262.74	   mark(U101(x0, x1, x2))
743.35/262.74	   mark(tt)
743.35/262.74	   mark(U102(x0, x1, x2))
743.35/262.74	   mark(isNatKind(x0))
743.35/262.74	   mark(U103(x0, x1, x2))
743.35/262.74	   mark(isNat(x0))
743.35/262.74	   mark(U104(x0, x1, x2))
743.35/262.74	   mark(plus(x0, x1))
743.35/262.74	   mark(x(x0, x1))
743.35/262.74	   mark(U11(x0, x1, x2))
743.35/262.74	   mark(U12(x0, x1, x2))
743.35/262.74	   mark(U13(x0, x1, x2))
743.35/262.74	   mark(U14(x0, x1, x2))
743.35/262.74	   mark(U15(x0, x1))
743.35/262.74	   mark(U16(x0))
743.35/262.74	   mark(U21(x0, x1))
743.35/262.74	   mark(U22(x0, x1))
743.35/262.74	   mark(U23(x0))
743.35/262.74	   mark(U31(x0, x1, x2))
743.35/262.74	   mark(U32(x0, x1, x2))
743.35/262.74	   mark(U33(x0, x1, x2))
743.35/262.74	   mark(U34(x0, x1, x2))
743.35/262.74	   mark(U35(x0, x1))
743.35/262.74	   mark(U36(x0))
743.35/262.74	   mark(U41(x0, x1))
743.35/262.74	   mark(U42(x0))
743.35/262.74	   mark(U51(x0))
743.35/262.74	   mark(U61(x0, x1))
743.35/262.74	   mark(U62(x0))
743.35/262.74	   mark(U71(x0, x1))
743.35/262.74	   mark(U72(x0, x1))
743.35/262.74	   mark(U81(x0, x1, x2))
743.35/262.74	   mark(U82(x0, x1, x2))
743.35/262.74	   mark(U83(x0, x1, x2))
743.35/262.74	   mark(U84(x0, x1, x2))
743.35/262.74	   mark(s(x0))
743.35/262.74	   mark(U91(x0, x1))
743.35/262.74	   mark(U92(x0))
743.35/262.74	   mark(0)
743.35/262.74	   U101(mark(x0), x1, x2)
743.35/262.74	   U101(x0, mark(x1), x2)
743.35/262.74	   U101(x0, x1, mark(x2))
743.35/262.74	   U101(active(x0), x1, x2)
743.35/262.74	   U101(x0, active(x1), x2)
743.35/262.74	   U101(x0, x1, active(x2))
743.35/262.74	   U102(mark(x0), x1, x2)
743.35/262.74	   U102(x0, mark(x1), x2)
743.35/262.74	   U102(x0, x1, mark(x2))
743.35/262.74	   U102(active(x0), x1, x2)
743.35/262.74	   U102(x0, active(x1), x2)
743.35/262.74	   U102(x0, x1, active(x2))
743.35/262.74	   isNatKind(mark(x0))
743.35/262.74	   isNatKind(active(x0))
743.35/262.74	   U103(mark(x0), x1, x2)
743.35/262.74	   U103(x0, mark(x1), x2)
743.35/262.74	   U103(x0, x1, mark(x2))
743.35/262.74	   U103(active(x0), x1, x2)
743.35/262.74	   U103(x0, active(x1), x2)
743.35/262.74	   U103(x0, x1, active(x2))
743.35/262.74	   isNat(mark(x0))
743.35/262.74	   isNat(active(x0))
743.35/262.74	   U104(mark(x0), x1, x2)
743.35/262.74	   U104(x0, mark(x1), x2)
743.35/262.74	   U104(x0, x1, mark(x2))
743.35/262.74	   U104(active(x0), x1, x2)
743.35/262.74	   U104(x0, active(x1), x2)
743.35/262.74	   U104(x0, x1, active(x2))
743.35/262.74	   plus(mark(x0), x1)
743.35/262.74	   plus(x0, mark(x1))
743.35/262.74	   plus(active(x0), x1)
743.35/262.74	   plus(x0, active(x1))
743.35/262.74	   x(mark(x0), x1)
743.35/262.74	   x(x0, mark(x1))
743.35/262.74	   x(active(x0), x1)
743.35/262.74	   x(x0, active(x1))
743.35/262.74	   U11(mark(x0), x1, x2)
743.35/262.74	   U11(x0, mark(x1), x2)
743.35/262.74	   U11(x0, x1, mark(x2))
743.35/262.74	   U11(active(x0), x1, x2)
743.35/262.74	   U11(x0, active(x1), x2)
743.35/262.74	   U11(x0, x1, active(x2))
743.35/262.74	   U12(mark(x0), x1, x2)
743.35/262.74	   U12(x0, mark(x1), x2)
743.35/262.74	   U12(x0, x1, mark(x2))
743.35/262.74	   U12(active(x0), x1, x2)
743.35/262.74	   U12(x0, active(x1), x2)
743.35/262.74	   U12(x0, x1, active(x2))
743.35/262.74	   U13(mark(x0), x1, x2)
743.35/262.74	   U13(x0, mark(x1), x2)
743.35/262.74	   U13(x0, x1, mark(x2))
743.35/262.74	   U13(active(x0), x1, x2)
743.35/262.74	   U13(x0, active(x1), x2)
743.35/262.74	   U13(x0, x1, active(x2))
743.35/262.74	   U14(mark(x0), x1, x2)
743.35/262.74	   U14(x0, mark(x1), x2)
743.35/262.74	   U14(x0, x1, mark(x2))
743.35/262.74	   U14(active(x0), x1, x2)
743.35/262.74	   U14(x0, active(x1), x2)
743.35/262.74	   U14(x0, x1, active(x2))
743.35/262.74	   U15(mark(x0), x1)
743.35/262.74	   U15(x0, mark(x1))
743.35/262.74	   U15(active(x0), x1)
743.35/262.74	   U15(x0, active(x1))
743.35/262.74	   U16(mark(x0))
743.35/262.74	   U16(active(x0))
743.35/262.74	   U21(mark(x0), x1)
743.35/262.74	   U21(x0, mark(x1))
743.35/262.74	   U21(active(x0), x1)
743.35/262.74	   U21(x0, active(x1))
743.35/262.74	   U22(mark(x0), x1)
743.35/262.74	   U22(x0, mark(x1))
743.35/262.74	   U22(active(x0), x1)
743.35/262.74	   U22(x0, active(x1))
743.35/262.74	   U23(mark(x0))
743.35/262.74	   U23(active(x0))
743.35/262.74	   U31(mark(x0), x1, x2)
743.35/262.74	   U31(x0, mark(x1), x2)
743.35/262.74	   U31(x0, x1, mark(x2))
743.35/262.74	   U31(active(x0), x1, x2)
743.35/262.74	   U31(x0, active(x1), x2)
743.35/262.74	   U31(x0, x1, active(x2))
743.35/262.74	   U32(mark(x0), x1, x2)
743.35/262.74	   U32(x0, mark(x1), x2)
743.35/262.74	   U32(x0, x1, mark(x2))
743.35/262.74	   U32(active(x0), x1, x2)
743.35/262.74	   U32(x0, active(x1), x2)
743.35/262.74	   U32(x0, x1, active(x2))
743.35/262.74	   U33(mark(x0), x1, x2)
743.35/262.74	   U33(x0, mark(x1), x2)
743.35/262.74	   U33(x0, x1, mark(x2))
743.35/262.74	   U33(active(x0), x1, x2)
743.35/262.74	   U33(x0, active(x1), x2)
743.35/262.74	   U33(x0, x1, active(x2))
743.35/262.74	   U34(mark(x0), x1, x2)
743.35/262.74	   U34(x0, mark(x1), x2)
743.35/262.74	   U34(x0, x1, mark(x2))
743.35/262.74	   U34(active(x0), x1, x2)
743.35/262.74	   U34(x0, active(x1), x2)
743.35/262.74	   U34(x0, x1, active(x2))
743.35/262.74	   U35(mark(x0), x1)
743.35/262.74	   U35(x0, mark(x1))
743.35/262.74	   U35(active(x0), x1)
743.35/262.74	   U35(x0, active(x1))
743.35/262.74	   U36(mark(x0))
743.35/262.74	   U36(active(x0))
743.35/262.74	   U41(mark(x0), x1)
743.35/262.74	   U41(x0, mark(x1))
743.35/262.74	   U41(active(x0), x1)
743.35/262.74	   U41(x0, active(x1))
743.35/262.74	   U42(mark(x0))
743.35/262.74	   U42(active(x0))
743.35/262.74	   U51(mark(x0))
743.35/262.74	   U51(active(x0))
743.35/262.74	   U61(mark(x0), x1)
743.35/262.74	   U61(x0, mark(x1))
743.35/262.74	   U61(active(x0), x1)
743.35/262.74	   U61(x0, active(x1))
743.35/262.74	   U62(mark(x0))
743.35/262.74	   U62(active(x0))
743.35/262.74	   U71(mark(x0), x1)
743.35/262.74	   U71(x0, mark(x1))
743.35/262.74	   U71(active(x0), x1)
743.35/262.74	   U71(x0, active(x1))
743.35/262.74	   U72(mark(x0), x1)
743.35/262.74	   U72(x0, mark(x1))
743.35/262.74	   U72(active(x0), x1)
743.35/262.74	   U72(x0, active(x1))
743.35/262.74	   U81(mark(x0), x1, x2)
743.35/262.74	   U81(x0, mark(x1), x2)
743.35/262.74	   U81(x0, x1, mark(x2))
743.35/262.74	   U81(active(x0), x1, x2)
743.35/262.74	   U81(x0, active(x1), x2)
743.35/262.74	   U81(x0, x1, active(x2))
743.35/262.74	   U82(mark(x0), x1, x2)
743.35/262.74	   U82(x0, mark(x1), x2)
743.35/262.74	   U82(x0, x1, mark(x2))
743.35/262.74	   U82(active(x0), x1, x2)
743.35/262.74	   U82(x0, active(x1), x2)
743.35/262.74	   U82(x0, x1, active(x2))
743.35/262.74	   U83(mark(x0), x1, x2)
743.35/262.74	   U83(x0, mark(x1), x2)
743.35/262.74	   U83(x0, x1, mark(x2))
743.35/262.74	   U83(active(x0), x1, x2)
743.35/262.74	   U83(x0, active(x1), x2)
743.35/262.74	   U83(x0, x1, active(x2))
743.35/262.74	   U84(mark(x0), x1, x2)
743.35/262.74	   U84(x0, mark(x1), x2)
743.35/262.74	   U84(x0, x1, mark(x2))
743.35/262.74	   U84(active(x0), x1, x2)
743.35/262.74	   U84(x0, active(x1), x2)
743.35/262.74	   U84(x0, x1, active(x2))
743.35/262.74	   s(mark(x0))
743.35/262.74	   s(active(x0))
743.35/262.74	   U91(mark(x0), x1)
743.35/262.74	   U91(x0, mark(x1))
743.35/262.74	   U91(active(x0), x1)
743.35/262.74	   U91(x0, active(x1))
743.35/262.74	   U92(mark(x0))
743.35/262.74	   U92(active(x0))
743.35/262.74	
743.35/262.74	
743.35/262.74	----------------------------------------
743.35/262.74	
743.35/262.74	(1) DependencyPairsProof (EQUIVALENT)
743.35/262.74	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
743.35/262.74	----------------------------------------
743.35/262.74	
743.35/262.74	(2)
743.35/262.74	Obligation:
743.35/262.74	Q DP problem:
743.35/262.74	The TRS P consists of the following rules:
743.35/262.74	
743.35/262.74	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
743.35/262.74	   ACTIVE(U101(tt, M, N)) -> U102^1(isNatKind(M), M, N)
743.35/262.74	   ACTIVE(U101(tt, M, N)) -> ISNATKIND(M)
743.35/262.74	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
743.35/262.74	   ACTIVE(U102(tt, M, N)) -> U103^1(isNat(N), M, N)
743.35/262.74	   ACTIVE(U102(tt, M, N)) -> ISNAT(N)
743.35/262.74	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
743.35/262.74	   ACTIVE(U103(tt, M, N)) -> U104^1(isNatKind(N), M, N)
743.35/262.74	   ACTIVE(U103(tt, M, N)) -> ISNATKIND(N)
743.35/262.74	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
743.35/262.74	   ACTIVE(U104(tt, M, N)) -> PLUS(x(N, M), N)
743.35/262.74	   ACTIVE(U104(tt, M, N)) -> X(N, M)
743.35/262.74	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
743.35/262.74	   ACTIVE(U11(tt, V1, V2)) -> U12^1(isNatKind(V1), V1, V2)
743.35/262.74	   ACTIVE(U11(tt, V1, V2)) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
743.35/262.74	   ACTIVE(U12(tt, V1, V2)) -> U13^1(isNatKind(V2), V1, V2)
743.35/262.74	   ACTIVE(U12(tt, V1, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
743.35/262.74	   ACTIVE(U13(tt, V1, V2)) -> U14^1(isNatKind(V2), V1, V2)
743.35/262.74	   ACTIVE(U13(tt, V1, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
743.35/262.74	   ACTIVE(U14(tt, V1, V2)) -> U15^1(isNat(V1), V2)
743.35/262.74	   ACTIVE(U14(tt, V1, V2)) -> ISNAT(V1)
743.35/262.74	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
743.35/262.74	   ACTIVE(U15(tt, V2)) -> U16^1(isNat(V2))
743.35/262.74	   ACTIVE(U15(tt, V2)) -> ISNAT(V2)
743.35/262.74	   ACTIVE(U16(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
743.35/262.74	   ACTIVE(U21(tt, V1)) -> U22^1(isNatKind(V1), V1)
743.35/262.74	   ACTIVE(U21(tt, V1)) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
743.35/262.74	   ACTIVE(U22(tt, V1)) -> U23^1(isNat(V1))
743.35/262.74	   ACTIVE(U22(tt, V1)) -> ISNAT(V1)
743.35/262.74	   ACTIVE(U23(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
743.35/262.74	   ACTIVE(U31(tt, V1, V2)) -> U32^1(isNatKind(V1), V1, V2)
743.35/262.74	   ACTIVE(U31(tt, V1, V2)) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
743.35/262.74	   ACTIVE(U32(tt, V1, V2)) -> U33^1(isNatKind(V2), V1, V2)
743.35/262.74	   ACTIVE(U32(tt, V1, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
743.35/262.74	   ACTIVE(U33(tt, V1, V2)) -> U34^1(isNatKind(V2), V1, V2)
743.35/262.74	   ACTIVE(U33(tt, V1, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
743.35/262.74	   ACTIVE(U34(tt, V1, V2)) -> U35^1(isNat(V1), V2)
743.35/262.74	   ACTIVE(U34(tt, V1, V2)) -> ISNAT(V1)
743.35/262.74	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
743.35/262.74	   ACTIVE(U35(tt, V2)) -> U36^1(isNat(V2))
743.35/262.74	   ACTIVE(U35(tt, V2)) -> ISNAT(V2)
743.35/262.74	   ACTIVE(U36(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
743.35/262.74	   ACTIVE(U41(tt, V2)) -> U42^1(isNatKind(V2))
743.35/262.74	   ACTIVE(U41(tt, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U42(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U51(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
743.35/262.74	   ACTIVE(U61(tt, V2)) -> U62^1(isNatKind(V2))
743.35/262.74	   ACTIVE(U61(tt, V2)) -> ISNATKIND(V2)
743.35/262.74	   ACTIVE(U62(tt)) -> MARK(tt)
743.35/262.74	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
743.35/262.74	   ACTIVE(U71(tt, N)) -> U72^1(isNatKind(N), N)
743.35/262.74	   ACTIVE(U71(tt, N)) -> ISNATKIND(N)
743.35/262.74	   ACTIVE(U72(tt, N)) -> MARK(N)
743.35/262.74	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
743.35/262.74	   ACTIVE(U81(tt, M, N)) -> U82^1(isNatKind(M), M, N)
743.35/262.74	   ACTIVE(U81(tt, M, N)) -> ISNATKIND(M)
743.35/262.74	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
743.35/262.74	   ACTIVE(U82(tt, M, N)) -> U83^1(isNat(N), M, N)
743.35/262.74	   ACTIVE(U82(tt, M, N)) -> ISNAT(N)
743.35/262.74	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
743.35/262.74	   ACTIVE(U83(tt, M, N)) -> U84^1(isNatKind(N), M, N)
743.35/262.74	   ACTIVE(U83(tt, M, N)) -> ISNATKIND(N)
743.35/262.74	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
743.35/262.74	   ACTIVE(U84(tt, M, N)) -> S(plus(N, M))
743.35/262.74	   ACTIVE(U84(tt, M, N)) -> PLUS(N, M)
743.35/262.74	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
743.35/262.74	   ACTIVE(U91(tt, N)) -> U92^1(isNatKind(N))
743.35/262.74	   ACTIVE(U91(tt, N)) -> ISNATKIND(N)
743.35/262.74	   ACTIVE(U92(tt)) -> MARK(0)
743.35/262.74	   ACTIVE(isNat(0)) -> MARK(tt)
743.35/262.74	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
743.35/262.74	   ACTIVE(isNat(plus(V1, V2))) -> U11^1(isNatKind(V1), V1, V2)
743.35/262.74	   ACTIVE(isNat(plus(V1, V2))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
743.35/262.74	   ACTIVE(isNat(s(V1))) -> U21^1(isNatKind(V1), V1)
743.35/262.74	   ACTIVE(isNat(s(V1))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
743.35/262.74	   ACTIVE(isNat(x(V1, V2))) -> U31^1(isNatKind(V1), V1, V2)
743.35/262.74	   ACTIVE(isNat(x(V1, V2))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(isNatKind(0)) -> MARK(tt)
743.35/262.74	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
743.35/262.74	   ACTIVE(isNatKind(plus(V1, V2))) -> U41^1(isNatKind(V1), V2)
743.35/262.74	   ACTIVE(isNatKind(plus(V1, V2))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
743.35/262.74	   ACTIVE(isNatKind(s(V1))) -> U51^1(isNatKind(V1))
743.35/262.74	   ACTIVE(isNatKind(s(V1))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
743.35/262.74	   ACTIVE(isNatKind(x(V1, V2))) -> U61^1(isNatKind(V1), V2)
743.35/262.74	   ACTIVE(isNatKind(x(V1, V2))) -> ISNATKIND(V1)
743.35/262.74	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
743.35/262.74	   ACTIVE(plus(N, 0)) -> U71^1(isNat(N), N)
743.35/262.74	   ACTIVE(plus(N, 0)) -> ISNAT(N)
743.35/262.74	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
743.35/262.74	   ACTIVE(plus(N, s(M))) -> U81^1(isNat(M), M, N)
743.35/262.74	   ACTIVE(plus(N, s(M))) -> ISNAT(M)
743.35/262.74	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
743.35/262.74	   ACTIVE(x(N, 0)) -> U91^1(isNat(N), N)
743.35/262.74	   ACTIVE(x(N, 0)) -> ISNAT(N)
743.35/262.74	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
743.35/262.74	   ACTIVE(x(N, s(M))) -> U101^1(isNat(M), M, N)
743.35/262.74	   ACTIVE(x(N, s(M))) -> ISNAT(M)
743.35/262.74	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
743.35/262.74	   MARK(U101(X1, X2, X3)) -> U101^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U101(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(tt) -> ACTIVE(tt)
743.35/262.74	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
743.35/262.74	   MARK(U102(X1, X2, X3)) -> U102^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U102(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
743.35/262.74	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
743.35/262.74	   MARK(U103(X1, X2, X3)) -> U103^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U103(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(isNat(X)) -> ACTIVE(isNat(X))
743.35/262.74	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
743.35/262.74	   MARK(U104(X1, X2, X3)) -> U104^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U104(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
743.35/262.74	   MARK(plus(X1, X2)) -> PLUS(mark(X1), mark(X2))
743.35/262.74	   MARK(plus(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(plus(X1, X2)) -> MARK(X2)
743.35/262.74	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
743.35/262.74	   MARK(x(X1, X2)) -> X(mark(X1), mark(X2))
743.35/262.74	   MARK(x(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(x(X1, X2)) -> MARK(X2)
743.35/262.74	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
743.35/262.74	   MARK(U11(X1, X2, X3)) -> U11^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U11(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
743.35/262.74	   MARK(U12(X1, X2, X3)) -> U12^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U12(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
743.35/262.74	   MARK(U13(X1, X2, X3)) -> U13^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U13(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
743.35/262.74	   MARK(U14(X1, X2, X3)) -> U14^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U14(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
743.35/262.74	   MARK(U15(X1, X2)) -> U15^1(mark(X1), X2)
743.35/262.74	   MARK(U15(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U16(X)) -> ACTIVE(U16(mark(X)))
743.35/262.74	   MARK(U16(X)) -> U16^1(mark(X))
743.35/262.74	   MARK(U16(X)) -> MARK(X)
743.35/262.74	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
743.35/262.74	   MARK(U21(X1, X2)) -> U21^1(mark(X1), X2)
743.35/262.74	   MARK(U21(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
743.35/262.74	   MARK(U22(X1, X2)) -> U22^1(mark(X1), X2)
743.35/262.74	   MARK(U22(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U23(X)) -> ACTIVE(U23(mark(X)))
743.35/262.74	   MARK(U23(X)) -> U23^1(mark(X))
743.35/262.74	   MARK(U23(X)) -> MARK(X)
743.35/262.74	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
743.35/262.74	   MARK(U31(X1, X2, X3)) -> U31^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U31(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
743.35/262.74	   MARK(U32(X1, X2, X3)) -> U32^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U32(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
743.35/262.74	   MARK(U33(X1, X2, X3)) -> U33^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U33(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
743.35/262.74	   MARK(U34(X1, X2, X3)) -> U34^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U34(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
743.35/262.74	   MARK(U35(X1, X2)) -> U35^1(mark(X1), X2)
743.35/262.74	   MARK(U35(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U36(X)) -> ACTIVE(U36(mark(X)))
743.35/262.74	   MARK(U36(X)) -> U36^1(mark(X))
743.35/262.74	   MARK(U36(X)) -> MARK(X)
743.35/262.74	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
743.35/262.74	   MARK(U41(X1, X2)) -> U41^1(mark(X1), X2)
743.35/262.74	   MARK(U41(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U42(X)) -> ACTIVE(U42(mark(X)))
743.35/262.74	   MARK(U42(X)) -> U42^1(mark(X))
743.35/262.74	   MARK(U42(X)) -> MARK(X)
743.35/262.74	   MARK(U51(X)) -> ACTIVE(U51(mark(X)))
743.35/262.74	   MARK(U51(X)) -> U51^1(mark(X))
743.35/262.74	   MARK(U51(X)) -> MARK(X)
743.35/262.74	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
743.35/262.74	   MARK(U61(X1, X2)) -> U61^1(mark(X1), X2)
743.35/262.74	   MARK(U61(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U62(X)) -> ACTIVE(U62(mark(X)))
743.35/262.74	   MARK(U62(X)) -> U62^1(mark(X))
743.35/262.74	   MARK(U62(X)) -> MARK(X)
743.35/262.74	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
743.35/262.74	   MARK(U71(X1, X2)) -> U71^1(mark(X1), X2)
743.35/262.74	   MARK(U71(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
743.35/262.74	   MARK(U72(X1, X2)) -> U72^1(mark(X1), X2)
743.35/262.74	   MARK(U72(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
743.35/262.74	   MARK(U81(X1, X2, X3)) -> U81^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U81(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
743.35/262.74	   MARK(U82(X1, X2, X3)) -> U82^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U82(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
743.35/262.74	   MARK(U83(X1, X2, X3)) -> U83^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U83(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
743.35/262.74	   MARK(U84(X1, X2, X3)) -> U84^1(mark(X1), X2, X3)
743.35/262.74	   MARK(U84(X1, X2, X3)) -> MARK(X1)
743.35/262.74	   MARK(s(X)) -> ACTIVE(s(mark(X)))
743.35/262.74	   MARK(s(X)) -> S(mark(X))
743.35/262.74	   MARK(s(X)) -> MARK(X)
743.35/262.74	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
743.35/262.74	   MARK(U91(X1, X2)) -> U91^1(mark(X1), X2)
743.35/262.74	   MARK(U91(X1, X2)) -> MARK(X1)
743.35/262.74	   MARK(U92(X)) -> ACTIVE(U92(mark(X)))
743.35/262.74	   MARK(U92(X)) -> U92^1(mark(X))
743.35/262.74	   MARK(U92(X)) -> MARK(X)
743.35/262.74	   MARK(0) -> ACTIVE(0)
743.35/262.74	   U101^1(mark(X1), X2, X3) -> U101^1(X1, X2, X3)
743.35/262.74	   U101^1(X1, mark(X2), X3) -> U101^1(X1, X2, X3)
743.35/262.74	   U101^1(X1, X2, mark(X3)) -> U101^1(X1, X2, X3)
743.35/262.74	   U101^1(active(X1), X2, X3) -> U101^1(X1, X2, X3)
743.35/262.74	   U101^1(X1, active(X2), X3) -> U101^1(X1, X2, X3)
743.35/262.74	   U101^1(X1, X2, active(X3)) -> U101^1(X1, X2, X3)
743.35/262.74	   U102^1(mark(X1), X2, X3) -> U102^1(X1, X2, X3)
743.35/262.74	   U102^1(X1, mark(X2), X3) -> U102^1(X1, X2, X3)
743.35/262.74	   U102^1(X1, X2, mark(X3)) -> U102^1(X1, X2, X3)
743.35/262.74	   U102^1(active(X1), X2, X3) -> U102^1(X1, X2, X3)
743.35/262.74	   U102^1(X1, active(X2), X3) -> U102^1(X1, X2, X3)
743.35/262.74	   U102^1(X1, X2, active(X3)) -> U102^1(X1, X2, X3)
743.35/262.74	   ISNATKIND(mark(X)) -> ISNATKIND(X)
743.35/262.74	   ISNATKIND(active(X)) -> ISNATKIND(X)
743.35/262.74	   U103^1(mark(X1), X2, X3) -> U103^1(X1, X2, X3)
743.35/262.74	   U103^1(X1, mark(X2), X3) -> U103^1(X1, X2, X3)
743.35/262.74	   U103^1(X1, X2, mark(X3)) -> U103^1(X1, X2, X3)
743.35/262.74	   U103^1(active(X1), X2, X3) -> U103^1(X1, X2, X3)
743.35/262.74	   U103^1(X1, active(X2), X3) -> U103^1(X1, X2, X3)
743.35/262.74	   U103^1(X1, X2, active(X3)) -> U103^1(X1, X2, X3)
743.35/262.74	   ISNAT(mark(X)) -> ISNAT(X)
743.35/262.74	   ISNAT(active(X)) -> ISNAT(X)
743.35/262.74	   U104^1(mark(X1), X2, X3) -> U104^1(X1, X2, X3)
743.35/262.74	   U104^1(X1, mark(X2), X3) -> U104^1(X1, X2, X3)
743.35/262.74	   U104^1(X1, X2, mark(X3)) -> U104^1(X1, X2, X3)
743.35/262.74	   U104^1(active(X1), X2, X3) -> U104^1(X1, X2, X3)
743.35/262.74	   U104^1(X1, active(X2), X3) -> U104^1(X1, X2, X3)
743.35/262.74	   U104^1(X1, X2, active(X3)) -> U104^1(X1, X2, X3)
743.35/262.74	   PLUS(mark(X1), X2) -> PLUS(X1, X2)
743.35/262.74	   PLUS(X1, mark(X2)) -> PLUS(X1, X2)
743.35/262.74	   PLUS(active(X1), X2) -> PLUS(X1, X2)
743.35/262.74	   PLUS(X1, active(X2)) -> PLUS(X1, X2)
743.35/262.74	   X(mark(X1), X2) -> X(X1, X2)
743.35/262.74	   X(X1, mark(X2)) -> X(X1, X2)
743.35/262.74	   X(active(X1), X2) -> X(X1, X2)
743.35/262.74	   X(X1, active(X2)) -> X(X1, X2)
743.35/262.74	   U11^1(mark(X1), X2, X3) -> U11^1(X1, X2, X3)
743.35/262.74	   U11^1(X1, mark(X2), X3) -> U11^1(X1, X2, X3)
743.35/262.74	   U11^1(X1, X2, mark(X3)) -> U11^1(X1, X2, X3)
743.35/262.74	   U11^1(active(X1), X2, X3) -> U11^1(X1, X2, X3)
743.35/262.74	   U11^1(X1, active(X2), X3) -> U11^1(X1, X2, X3)
743.35/262.74	   U11^1(X1, X2, active(X3)) -> U11^1(X1, X2, X3)
743.35/262.74	   U12^1(mark(X1), X2, X3) -> U12^1(X1, X2, X3)
743.35/262.74	   U12^1(X1, mark(X2), X3) -> U12^1(X1, X2, X3)
743.35/262.74	   U12^1(X1, X2, mark(X3)) -> U12^1(X1, X2, X3)
743.35/262.74	   U12^1(active(X1), X2, X3) -> U12^1(X1, X2, X3)
743.35/262.74	   U12^1(X1, active(X2), X3) -> U12^1(X1, X2, X3)
743.35/262.74	   U12^1(X1, X2, active(X3)) -> U12^1(X1, X2, X3)
743.35/262.74	   U13^1(mark(X1), X2, X3) -> U13^1(X1, X2, X3)
743.35/262.74	   U13^1(X1, mark(X2), X3) -> U13^1(X1, X2, X3)
743.35/262.74	   U13^1(X1, X2, mark(X3)) -> U13^1(X1, X2, X3)
743.35/262.74	   U13^1(active(X1), X2, X3) -> U13^1(X1, X2, X3)
743.35/262.74	   U13^1(X1, active(X2), X3) -> U13^1(X1, X2, X3)
743.35/262.74	   U13^1(X1, X2, active(X3)) -> U13^1(X1, X2, X3)
743.35/262.74	   U14^1(mark(X1), X2, X3) -> U14^1(X1, X2, X3)
743.35/262.74	   U14^1(X1, mark(X2), X3) -> U14^1(X1, X2, X3)
743.35/262.74	   U14^1(X1, X2, mark(X3)) -> U14^1(X1, X2, X3)
743.35/262.74	   U14^1(active(X1), X2, X3) -> U14^1(X1, X2, X3)
743.35/262.74	   U14^1(X1, active(X2), X3) -> U14^1(X1, X2, X3)
743.35/262.74	   U14^1(X1, X2, active(X3)) -> U14^1(X1, X2, X3)
743.35/262.74	   U15^1(mark(X1), X2) -> U15^1(X1, X2)
743.35/262.74	   U15^1(X1, mark(X2)) -> U15^1(X1, X2)
743.35/262.74	   U15^1(active(X1), X2) -> U15^1(X1, X2)
743.35/262.74	   U15^1(X1, active(X2)) -> U15^1(X1, X2)
743.35/262.74	   U16^1(mark(X)) -> U16^1(X)
743.35/262.74	   U16^1(active(X)) -> U16^1(X)
743.35/262.74	   U21^1(mark(X1), X2) -> U21^1(X1, X2)
743.35/262.74	   U21^1(X1, mark(X2)) -> U21^1(X1, X2)
743.35/262.74	   U21^1(active(X1), X2) -> U21^1(X1, X2)
743.35/262.74	   U21^1(X1, active(X2)) -> U21^1(X1, X2)
743.35/262.74	   U22^1(mark(X1), X2) -> U22^1(X1, X2)
743.35/262.74	   U22^1(X1, mark(X2)) -> U22^1(X1, X2)
743.35/262.74	   U22^1(active(X1), X2) -> U22^1(X1, X2)
743.35/262.74	   U22^1(X1, active(X2)) -> U22^1(X1, X2)
743.35/262.74	   U23^1(mark(X)) -> U23^1(X)
743.35/262.74	   U23^1(active(X)) -> U23^1(X)
743.35/262.74	   U31^1(mark(X1), X2, X3) -> U31^1(X1, X2, X3)
743.35/262.74	   U31^1(X1, mark(X2), X3) -> U31^1(X1, X2, X3)
743.35/262.74	   U31^1(X1, X2, mark(X3)) -> U31^1(X1, X2, X3)
743.35/262.74	   U31^1(active(X1), X2, X3) -> U31^1(X1, X2, X3)
743.35/262.74	   U31^1(X1, active(X2), X3) -> U31^1(X1, X2, X3)
743.35/262.74	   U31^1(X1, X2, active(X3)) -> U31^1(X1, X2, X3)
743.35/262.74	   U32^1(mark(X1), X2, X3) -> U32^1(X1, X2, X3)
743.35/262.74	   U32^1(X1, mark(X2), X3) -> U32^1(X1, X2, X3)
743.35/262.74	   U32^1(X1, X2, mark(X3)) -> U32^1(X1, X2, X3)
743.35/262.74	   U32^1(active(X1), X2, X3) -> U32^1(X1, X2, X3)
743.35/262.74	   U32^1(X1, active(X2), X3) -> U32^1(X1, X2, X3)
743.35/262.74	   U32^1(X1, X2, active(X3)) -> U32^1(X1, X2, X3)
743.35/262.74	   U33^1(mark(X1), X2, X3) -> U33^1(X1, X2, X3)
743.35/262.74	   U33^1(X1, mark(X2), X3) -> U33^1(X1, X2, X3)
743.35/262.74	   U33^1(X1, X2, mark(X3)) -> U33^1(X1, X2, X3)
743.35/262.74	   U33^1(active(X1), X2, X3) -> U33^1(X1, X2, X3)
743.35/262.74	   U33^1(X1, active(X2), X3) -> U33^1(X1, X2, X3)
743.35/262.74	   U33^1(X1, X2, active(X3)) -> U33^1(X1, X2, X3)
743.35/262.74	   U34^1(mark(X1), X2, X3) -> U34^1(X1, X2, X3)
743.35/262.74	   U34^1(X1, mark(X2), X3) -> U34^1(X1, X2, X3)
743.35/262.74	   U34^1(X1, X2, mark(X3)) -> U34^1(X1, X2, X3)
743.35/262.74	   U34^1(active(X1), X2, X3) -> U34^1(X1, X2, X3)
743.35/262.74	   U34^1(X1, active(X2), X3) -> U34^1(X1, X2, X3)
743.35/262.74	   U34^1(X1, X2, active(X3)) -> U34^1(X1, X2, X3)
743.35/262.74	   U35^1(mark(X1), X2) -> U35^1(X1, X2)
743.35/262.74	   U35^1(X1, mark(X2)) -> U35^1(X1, X2)
743.35/262.74	   U35^1(active(X1), X2) -> U35^1(X1, X2)
743.35/262.74	   U35^1(X1, active(X2)) -> U35^1(X1, X2)
743.35/262.74	   U36^1(mark(X)) -> U36^1(X)
743.35/262.74	   U36^1(active(X)) -> U36^1(X)
743.35/262.74	   U41^1(mark(X1), X2) -> U41^1(X1, X2)
743.35/262.74	   U41^1(X1, mark(X2)) -> U41^1(X1, X2)
743.35/262.74	   U41^1(active(X1), X2) -> U41^1(X1, X2)
743.35/262.74	   U41^1(X1, active(X2)) -> U41^1(X1, X2)
743.35/262.74	   U42^1(mark(X)) -> U42^1(X)
743.35/262.74	   U42^1(active(X)) -> U42^1(X)
743.35/262.74	   U51^1(mark(X)) -> U51^1(X)
743.35/262.74	   U51^1(active(X)) -> U51^1(X)
743.35/262.74	   U61^1(mark(X1), X2) -> U61^1(X1, X2)
743.35/262.74	   U61^1(X1, mark(X2)) -> U61^1(X1, X2)
743.35/262.74	   U61^1(active(X1), X2) -> U61^1(X1, X2)
743.35/262.74	   U61^1(X1, active(X2)) -> U61^1(X1, X2)
743.35/262.74	   U62^1(mark(X)) -> U62^1(X)
743.35/262.74	   U62^1(active(X)) -> U62^1(X)
743.35/262.74	   U71^1(mark(X1), X2) -> U71^1(X1, X2)
743.35/262.74	   U71^1(X1, mark(X2)) -> U71^1(X1, X2)
743.35/262.74	   U71^1(active(X1), X2) -> U71^1(X1, X2)
743.35/262.74	   U71^1(X1, active(X2)) -> U71^1(X1, X2)
743.35/262.74	   U72^1(mark(X1), X2) -> U72^1(X1, X2)
743.35/262.74	   U72^1(X1, mark(X2)) -> U72^1(X1, X2)
743.35/262.74	   U72^1(active(X1), X2) -> U72^1(X1, X2)
743.35/262.74	   U72^1(X1, active(X2)) -> U72^1(X1, X2)
743.35/262.74	   U81^1(mark(X1), X2, X3) -> U81^1(X1, X2, X3)
743.35/262.74	   U81^1(X1, mark(X2), X3) -> U81^1(X1, X2, X3)
743.35/262.74	   U81^1(X1, X2, mark(X3)) -> U81^1(X1, X2, X3)
743.35/262.74	   U81^1(active(X1), X2, X3) -> U81^1(X1, X2, X3)
743.35/262.74	   U81^1(X1, active(X2), X3) -> U81^1(X1, X2, X3)
743.35/262.74	   U81^1(X1, X2, active(X3)) -> U81^1(X1, X2, X3)
743.35/262.74	   U82^1(mark(X1), X2, X3) -> U82^1(X1, X2, X3)
743.35/262.74	   U82^1(X1, mark(X2), X3) -> U82^1(X1, X2, X3)
743.35/262.74	   U82^1(X1, X2, mark(X3)) -> U82^1(X1, X2, X3)
743.35/262.74	   U82^1(active(X1), X2, X3) -> U82^1(X1, X2, X3)
743.35/262.74	   U82^1(X1, active(X2), X3) -> U82^1(X1, X2, X3)
743.35/262.74	   U82^1(X1, X2, active(X3)) -> U82^1(X1, X2, X3)
743.35/262.74	   U83^1(mark(X1), X2, X3) -> U83^1(X1, X2, X3)
743.35/262.74	   U83^1(X1, mark(X2), X3) -> U83^1(X1, X2, X3)
743.35/262.74	   U83^1(X1, X2, mark(X3)) -> U83^1(X1, X2, X3)
743.35/262.74	   U83^1(active(X1), X2, X3) -> U83^1(X1, X2, X3)
743.35/262.74	   U83^1(X1, active(X2), X3) -> U83^1(X1, X2, X3)
743.35/262.74	   U83^1(X1, X2, active(X3)) -> U83^1(X1, X2, X3)
743.35/262.74	   U84^1(mark(X1), X2, X3) -> U84^1(X1, X2, X3)
743.35/262.74	   U84^1(X1, mark(X2), X3) -> U84^1(X1, X2, X3)
743.35/262.74	   U84^1(X1, X2, mark(X3)) -> U84^1(X1, X2, X3)
743.35/262.74	   U84^1(active(X1), X2, X3) -> U84^1(X1, X2, X3)
743.35/262.74	   U84^1(X1, active(X2), X3) -> U84^1(X1, X2, X3)
743.35/262.74	   U84^1(X1, X2, active(X3)) -> U84^1(X1, X2, X3)
743.35/262.74	   S(mark(X)) -> S(X)
743.35/262.74	   S(active(X)) -> S(X)
743.35/262.74	   U91^1(mark(X1), X2) -> U91^1(X1, X2)
743.35/262.74	   U91^1(X1, mark(X2)) -> U91^1(X1, X2)
743.35/262.74	   U91^1(active(X1), X2) -> U91^1(X1, X2)
743.35/262.74	   U91^1(X1, active(X2)) -> U91^1(X1, X2)
743.35/262.74	   U92^1(mark(X)) -> U92^1(X)
743.35/262.74	   U92^1(active(X)) -> U92^1(X)
743.35/262.74	
743.35/262.74	The TRS R consists of the following rules:
743.35/262.74	
743.35/262.74	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.74	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.74	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.74	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.74	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.74	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.74	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.74	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.74	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.74	   active(U16(tt)) -> mark(tt)
743.35/262.74	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.74	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.74	   active(U23(tt)) -> mark(tt)
743.35/262.74	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.74	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.74	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.74	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.74	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.74	   active(U36(tt)) -> mark(tt)
743.35/262.74	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.74	   active(U42(tt)) -> mark(tt)
743.35/262.74	   active(U51(tt)) -> mark(tt)
743.35/262.74	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.74	   active(U62(tt)) -> mark(tt)
743.35/262.74	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.74	   active(U72(tt, N)) -> mark(N)
743.35/262.74	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.74	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.74	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.74	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.74	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.74	   active(U92(tt)) -> mark(0)
743.35/262.74	   active(isNat(0)) -> mark(tt)
743.35/262.74	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.74	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.74	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.74	   active(isNatKind(0)) -> mark(tt)
743.35/262.74	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.74	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.74	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.74	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.74	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.74	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.74	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.74	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.74	   mark(tt) -> active(tt)
743.35/262.74	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.74	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.74	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.74	   mark(isNat(X)) -> active(isNat(X))
743.35/262.74	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.74	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.74	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.74	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.74	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.74	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.74	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.74	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.74	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.74	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.74	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.74	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.74	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.74	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.74	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.74	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.74	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.74	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.74	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.74	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.74	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.74	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.74	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.74	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.74	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.74	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.74	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.74	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.74	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.74	   mark(s(X)) -> active(s(mark(X)))
743.35/262.74	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.74	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.74	   mark(0) -> active(0)
743.35/262.74	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.74	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.74	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.74	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.74	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.74	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.74	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.74	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.74	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.74	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.74	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.74	   isNat(mark(X)) -> isNat(X)
743.35/262.74	   isNat(active(X)) -> isNat(X)
743.35/262.74	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.74	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.74	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.74	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.74	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.74	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.74	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.74	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.74	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.74	   x(active(X1), X2) -> x(X1, X2)
743.35/262.74	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.74	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.74	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.74	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.74	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.74	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.74	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.74	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.74	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.74	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.74	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.74	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.74	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.74	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.74	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.74	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.74	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.74	   U16(mark(X)) -> U16(X)
743.35/262.74	   U16(active(X)) -> U16(X)
743.35/262.74	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.74	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.74	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.74	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.74	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.74	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.74	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.74	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.74	   U23(mark(X)) -> U23(X)
743.35/262.74	   U23(active(X)) -> U23(X)
743.35/262.74	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.74	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.74	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.74	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.74	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.74	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.74	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.74	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.74	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.74	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.74	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.74	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.74	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.74	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.74	   U35(active(X1), X2) -> U35(X1, X2)
743.35/262.74	   U35(X1, active(X2)) -> U35(X1, X2)
743.35/262.74	   U36(mark(X)) -> U36(X)
743.35/262.74	   U36(active(X)) -> U36(X)
743.35/262.74	   U41(mark(X1), X2) -> U41(X1, X2)
743.35/262.74	   U41(X1, mark(X2)) -> U41(X1, X2)
743.35/262.74	   U41(active(X1), X2) -> U41(X1, X2)
743.35/262.74	   U41(X1, active(X2)) -> U41(X1, X2)
743.35/262.74	   U42(mark(X)) -> U42(X)
743.35/262.74	   U42(active(X)) -> U42(X)
743.35/262.74	   U51(mark(X)) -> U51(X)
743.35/262.74	   U51(active(X)) -> U51(X)
743.35/262.74	   U61(mark(X1), X2) -> U61(X1, X2)
743.35/262.74	   U61(X1, mark(X2)) -> U61(X1, X2)
743.35/262.74	   U61(active(X1), X2) -> U61(X1, X2)
743.35/262.74	   U61(X1, active(X2)) -> U61(X1, X2)
743.35/262.74	   U62(mark(X)) -> U62(X)
743.35/262.74	   U62(active(X)) -> U62(X)
743.35/262.74	   U71(mark(X1), X2) -> U71(X1, X2)
743.35/262.74	   U71(X1, mark(X2)) -> U71(X1, X2)
743.35/262.74	   U71(active(X1), X2) -> U71(X1, X2)
743.35/262.74	   U71(X1, active(X2)) -> U71(X1, X2)
743.35/262.74	   U72(mark(X1), X2) -> U72(X1, X2)
743.35/262.74	   U72(X1, mark(X2)) -> U72(X1, X2)
743.35/262.74	   U72(active(X1), X2) -> U72(X1, X2)
743.35/262.74	   U72(X1, active(X2)) -> U72(X1, X2)
743.35/262.74	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.35/262.74	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.35/262.74	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.35/262.74	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.35/262.74	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.35/262.74	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.35/262.74	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.35/262.74	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.35/262.74	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.35/262.74	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.35/262.74	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.35/262.74	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.35/262.74	   s(mark(X)) -> s(X)
743.35/262.74	   s(active(X)) -> s(X)
743.35/262.74	   U91(mark(X1), X2) -> U91(X1, X2)
743.35/262.74	   U91(X1, mark(X2)) -> U91(X1, X2)
743.35/262.74	   U91(active(X1), X2) -> U91(X1, X2)
743.35/262.74	   U91(X1, active(X2)) -> U91(X1, X2)
743.35/262.74	   U92(mark(X)) -> U92(X)
743.35/262.74	   U92(active(X)) -> U92(X)
743.35/262.74	
743.35/262.74	The set Q consists of the following terms:
743.35/262.74	
743.35/262.74	   active(U101(tt, x0, x1))
743.35/262.74	   active(U102(tt, x0, x1))
743.35/262.74	   active(U103(tt, x0, x1))
743.35/262.74	   active(U104(tt, x0, x1))
743.35/262.74	   active(U11(tt, x0, x1))
743.35/262.74	   active(U12(tt, x0, x1))
743.35/262.74	   active(U13(tt, x0, x1))
743.35/262.74	   active(U14(tt, x0, x1))
743.35/262.74	   active(U15(tt, x0))
743.35/262.74	   active(U16(tt))
743.35/262.74	   active(U21(tt, x0))
743.35/262.74	   active(U22(tt, x0))
743.35/262.74	   active(U23(tt))
743.35/262.74	   active(U31(tt, x0, x1))
743.35/262.74	   active(U32(tt, x0, x1))
743.35/262.74	   active(U33(tt, x0, x1))
743.35/262.74	   active(U34(tt, x0, x1))
743.35/262.74	   active(U35(tt, x0))
743.35/262.74	   active(U36(tt))
743.35/262.74	   active(U41(tt, x0))
743.35/262.74	   active(U42(tt))
743.35/262.74	   active(U51(tt))
743.35/262.74	   active(U61(tt, x0))
743.35/262.74	   active(U62(tt))
743.35/262.74	   active(U71(tt, x0))
743.35/262.74	   active(U72(tt, x0))
743.35/262.74	   active(U81(tt, x0, x1))
743.35/262.74	   active(U82(tt, x0, x1))
743.35/262.74	   active(U83(tt, x0, x1))
743.35/262.74	   active(U84(tt, x0, x1))
743.35/262.74	   active(U91(tt, x0))
743.35/262.74	   active(U92(tt))
743.35/262.74	   active(isNat(0))
743.35/262.74	   active(isNat(plus(x0, x1)))
743.35/262.74	   active(isNat(s(x0)))
743.35/262.74	   active(isNat(x(x0, x1)))
743.35/262.74	   active(isNatKind(0))
743.35/262.74	   active(isNatKind(plus(x0, x1)))
743.35/262.74	   active(isNatKind(s(x0)))
743.35/262.74	   active(isNatKind(x(x0, x1)))
743.35/262.74	   active(plus(x0, 0))
743.35/262.74	   active(plus(x0, s(x1)))
743.35/262.74	   active(x(x0, 0))
743.35/262.74	   active(x(x0, s(x1)))
743.35/262.74	   mark(U101(x0, x1, x2))
743.35/262.74	   mark(tt)
743.35/262.74	   mark(U102(x0, x1, x2))
743.35/262.74	   mark(isNatKind(x0))
743.35/262.74	   mark(U103(x0, x1, x2))
743.35/262.74	   mark(isNat(x0))
743.35/262.74	   mark(U104(x0, x1, x2))
743.35/262.74	   mark(plus(x0, x1))
743.35/262.74	   mark(x(x0, x1))
743.35/262.74	   mark(U11(x0, x1, x2))
743.35/262.74	   mark(U12(x0, x1, x2))
743.35/262.74	   mark(U13(x0, x1, x2))
743.35/262.74	   mark(U14(x0, x1, x2))
743.35/262.74	   mark(U15(x0, x1))
743.35/262.74	   mark(U16(x0))
743.35/262.74	   mark(U21(x0, x1))
743.35/262.74	   mark(U22(x0, x1))
743.35/262.74	   mark(U23(x0))
743.35/262.74	   mark(U31(x0, x1, x2))
743.35/262.74	   mark(U32(x0, x1, x2))
743.35/262.74	   mark(U33(x0, x1, x2))
743.35/262.74	   mark(U34(x0, x1, x2))
743.35/262.74	   mark(U35(x0, x1))
743.35/262.74	   mark(U36(x0))
743.35/262.74	   mark(U41(x0, x1))
743.35/262.74	   mark(U42(x0))
743.35/262.74	   mark(U51(x0))
743.35/262.74	   mark(U61(x0, x1))
743.35/262.74	   mark(U62(x0))
743.35/262.74	   mark(U71(x0, x1))
743.35/262.74	   mark(U72(x0, x1))
743.35/262.74	   mark(U81(x0, x1, x2))
743.35/262.74	   mark(U82(x0, x1, x2))
743.35/262.74	   mark(U83(x0, x1, x2))
743.35/262.74	   mark(U84(x0, x1, x2))
743.35/262.74	   mark(s(x0))
743.35/262.74	   mark(U91(x0, x1))
743.35/262.74	   mark(U92(x0))
743.35/262.74	   mark(0)
743.35/262.74	   U101(mark(x0), x1, x2)
743.35/262.74	   U101(x0, mark(x1), x2)
743.35/262.74	   U101(x0, x1, mark(x2))
743.35/262.74	   U101(active(x0), x1, x2)
743.35/262.74	   U101(x0, active(x1), x2)
743.35/262.74	   U101(x0, x1, active(x2))
743.35/262.74	   U102(mark(x0), x1, x2)
743.35/262.74	   U102(x0, mark(x1), x2)
743.35/262.74	   U102(x0, x1, mark(x2))
743.35/262.74	   U102(active(x0), x1, x2)
743.35/262.74	   U102(x0, active(x1), x2)
743.35/262.74	   U102(x0, x1, active(x2))
743.35/262.74	   isNatKind(mark(x0))
743.35/262.74	   isNatKind(active(x0))
743.35/262.74	   U103(mark(x0), x1, x2)
743.35/262.74	   U103(x0, mark(x1), x2)
743.35/262.74	   U103(x0, x1, mark(x2))
743.35/262.74	   U103(active(x0), x1, x2)
743.35/262.74	   U103(x0, active(x1), x2)
743.35/262.74	   U103(x0, x1, active(x2))
743.35/262.74	   isNat(mark(x0))
743.35/262.74	   isNat(active(x0))
743.35/262.74	   U104(mark(x0), x1, x2)
743.35/262.74	   U104(x0, mark(x1), x2)
743.35/262.74	   U104(x0, x1, mark(x2))
743.35/262.74	   U104(active(x0), x1, x2)
743.35/262.74	   U104(x0, active(x1), x2)
743.35/262.74	   U104(x0, x1, active(x2))
743.35/262.74	   plus(mark(x0), x1)
743.35/262.74	   plus(x0, mark(x1))
743.35/262.74	   plus(active(x0), x1)
743.35/262.74	   plus(x0, active(x1))
743.35/262.74	   x(mark(x0), x1)
743.35/262.74	   x(x0, mark(x1))
743.35/262.74	   x(active(x0), x1)
743.35/262.74	   x(x0, active(x1))
743.35/262.74	   U11(mark(x0), x1, x2)
743.35/262.74	   U11(x0, mark(x1), x2)
743.35/262.74	   U11(x0, x1, mark(x2))
743.35/262.74	   U11(active(x0), x1, x2)
743.35/262.74	   U11(x0, active(x1), x2)
743.35/262.74	   U11(x0, x1, active(x2))
743.35/262.74	   U12(mark(x0), x1, x2)
743.35/262.74	   U12(x0, mark(x1), x2)
743.35/262.74	   U12(x0, x1, mark(x2))
743.35/262.74	   U12(active(x0), x1, x2)
743.35/262.74	   U12(x0, active(x1), x2)
743.35/262.74	   U12(x0, x1, active(x2))
743.35/262.74	   U13(mark(x0), x1, x2)
743.35/262.74	   U13(x0, mark(x1), x2)
743.35/262.74	   U13(x0, x1, mark(x2))
743.35/262.74	   U13(active(x0), x1, x2)
743.35/262.74	   U13(x0, active(x1), x2)
743.35/262.74	   U13(x0, x1, active(x2))
743.35/262.74	   U14(mark(x0), x1, x2)
743.35/262.74	   U14(x0, mark(x1), x2)
743.35/262.74	   U14(x0, x1, mark(x2))
743.35/262.74	   U14(active(x0), x1, x2)
743.35/262.74	   U14(x0, active(x1), x2)
743.35/262.74	   U14(x0, x1, active(x2))
743.35/262.74	   U15(mark(x0), x1)
743.35/262.74	   U15(x0, mark(x1))
743.35/262.74	   U15(active(x0), x1)
743.35/262.74	   U15(x0, active(x1))
743.35/262.74	   U16(mark(x0))
743.35/262.74	   U16(active(x0))
743.35/262.74	   U21(mark(x0), x1)
743.35/262.74	   U21(x0, mark(x1))
743.35/262.74	   U21(active(x0), x1)
743.35/262.74	   U21(x0, active(x1))
743.35/262.74	   U22(mark(x0), x1)
743.35/262.74	   U22(x0, mark(x1))
743.35/262.74	   U22(active(x0), x1)
743.35/262.74	   U22(x0, active(x1))
743.35/262.74	   U23(mark(x0))
743.35/262.74	   U23(active(x0))
743.35/262.74	   U31(mark(x0), x1, x2)
743.35/262.74	   U31(x0, mark(x1), x2)
743.35/262.74	   U31(x0, x1, mark(x2))
743.35/262.74	   U31(active(x0), x1, x2)
743.35/262.74	   U31(x0, active(x1), x2)
743.35/262.74	   U31(x0, x1, active(x2))
743.35/262.74	   U32(mark(x0), x1, x2)
743.35/262.74	   U32(x0, mark(x1), x2)
743.35/262.74	   U32(x0, x1, mark(x2))
743.35/262.74	   U32(active(x0), x1, x2)
743.35/262.74	   U32(x0, active(x1), x2)
743.35/262.74	   U32(x0, x1, active(x2))
743.35/262.74	   U33(mark(x0), x1, x2)
743.35/262.74	   U33(x0, mark(x1), x2)
743.35/262.74	   U33(x0, x1, mark(x2))
743.35/262.74	   U33(active(x0), x1, x2)
743.35/262.74	   U33(x0, active(x1), x2)
743.35/262.74	   U33(x0, x1, active(x2))
743.35/262.74	   U34(mark(x0), x1, x2)
743.35/262.74	   U34(x0, mark(x1), x2)
743.35/262.74	   U34(x0, x1, mark(x2))
743.35/262.74	   U34(active(x0), x1, x2)
743.35/262.74	   U34(x0, active(x1), x2)
743.35/262.74	   U34(x0, x1, active(x2))
743.35/262.74	   U35(mark(x0), x1)
743.35/262.74	   U35(x0, mark(x1))
743.35/262.74	   U35(active(x0), x1)
743.35/262.74	   U35(x0, active(x1))
743.35/262.74	   U36(mark(x0))
743.35/262.74	   U36(active(x0))
743.35/262.74	   U41(mark(x0), x1)
743.35/262.74	   U41(x0, mark(x1))
743.35/262.74	   U41(active(x0), x1)
743.35/262.74	   U41(x0, active(x1))
743.35/262.74	   U42(mark(x0))
743.35/262.74	   U42(active(x0))
743.35/262.74	   U51(mark(x0))
743.35/262.74	   U51(active(x0))
743.35/262.74	   U61(mark(x0), x1)
743.35/262.74	   U61(x0, mark(x1))
743.35/262.74	   U61(active(x0), x1)
743.35/262.74	   U61(x0, active(x1))
743.35/262.74	   U62(mark(x0))
743.35/262.74	   U62(active(x0))
743.35/262.74	   U71(mark(x0), x1)
743.35/262.74	   U71(x0, mark(x1))
743.35/262.74	   U71(active(x0), x1)
743.35/262.74	   U71(x0, active(x1))
743.35/262.74	   U72(mark(x0), x1)
743.35/262.74	   U72(x0, mark(x1))
743.35/262.74	   U72(active(x0), x1)
743.35/262.74	   U72(x0, active(x1))
743.35/262.74	   U81(mark(x0), x1, x2)
743.35/262.74	   U81(x0, mark(x1), x2)
743.35/262.74	   U81(x0, x1, mark(x2))
743.35/262.74	   U81(active(x0), x1, x2)
743.35/262.74	   U81(x0, active(x1), x2)
743.35/262.74	   U81(x0, x1, active(x2))
743.35/262.74	   U82(mark(x0), x1, x2)
743.35/262.74	   U82(x0, mark(x1), x2)
743.35/262.74	   U82(x0, x1, mark(x2))
743.35/262.74	   U82(active(x0), x1, x2)
743.35/262.74	   U82(x0, active(x1), x2)
743.35/262.74	   U82(x0, x1, active(x2))
743.35/262.74	   U83(mark(x0), x1, x2)
743.35/262.74	   U83(x0, mark(x1), x2)
743.35/262.74	   U83(x0, x1, mark(x2))
743.35/262.74	   U83(active(x0), x1, x2)
743.35/262.74	   U83(x0, active(x1), x2)
743.35/262.74	   U83(x0, x1, active(x2))
743.35/262.74	   U84(mark(x0), x1, x2)
743.35/262.74	   U84(x0, mark(x1), x2)
743.35/262.74	   U84(x0, x1, mark(x2))
743.35/262.74	   U84(active(x0), x1, x2)
743.35/262.74	   U84(x0, active(x1), x2)
743.35/262.74	   U84(x0, x1, active(x2))
743.35/262.74	   s(mark(x0))
743.35/262.74	   s(active(x0))
743.35/262.74	   U91(mark(x0), x1)
743.35/262.74	   U91(x0, mark(x1))
743.35/262.74	   U91(active(x0), x1)
743.35/262.74	   U91(x0, active(x1))
743.35/262.74	   U92(mark(x0))
743.35/262.74	   U92(active(x0))
743.35/262.74	
743.35/262.74	We have to consider all minimal (P,Q,R)-chains.
743.35/262.74	----------------------------------------
743.35/262.74	
743.35/262.74	(3) DependencyGraphProof (EQUIVALENT)
743.35/262.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 38 SCCs with 114 less nodes.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(4)
743.35/262.75	Complex Obligation (AND)
743.35/262.75	
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(5)
743.35/262.75	Obligation:
743.35/262.75	Q DP problem:
743.35/262.75	The TRS P consists of the following rules:
743.35/262.75	
743.35/262.75	   U92^1(active(X)) -> U92^1(X)
743.35/262.75	   U92^1(mark(X)) -> U92^1(X)
743.35/262.75	
743.35/262.75	The TRS R consists of the following rules:
743.35/262.75	
743.35/262.75	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.75	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.75	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.75	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.75	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.75	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.75	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.75	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.75	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.75	   active(U16(tt)) -> mark(tt)
743.35/262.75	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.75	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.75	   active(U23(tt)) -> mark(tt)
743.35/262.75	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.75	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.75	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.75	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.75	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.75	   active(U36(tt)) -> mark(tt)
743.35/262.75	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.75	   active(U42(tt)) -> mark(tt)
743.35/262.75	   active(U51(tt)) -> mark(tt)
743.35/262.75	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.75	   active(U62(tt)) -> mark(tt)
743.35/262.75	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.75	   active(U72(tt, N)) -> mark(N)
743.35/262.75	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.75	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.75	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.75	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.75	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.75	   active(U92(tt)) -> mark(0)
743.35/262.75	   active(isNat(0)) -> mark(tt)
743.35/262.75	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.75	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.75	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.75	   active(isNatKind(0)) -> mark(tt)
743.35/262.75	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.75	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.75	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.75	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.75	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.75	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.75	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.75	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.75	   mark(tt) -> active(tt)
743.35/262.75	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.75	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.75	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.75	   mark(isNat(X)) -> active(isNat(X))
743.35/262.75	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.75	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.75	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.75	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.75	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.75	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.75	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.75	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.75	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.75	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.75	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.75	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.75	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.75	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.75	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.75	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.75	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.75	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.75	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.75	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.75	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.75	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.75	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.75	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.75	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.75	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.75	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.75	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.75	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.75	   mark(s(X)) -> active(s(mark(X)))
743.35/262.75	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.75	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.75	   mark(0) -> active(0)
743.35/262.75	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.75	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.75	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.75	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.75	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.75	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.75	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.75	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.75	   isNat(mark(X)) -> isNat(X)
743.35/262.75	   isNat(active(X)) -> isNat(X)
743.35/262.75	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.75	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.75	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.75	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.75	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.75	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.75	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.75	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.75	   x(active(X1), X2) -> x(X1, X2)
743.35/262.75	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.75	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.75	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.75	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.75	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.75	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.75	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.75	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.75	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.75	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.75	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.75	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.75	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.75	   U16(mark(X)) -> U16(X)
743.35/262.75	   U16(active(X)) -> U16(X)
743.35/262.75	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.75	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.75	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.75	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.75	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.75	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.75	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.75	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.75	   U23(mark(X)) -> U23(X)
743.35/262.75	   U23(active(X)) -> U23(X)
743.35/262.75	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.75	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.75	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.75	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.75	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.75	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.75	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.75	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.75	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.75	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.75	   U35(active(X1), X2) -> U35(X1, X2)
743.35/262.75	   U35(X1, active(X2)) -> U35(X1, X2)
743.35/262.75	   U36(mark(X)) -> U36(X)
743.35/262.75	   U36(active(X)) -> U36(X)
743.35/262.75	   U41(mark(X1), X2) -> U41(X1, X2)
743.35/262.75	   U41(X1, mark(X2)) -> U41(X1, X2)
743.35/262.75	   U41(active(X1), X2) -> U41(X1, X2)
743.35/262.75	   U41(X1, active(X2)) -> U41(X1, X2)
743.35/262.75	   U42(mark(X)) -> U42(X)
743.35/262.75	   U42(active(X)) -> U42(X)
743.35/262.75	   U51(mark(X)) -> U51(X)
743.35/262.75	   U51(active(X)) -> U51(X)
743.35/262.75	   U61(mark(X1), X2) -> U61(X1, X2)
743.35/262.75	   U61(X1, mark(X2)) -> U61(X1, X2)
743.35/262.75	   U61(active(X1), X2) -> U61(X1, X2)
743.35/262.75	   U61(X1, active(X2)) -> U61(X1, X2)
743.35/262.75	   U62(mark(X)) -> U62(X)
743.35/262.75	   U62(active(X)) -> U62(X)
743.35/262.75	   U71(mark(X1), X2) -> U71(X1, X2)
743.35/262.75	   U71(X1, mark(X2)) -> U71(X1, X2)
743.35/262.75	   U71(active(X1), X2) -> U71(X1, X2)
743.35/262.75	   U71(X1, active(X2)) -> U71(X1, X2)
743.35/262.75	   U72(mark(X1), X2) -> U72(X1, X2)
743.35/262.75	   U72(X1, mark(X2)) -> U72(X1, X2)
743.35/262.75	   U72(active(X1), X2) -> U72(X1, X2)
743.35/262.75	   U72(X1, active(X2)) -> U72(X1, X2)
743.35/262.75	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.35/262.75	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.35/262.75	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.35/262.75	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.35/262.75	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.35/262.75	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.35/262.75	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.35/262.75	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.35/262.75	   s(mark(X)) -> s(X)
743.35/262.75	   s(active(X)) -> s(X)
743.35/262.75	   U91(mark(X1), X2) -> U91(X1, X2)
743.35/262.75	   U91(X1, mark(X2)) -> U91(X1, X2)
743.35/262.75	   U91(active(X1), X2) -> U91(X1, X2)
743.35/262.75	   U91(X1, active(X2)) -> U91(X1, X2)
743.35/262.75	   U92(mark(X)) -> U92(X)
743.35/262.75	   U92(active(X)) -> U92(X)
743.35/262.75	
743.35/262.75	The set Q consists of the following terms:
743.35/262.75	
743.35/262.75	   active(U101(tt, x0, x1))
743.35/262.75	   active(U102(tt, x0, x1))
743.35/262.75	   active(U103(tt, x0, x1))
743.35/262.75	   active(U104(tt, x0, x1))
743.35/262.75	   active(U11(tt, x0, x1))
743.35/262.75	   active(U12(tt, x0, x1))
743.35/262.75	   active(U13(tt, x0, x1))
743.35/262.75	   active(U14(tt, x0, x1))
743.35/262.75	   active(U15(tt, x0))
743.35/262.75	   active(U16(tt))
743.35/262.75	   active(U21(tt, x0))
743.35/262.75	   active(U22(tt, x0))
743.35/262.75	   active(U23(tt))
743.35/262.75	   active(U31(tt, x0, x1))
743.35/262.75	   active(U32(tt, x0, x1))
743.35/262.75	   active(U33(tt, x0, x1))
743.35/262.75	   active(U34(tt, x0, x1))
743.35/262.75	   active(U35(tt, x0))
743.35/262.75	   active(U36(tt))
743.35/262.75	   active(U41(tt, x0))
743.35/262.75	   active(U42(tt))
743.35/262.75	   active(U51(tt))
743.35/262.75	   active(U61(tt, x0))
743.35/262.75	   active(U62(tt))
743.35/262.75	   active(U71(tt, x0))
743.35/262.75	   active(U72(tt, x0))
743.35/262.75	   active(U81(tt, x0, x1))
743.35/262.75	   active(U82(tt, x0, x1))
743.35/262.75	   active(U83(tt, x0, x1))
743.35/262.75	   active(U84(tt, x0, x1))
743.35/262.75	   active(U91(tt, x0))
743.35/262.75	   active(U92(tt))
743.35/262.75	   active(isNat(0))
743.35/262.75	   active(isNat(plus(x0, x1)))
743.35/262.75	   active(isNat(s(x0)))
743.35/262.75	   active(isNat(x(x0, x1)))
743.35/262.75	   active(isNatKind(0))
743.35/262.75	   active(isNatKind(plus(x0, x1)))
743.35/262.75	   active(isNatKind(s(x0)))
743.35/262.75	   active(isNatKind(x(x0, x1)))
743.35/262.75	   active(plus(x0, 0))
743.35/262.75	   active(plus(x0, s(x1)))
743.35/262.75	   active(x(x0, 0))
743.35/262.75	   active(x(x0, s(x1)))
743.35/262.75	   mark(U101(x0, x1, x2))
743.35/262.75	   mark(tt)
743.35/262.75	   mark(U102(x0, x1, x2))
743.35/262.75	   mark(isNatKind(x0))
743.35/262.75	   mark(U103(x0, x1, x2))
743.35/262.75	   mark(isNat(x0))
743.35/262.75	   mark(U104(x0, x1, x2))
743.35/262.75	   mark(plus(x0, x1))
743.35/262.75	   mark(x(x0, x1))
743.35/262.75	   mark(U11(x0, x1, x2))
743.35/262.75	   mark(U12(x0, x1, x2))
743.35/262.75	   mark(U13(x0, x1, x2))
743.35/262.75	   mark(U14(x0, x1, x2))
743.35/262.75	   mark(U15(x0, x1))
743.35/262.75	   mark(U16(x0))
743.35/262.75	   mark(U21(x0, x1))
743.35/262.75	   mark(U22(x0, x1))
743.35/262.75	   mark(U23(x0))
743.35/262.75	   mark(U31(x0, x1, x2))
743.35/262.75	   mark(U32(x0, x1, x2))
743.35/262.75	   mark(U33(x0, x1, x2))
743.35/262.75	   mark(U34(x0, x1, x2))
743.35/262.75	   mark(U35(x0, x1))
743.35/262.75	   mark(U36(x0))
743.35/262.75	   mark(U41(x0, x1))
743.35/262.75	   mark(U42(x0))
743.35/262.75	   mark(U51(x0))
743.35/262.75	   mark(U61(x0, x1))
743.35/262.75	   mark(U62(x0))
743.35/262.75	   mark(U71(x0, x1))
743.35/262.75	   mark(U72(x0, x1))
743.35/262.75	   mark(U81(x0, x1, x2))
743.35/262.75	   mark(U82(x0, x1, x2))
743.35/262.75	   mark(U83(x0, x1, x2))
743.35/262.75	   mark(U84(x0, x1, x2))
743.35/262.75	   mark(s(x0))
743.35/262.75	   mark(U91(x0, x1))
743.35/262.75	   mark(U92(x0))
743.35/262.75	   mark(0)
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.75	   U91(x0, mark(x1))
743.35/262.75	   U91(active(x0), x1)
743.35/262.75	   U91(x0, active(x1))
743.35/262.75	   U92(mark(x0))
743.35/262.75	   U92(active(x0))
743.35/262.75	
743.35/262.75	We have to consider all minimal (P,Q,R)-chains.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(6) UsableRulesProof (EQUIVALENT)
743.35/262.75	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.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(7)
743.35/262.75	Obligation:
743.35/262.75	Q DP problem:
743.35/262.75	The TRS P consists of the following rules:
743.35/262.75	
743.35/262.75	   U92^1(active(X)) -> U92^1(X)
743.35/262.75	   U92^1(mark(X)) -> U92^1(X)
743.35/262.75	
743.35/262.75	R is empty.
743.35/262.75	The set Q consists of the following terms:
743.35/262.75	
743.35/262.75	   active(U101(tt, x0, x1))
743.35/262.75	   active(U102(tt, x0, x1))
743.35/262.75	   active(U103(tt, x0, x1))
743.35/262.75	   active(U104(tt, x0, x1))
743.35/262.75	   active(U11(tt, x0, x1))
743.35/262.75	   active(U12(tt, x0, x1))
743.35/262.75	   active(U13(tt, x0, x1))
743.35/262.75	   active(U14(tt, x0, x1))
743.35/262.75	   active(U15(tt, x0))
743.35/262.75	   active(U16(tt))
743.35/262.75	   active(U21(tt, x0))
743.35/262.75	   active(U22(tt, x0))
743.35/262.75	   active(U23(tt))
743.35/262.75	   active(U31(tt, x0, x1))
743.35/262.75	   active(U32(tt, x0, x1))
743.35/262.75	   active(U33(tt, x0, x1))
743.35/262.75	   active(U34(tt, x0, x1))
743.35/262.75	   active(U35(tt, x0))
743.35/262.75	   active(U36(tt))
743.35/262.75	   active(U41(tt, x0))
743.35/262.75	   active(U42(tt))
743.35/262.75	   active(U51(tt))
743.35/262.75	   active(U61(tt, x0))
743.35/262.75	   active(U62(tt))
743.35/262.75	   active(U71(tt, x0))
743.35/262.75	   active(U72(tt, x0))
743.35/262.75	   active(U81(tt, x0, x1))
743.35/262.75	   active(U82(tt, x0, x1))
743.35/262.75	   active(U83(tt, x0, x1))
743.35/262.75	   active(U84(tt, x0, x1))
743.35/262.75	   active(U91(tt, x0))
743.35/262.75	   active(U92(tt))
743.35/262.75	   active(isNat(0))
743.35/262.75	   active(isNat(plus(x0, x1)))
743.35/262.75	   active(isNat(s(x0)))
743.35/262.75	   active(isNat(x(x0, x1)))
743.35/262.75	   active(isNatKind(0))
743.35/262.75	   active(isNatKind(plus(x0, x1)))
743.35/262.75	   active(isNatKind(s(x0)))
743.35/262.75	   active(isNatKind(x(x0, x1)))
743.35/262.75	   active(plus(x0, 0))
743.35/262.75	   active(plus(x0, s(x1)))
743.35/262.75	   active(x(x0, 0))
743.35/262.75	   active(x(x0, s(x1)))
743.35/262.75	   mark(U101(x0, x1, x2))
743.35/262.75	   mark(tt)
743.35/262.75	   mark(U102(x0, x1, x2))
743.35/262.75	   mark(isNatKind(x0))
743.35/262.75	   mark(U103(x0, x1, x2))
743.35/262.75	   mark(isNat(x0))
743.35/262.75	   mark(U104(x0, x1, x2))
743.35/262.75	   mark(plus(x0, x1))
743.35/262.75	   mark(x(x0, x1))
743.35/262.75	   mark(U11(x0, x1, x2))
743.35/262.75	   mark(U12(x0, x1, x2))
743.35/262.75	   mark(U13(x0, x1, x2))
743.35/262.75	   mark(U14(x0, x1, x2))
743.35/262.75	   mark(U15(x0, x1))
743.35/262.75	   mark(U16(x0))
743.35/262.75	   mark(U21(x0, x1))
743.35/262.75	   mark(U22(x0, x1))
743.35/262.75	   mark(U23(x0))
743.35/262.75	   mark(U31(x0, x1, x2))
743.35/262.75	   mark(U32(x0, x1, x2))
743.35/262.75	   mark(U33(x0, x1, x2))
743.35/262.75	   mark(U34(x0, x1, x2))
743.35/262.75	   mark(U35(x0, x1))
743.35/262.75	   mark(U36(x0))
743.35/262.75	   mark(U41(x0, x1))
743.35/262.75	   mark(U42(x0))
743.35/262.75	   mark(U51(x0))
743.35/262.75	   mark(U61(x0, x1))
743.35/262.75	   mark(U62(x0))
743.35/262.75	   mark(U71(x0, x1))
743.35/262.75	   mark(U72(x0, x1))
743.35/262.75	   mark(U81(x0, x1, x2))
743.35/262.75	   mark(U82(x0, x1, x2))
743.35/262.75	   mark(U83(x0, x1, x2))
743.35/262.75	   mark(U84(x0, x1, x2))
743.35/262.75	   mark(s(x0))
743.35/262.75	   mark(U91(x0, x1))
743.35/262.75	   mark(U92(x0))
743.35/262.75	   mark(0)
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.75	   U91(x0, mark(x1))
743.35/262.75	   U91(active(x0), x1)
743.35/262.75	   U91(x0, active(x1))
743.35/262.75	   U92(mark(x0))
743.35/262.75	   U92(active(x0))
743.35/262.75	
743.35/262.75	We have to consider all minimal (P,Q,R)-chains.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(8) QReductionProof (EQUIVALENT)
743.35/262.75	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.35/262.75	
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.75	   U91(x0, mark(x1))
743.35/262.75	   U91(active(x0), x1)
743.35/262.75	   U91(x0, active(x1))
743.35/262.75	   U92(mark(x0))
743.35/262.75	   U92(active(x0))
743.35/262.75	
743.35/262.75	
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(9)
743.35/262.75	Obligation:
743.35/262.75	Q DP problem:
743.35/262.75	The TRS P consists of the following rules:
743.35/262.75	
743.35/262.75	   U92^1(active(X)) -> U92^1(X)
743.35/262.75	   U92^1(mark(X)) -> U92^1(X)
743.35/262.75	
743.35/262.75	R is empty.
743.35/262.75	The set Q consists of the following terms:
743.35/262.75	
743.35/262.75	   active(U101(tt, x0, x1))
743.35/262.75	   active(U102(tt, x0, x1))
743.35/262.75	   active(U103(tt, x0, x1))
743.35/262.75	   active(U104(tt, x0, x1))
743.35/262.75	   active(U11(tt, x0, x1))
743.35/262.75	   active(U12(tt, x0, x1))
743.35/262.75	   active(U13(tt, x0, x1))
743.35/262.75	   active(U14(tt, x0, x1))
743.35/262.75	   active(U15(tt, x0))
743.35/262.75	   active(U16(tt))
743.35/262.75	   active(U21(tt, x0))
743.35/262.75	   active(U22(tt, x0))
743.35/262.75	   active(U23(tt))
743.35/262.75	   active(U31(tt, x0, x1))
743.35/262.75	   active(U32(tt, x0, x1))
743.35/262.75	   active(U33(tt, x0, x1))
743.35/262.75	   active(U34(tt, x0, x1))
743.35/262.75	   active(U35(tt, x0))
743.35/262.75	   active(U36(tt))
743.35/262.75	   active(U41(tt, x0))
743.35/262.75	   active(U42(tt))
743.35/262.75	   active(U51(tt))
743.35/262.75	   active(U61(tt, x0))
743.35/262.75	   active(U62(tt))
743.35/262.75	   active(U71(tt, x0))
743.35/262.75	   active(U72(tt, x0))
743.35/262.75	   active(U81(tt, x0, x1))
743.35/262.75	   active(U82(tt, x0, x1))
743.35/262.75	   active(U83(tt, x0, x1))
743.35/262.75	   active(U84(tt, x0, x1))
743.35/262.75	   active(U91(tt, x0))
743.35/262.75	   active(U92(tt))
743.35/262.75	   active(isNat(0))
743.35/262.75	   active(isNat(plus(x0, x1)))
743.35/262.75	   active(isNat(s(x0)))
743.35/262.75	   active(isNat(x(x0, x1)))
743.35/262.75	   active(isNatKind(0))
743.35/262.75	   active(isNatKind(plus(x0, x1)))
743.35/262.75	   active(isNatKind(s(x0)))
743.35/262.75	   active(isNatKind(x(x0, x1)))
743.35/262.75	   active(plus(x0, 0))
743.35/262.75	   active(plus(x0, s(x1)))
743.35/262.75	   active(x(x0, 0))
743.35/262.75	   active(x(x0, s(x1)))
743.35/262.75	   mark(U101(x0, x1, x2))
743.35/262.75	   mark(tt)
743.35/262.75	   mark(U102(x0, x1, x2))
743.35/262.75	   mark(isNatKind(x0))
743.35/262.75	   mark(U103(x0, x1, x2))
743.35/262.75	   mark(isNat(x0))
743.35/262.75	   mark(U104(x0, x1, x2))
743.35/262.75	   mark(plus(x0, x1))
743.35/262.75	   mark(x(x0, x1))
743.35/262.75	   mark(U11(x0, x1, x2))
743.35/262.75	   mark(U12(x0, x1, x2))
743.35/262.75	   mark(U13(x0, x1, x2))
743.35/262.75	   mark(U14(x0, x1, x2))
743.35/262.75	   mark(U15(x0, x1))
743.35/262.75	   mark(U16(x0))
743.35/262.75	   mark(U21(x0, x1))
743.35/262.75	   mark(U22(x0, x1))
743.35/262.75	   mark(U23(x0))
743.35/262.75	   mark(U31(x0, x1, x2))
743.35/262.75	   mark(U32(x0, x1, x2))
743.35/262.75	   mark(U33(x0, x1, x2))
743.35/262.75	   mark(U34(x0, x1, x2))
743.35/262.75	   mark(U35(x0, x1))
743.35/262.75	   mark(U36(x0))
743.35/262.75	   mark(U41(x0, x1))
743.35/262.75	   mark(U42(x0))
743.35/262.75	   mark(U51(x0))
743.35/262.75	   mark(U61(x0, x1))
743.35/262.75	   mark(U62(x0))
743.35/262.75	   mark(U71(x0, x1))
743.35/262.75	   mark(U72(x0, x1))
743.35/262.75	   mark(U81(x0, x1, x2))
743.35/262.75	   mark(U82(x0, x1, x2))
743.35/262.75	   mark(U83(x0, x1, x2))
743.35/262.75	   mark(U84(x0, x1, x2))
743.35/262.75	   mark(s(x0))
743.35/262.75	   mark(U91(x0, x1))
743.35/262.75	   mark(U92(x0))
743.35/262.75	   mark(0)
743.35/262.75	
743.35/262.75	We have to consider all minimal (P,Q,R)-chains.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(10) QDPSizeChangeProof (EQUIVALENT)
743.35/262.75	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. 
743.35/262.75	
743.35/262.75	From the DPs we obtained the following set of size-change graphs:
743.35/262.75	*U92^1(active(X)) -> U92^1(X)
743.35/262.75	The graph contains the following edges 1 > 1
743.35/262.75	
743.35/262.75	
743.35/262.75	*U92^1(mark(X)) -> U92^1(X)
743.35/262.75	The graph contains the following edges 1 > 1
743.35/262.75	
743.35/262.75	
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(11)
743.35/262.75	YES
743.35/262.75	
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(12)
743.35/262.75	Obligation:
743.35/262.75	Q DP problem:
743.35/262.75	The TRS P consists of the following rules:
743.35/262.75	
743.35/262.75	   U91^1(X1, mark(X2)) -> U91^1(X1, X2)
743.35/262.75	   U91^1(mark(X1), X2) -> U91^1(X1, X2)
743.35/262.75	   U91^1(active(X1), X2) -> U91^1(X1, X2)
743.35/262.75	   U91^1(X1, active(X2)) -> U91^1(X1, X2)
743.35/262.75	
743.35/262.75	The TRS R consists of the following rules:
743.35/262.75	
743.35/262.75	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.75	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.75	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.75	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.75	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.75	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.75	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.75	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.75	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.75	   active(U16(tt)) -> mark(tt)
743.35/262.75	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.75	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.75	   active(U23(tt)) -> mark(tt)
743.35/262.75	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.75	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.75	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.75	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.75	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.75	   active(U36(tt)) -> mark(tt)
743.35/262.75	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.75	   active(U42(tt)) -> mark(tt)
743.35/262.75	   active(U51(tt)) -> mark(tt)
743.35/262.75	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.75	   active(U62(tt)) -> mark(tt)
743.35/262.75	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.75	   active(U72(tt, N)) -> mark(N)
743.35/262.75	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.75	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.75	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.75	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.75	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.75	   active(U92(tt)) -> mark(0)
743.35/262.75	   active(isNat(0)) -> mark(tt)
743.35/262.75	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.75	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.75	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.75	   active(isNatKind(0)) -> mark(tt)
743.35/262.75	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.75	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.75	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.75	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.75	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.75	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.75	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.75	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.75	   mark(tt) -> active(tt)
743.35/262.75	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.75	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.75	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.75	   mark(isNat(X)) -> active(isNat(X))
743.35/262.75	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.75	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.75	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.75	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.75	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.75	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.75	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.75	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.75	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.75	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.75	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.75	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.75	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.75	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.75	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.75	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.75	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.75	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.75	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.75	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.75	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.75	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.75	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.75	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.75	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.75	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.75	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.75	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.75	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.75	   mark(s(X)) -> active(s(mark(X)))
743.35/262.75	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.75	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.75	   mark(0) -> active(0)
743.35/262.75	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.75	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.75	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.75	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.75	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.75	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.75	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.75	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.75	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.75	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.75	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.75	   isNat(mark(X)) -> isNat(X)
743.35/262.75	   isNat(active(X)) -> isNat(X)
743.35/262.75	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.75	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.75	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.75	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.75	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.75	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.75	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.75	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.75	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.75	   x(active(X1), X2) -> x(X1, X2)
743.35/262.75	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.75	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.75	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.75	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.75	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.75	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.75	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.75	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.75	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.75	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.75	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.75	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.75	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.75	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.75	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.75	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.75	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.75	   U16(mark(X)) -> U16(X)
743.35/262.75	   U16(active(X)) -> U16(X)
743.35/262.75	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.75	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.75	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.75	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.75	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.75	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.75	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.75	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.75	   U23(mark(X)) -> U23(X)
743.35/262.75	   U23(active(X)) -> U23(X)
743.35/262.75	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.75	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.75	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.75	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.75	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.75	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.75	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.75	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.75	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.75	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.75	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.75	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.75	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.75	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.75	   U35(active(X1), X2) -> U35(X1, X2)
743.35/262.75	   U35(X1, active(X2)) -> U35(X1, X2)
743.35/262.75	   U36(mark(X)) -> U36(X)
743.35/262.75	   U36(active(X)) -> U36(X)
743.35/262.75	   U41(mark(X1), X2) -> U41(X1, X2)
743.35/262.75	   U41(X1, mark(X2)) -> U41(X1, X2)
743.35/262.75	   U41(active(X1), X2) -> U41(X1, X2)
743.35/262.75	   U41(X1, active(X2)) -> U41(X1, X2)
743.35/262.75	   U42(mark(X)) -> U42(X)
743.35/262.75	   U42(active(X)) -> U42(X)
743.35/262.75	   U51(mark(X)) -> U51(X)
743.35/262.75	   U51(active(X)) -> U51(X)
743.35/262.75	   U61(mark(X1), X2) -> U61(X1, X2)
743.35/262.75	   U61(X1, mark(X2)) -> U61(X1, X2)
743.35/262.75	   U61(active(X1), X2) -> U61(X1, X2)
743.35/262.75	   U61(X1, active(X2)) -> U61(X1, X2)
743.35/262.75	   U62(mark(X)) -> U62(X)
743.35/262.75	   U62(active(X)) -> U62(X)
743.35/262.75	   U71(mark(X1), X2) -> U71(X1, X2)
743.35/262.75	   U71(X1, mark(X2)) -> U71(X1, X2)
743.35/262.75	   U71(active(X1), X2) -> U71(X1, X2)
743.35/262.75	   U71(X1, active(X2)) -> U71(X1, X2)
743.35/262.75	   U72(mark(X1), X2) -> U72(X1, X2)
743.35/262.75	   U72(X1, mark(X2)) -> U72(X1, X2)
743.35/262.75	   U72(active(X1), X2) -> U72(X1, X2)
743.35/262.75	   U72(X1, active(X2)) -> U72(X1, X2)
743.35/262.75	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.35/262.75	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.35/262.75	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.35/262.75	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.35/262.75	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.35/262.75	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.35/262.75	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.35/262.75	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.35/262.75	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.35/262.75	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.35/262.75	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.35/262.75	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.35/262.75	   s(mark(X)) -> s(X)
743.35/262.75	   s(active(X)) -> s(X)
743.35/262.75	   U91(mark(X1), X2) -> U91(X1, X2)
743.35/262.75	   U91(X1, mark(X2)) -> U91(X1, X2)
743.35/262.75	   U91(active(X1), X2) -> U91(X1, X2)
743.35/262.75	   U91(X1, active(X2)) -> U91(X1, X2)
743.35/262.75	   U92(mark(X)) -> U92(X)
743.35/262.75	   U92(active(X)) -> U92(X)
743.35/262.75	
743.35/262.75	The set Q consists of the following terms:
743.35/262.75	
743.35/262.75	   active(U101(tt, x0, x1))
743.35/262.75	   active(U102(tt, x0, x1))
743.35/262.75	   active(U103(tt, x0, x1))
743.35/262.75	   active(U104(tt, x0, x1))
743.35/262.75	   active(U11(tt, x0, x1))
743.35/262.75	   active(U12(tt, x0, x1))
743.35/262.75	   active(U13(tt, x0, x1))
743.35/262.75	   active(U14(tt, x0, x1))
743.35/262.75	   active(U15(tt, x0))
743.35/262.75	   active(U16(tt))
743.35/262.75	   active(U21(tt, x0))
743.35/262.75	   active(U22(tt, x0))
743.35/262.75	   active(U23(tt))
743.35/262.75	   active(U31(tt, x0, x1))
743.35/262.75	   active(U32(tt, x0, x1))
743.35/262.75	   active(U33(tt, x0, x1))
743.35/262.75	   active(U34(tt, x0, x1))
743.35/262.75	   active(U35(tt, x0))
743.35/262.75	   active(U36(tt))
743.35/262.75	   active(U41(tt, x0))
743.35/262.75	   active(U42(tt))
743.35/262.75	   active(U51(tt))
743.35/262.75	   active(U61(tt, x0))
743.35/262.75	   active(U62(tt))
743.35/262.75	   active(U71(tt, x0))
743.35/262.75	   active(U72(tt, x0))
743.35/262.75	   active(U81(tt, x0, x1))
743.35/262.75	   active(U82(tt, x0, x1))
743.35/262.75	   active(U83(tt, x0, x1))
743.35/262.75	   active(U84(tt, x0, x1))
743.35/262.75	   active(U91(tt, x0))
743.35/262.75	   active(U92(tt))
743.35/262.75	   active(isNat(0))
743.35/262.75	   active(isNat(plus(x0, x1)))
743.35/262.75	   active(isNat(s(x0)))
743.35/262.75	   active(isNat(x(x0, x1)))
743.35/262.75	   active(isNatKind(0))
743.35/262.75	   active(isNatKind(plus(x0, x1)))
743.35/262.75	   active(isNatKind(s(x0)))
743.35/262.75	   active(isNatKind(x(x0, x1)))
743.35/262.75	   active(plus(x0, 0))
743.35/262.75	   active(plus(x0, s(x1)))
743.35/262.75	   active(x(x0, 0))
743.35/262.75	   active(x(x0, s(x1)))
743.35/262.75	   mark(U101(x0, x1, x2))
743.35/262.75	   mark(tt)
743.35/262.75	   mark(U102(x0, x1, x2))
743.35/262.75	   mark(isNatKind(x0))
743.35/262.75	   mark(U103(x0, x1, x2))
743.35/262.75	   mark(isNat(x0))
743.35/262.75	   mark(U104(x0, x1, x2))
743.35/262.75	   mark(plus(x0, x1))
743.35/262.75	   mark(x(x0, x1))
743.35/262.75	   mark(U11(x0, x1, x2))
743.35/262.75	   mark(U12(x0, x1, x2))
743.35/262.75	   mark(U13(x0, x1, x2))
743.35/262.75	   mark(U14(x0, x1, x2))
743.35/262.75	   mark(U15(x0, x1))
743.35/262.75	   mark(U16(x0))
743.35/262.75	   mark(U21(x0, x1))
743.35/262.75	   mark(U22(x0, x1))
743.35/262.75	   mark(U23(x0))
743.35/262.75	   mark(U31(x0, x1, x2))
743.35/262.75	   mark(U32(x0, x1, x2))
743.35/262.75	   mark(U33(x0, x1, x2))
743.35/262.75	   mark(U34(x0, x1, x2))
743.35/262.75	   mark(U35(x0, x1))
743.35/262.75	   mark(U36(x0))
743.35/262.75	   mark(U41(x0, x1))
743.35/262.75	   mark(U42(x0))
743.35/262.75	   mark(U51(x0))
743.35/262.75	   mark(U61(x0, x1))
743.35/262.75	   mark(U62(x0))
743.35/262.75	   mark(U71(x0, x1))
743.35/262.75	   mark(U72(x0, x1))
743.35/262.75	   mark(U81(x0, x1, x2))
743.35/262.75	   mark(U82(x0, x1, x2))
743.35/262.75	   mark(U83(x0, x1, x2))
743.35/262.75	   mark(U84(x0, x1, x2))
743.35/262.75	   mark(s(x0))
743.35/262.75	   mark(U91(x0, x1))
743.35/262.75	   mark(U92(x0))
743.35/262.75	   mark(0)
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.75	   U91(x0, mark(x1))
743.35/262.75	   U91(active(x0), x1)
743.35/262.75	   U91(x0, active(x1))
743.35/262.75	   U92(mark(x0))
743.35/262.75	   U92(active(x0))
743.35/262.75	
743.35/262.75	We have to consider all minimal (P,Q,R)-chains.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(13) UsableRulesProof (EQUIVALENT)
743.35/262.75	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.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(14)
743.35/262.75	Obligation:
743.35/262.75	Q DP problem:
743.35/262.75	The TRS P consists of the following rules:
743.35/262.75	
743.35/262.75	   U91^1(X1, mark(X2)) -> U91^1(X1, X2)
743.35/262.75	   U91^1(mark(X1), X2) -> U91^1(X1, X2)
743.35/262.75	   U91^1(active(X1), X2) -> U91^1(X1, X2)
743.35/262.75	   U91^1(X1, active(X2)) -> U91^1(X1, X2)
743.35/262.75	
743.35/262.75	R is empty.
743.35/262.75	The set Q consists of the following terms:
743.35/262.75	
743.35/262.75	   active(U101(tt, x0, x1))
743.35/262.75	   active(U102(tt, x0, x1))
743.35/262.75	   active(U103(tt, x0, x1))
743.35/262.75	   active(U104(tt, x0, x1))
743.35/262.75	   active(U11(tt, x0, x1))
743.35/262.75	   active(U12(tt, x0, x1))
743.35/262.75	   active(U13(tt, x0, x1))
743.35/262.75	   active(U14(tt, x0, x1))
743.35/262.75	   active(U15(tt, x0))
743.35/262.75	   active(U16(tt))
743.35/262.75	   active(U21(tt, x0))
743.35/262.75	   active(U22(tt, x0))
743.35/262.75	   active(U23(tt))
743.35/262.75	   active(U31(tt, x0, x1))
743.35/262.75	   active(U32(tt, x0, x1))
743.35/262.75	   active(U33(tt, x0, x1))
743.35/262.75	   active(U34(tt, x0, x1))
743.35/262.75	   active(U35(tt, x0))
743.35/262.75	   active(U36(tt))
743.35/262.75	   active(U41(tt, x0))
743.35/262.75	   active(U42(tt))
743.35/262.75	   active(U51(tt))
743.35/262.75	   active(U61(tt, x0))
743.35/262.75	   active(U62(tt))
743.35/262.75	   active(U71(tt, x0))
743.35/262.75	   active(U72(tt, x0))
743.35/262.75	   active(U81(tt, x0, x1))
743.35/262.75	   active(U82(tt, x0, x1))
743.35/262.75	   active(U83(tt, x0, x1))
743.35/262.75	   active(U84(tt, x0, x1))
743.35/262.75	   active(U91(tt, x0))
743.35/262.75	   active(U92(tt))
743.35/262.75	   active(isNat(0))
743.35/262.75	   active(isNat(plus(x0, x1)))
743.35/262.75	   active(isNat(s(x0)))
743.35/262.75	   active(isNat(x(x0, x1)))
743.35/262.75	   active(isNatKind(0))
743.35/262.75	   active(isNatKind(plus(x0, x1)))
743.35/262.75	   active(isNatKind(s(x0)))
743.35/262.75	   active(isNatKind(x(x0, x1)))
743.35/262.75	   active(plus(x0, 0))
743.35/262.75	   active(plus(x0, s(x1)))
743.35/262.75	   active(x(x0, 0))
743.35/262.75	   active(x(x0, s(x1)))
743.35/262.75	   mark(U101(x0, x1, x2))
743.35/262.75	   mark(tt)
743.35/262.75	   mark(U102(x0, x1, x2))
743.35/262.75	   mark(isNatKind(x0))
743.35/262.75	   mark(U103(x0, x1, x2))
743.35/262.75	   mark(isNat(x0))
743.35/262.75	   mark(U104(x0, x1, x2))
743.35/262.75	   mark(plus(x0, x1))
743.35/262.75	   mark(x(x0, x1))
743.35/262.75	   mark(U11(x0, x1, x2))
743.35/262.75	   mark(U12(x0, x1, x2))
743.35/262.75	   mark(U13(x0, x1, x2))
743.35/262.75	   mark(U14(x0, x1, x2))
743.35/262.75	   mark(U15(x0, x1))
743.35/262.75	   mark(U16(x0))
743.35/262.75	   mark(U21(x0, x1))
743.35/262.75	   mark(U22(x0, x1))
743.35/262.75	   mark(U23(x0))
743.35/262.75	   mark(U31(x0, x1, x2))
743.35/262.75	   mark(U32(x0, x1, x2))
743.35/262.75	   mark(U33(x0, x1, x2))
743.35/262.75	   mark(U34(x0, x1, x2))
743.35/262.75	   mark(U35(x0, x1))
743.35/262.75	   mark(U36(x0))
743.35/262.75	   mark(U41(x0, x1))
743.35/262.75	   mark(U42(x0))
743.35/262.75	   mark(U51(x0))
743.35/262.75	   mark(U61(x0, x1))
743.35/262.75	   mark(U62(x0))
743.35/262.75	   mark(U71(x0, x1))
743.35/262.75	   mark(U72(x0, x1))
743.35/262.75	   mark(U81(x0, x1, x2))
743.35/262.75	   mark(U82(x0, x1, x2))
743.35/262.75	   mark(U83(x0, x1, x2))
743.35/262.75	   mark(U84(x0, x1, x2))
743.35/262.75	   mark(s(x0))
743.35/262.75	   mark(U91(x0, x1))
743.35/262.75	   mark(U92(x0))
743.35/262.75	   mark(0)
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.75	   U91(x0, mark(x1))
743.35/262.75	   U91(active(x0), x1)
743.35/262.75	   U91(x0, active(x1))
743.35/262.75	   U92(mark(x0))
743.35/262.75	   U92(active(x0))
743.35/262.75	
743.35/262.75	We have to consider all minimal (P,Q,R)-chains.
743.35/262.75	----------------------------------------
743.35/262.75	
743.35/262.75	(15) QReductionProof (EQUIVALENT)
743.35/262.75	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.35/262.75	
743.35/262.75	   U101(mark(x0), x1, x2)
743.35/262.75	   U101(x0, mark(x1), x2)
743.35/262.75	   U101(x0, x1, mark(x2))
743.35/262.75	   U101(active(x0), x1, x2)
743.35/262.75	   U101(x0, active(x1), x2)
743.35/262.75	   U101(x0, x1, active(x2))
743.35/262.75	   U102(mark(x0), x1, x2)
743.35/262.75	   U102(x0, mark(x1), x2)
743.35/262.75	   U102(x0, x1, mark(x2))
743.35/262.75	   U102(active(x0), x1, x2)
743.35/262.75	   U102(x0, active(x1), x2)
743.35/262.75	   U102(x0, x1, active(x2))
743.35/262.75	   isNatKind(mark(x0))
743.35/262.75	   isNatKind(active(x0))
743.35/262.75	   U103(mark(x0), x1, x2)
743.35/262.75	   U103(x0, mark(x1), x2)
743.35/262.75	   U103(x0, x1, mark(x2))
743.35/262.75	   U103(active(x0), x1, x2)
743.35/262.75	   U103(x0, active(x1), x2)
743.35/262.75	   U103(x0, x1, active(x2))
743.35/262.75	   isNat(mark(x0))
743.35/262.75	   isNat(active(x0))
743.35/262.75	   U104(mark(x0), x1, x2)
743.35/262.75	   U104(x0, mark(x1), x2)
743.35/262.75	   U104(x0, x1, mark(x2))
743.35/262.75	   U104(active(x0), x1, x2)
743.35/262.75	   U104(x0, active(x1), x2)
743.35/262.75	   U104(x0, x1, active(x2))
743.35/262.75	   plus(mark(x0), x1)
743.35/262.75	   plus(x0, mark(x1))
743.35/262.75	   plus(active(x0), x1)
743.35/262.75	   plus(x0, active(x1))
743.35/262.75	   x(mark(x0), x1)
743.35/262.75	   x(x0, mark(x1))
743.35/262.75	   x(active(x0), x1)
743.35/262.75	   x(x0, active(x1))
743.35/262.75	   U11(mark(x0), x1, x2)
743.35/262.75	   U11(x0, mark(x1), x2)
743.35/262.75	   U11(x0, x1, mark(x2))
743.35/262.75	   U11(active(x0), x1, x2)
743.35/262.75	   U11(x0, active(x1), x2)
743.35/262.75	   U11(x0, x1, active(x2))
743.35/262.75	   U12(mark(x0), x1, x2)
743.35/262.75	   U12(x0, mark(x1), x2)
743.35/262.75	   U12(x0, x1, mark(x2))
743.35/262.75	   U12(active(x0), x1, x2)
743.35/262.75	   U12(x0, active(x1), x2)
743.35/262.75	   U12(x0, x1, active(x2))
743.35/262.75	   U13(mark(x0), x1, x2)
743.35/262.75	   U13(x0, mark(x1), x2)
743.35/262.75	   U13(x0, x1, mark(x2))
743.35/262.75	   U13(active(x0), x1, x2)
743.35/262.75	   U13(x0, active(x1), x2)
743.35/262.75	   U13(x0, x1, active(x2))
743.35/262.75	   U14(mark(x0), x1, x2)
743.35/262.75	   U14(x0, mark(x1), x2)
743.35/262.75	   U14(x0, x1, mark(x2))
743.35/262.75	   U14(active(x0), x1, x2)
743.35/262.75	   U14(x0, active(x1), x2)
743.35/262.75	   U14(x0, x1, active(x2))
743.35/262.75	   U15(mark(x0), x1)
743.35/262.75	   U15(x0, mark(x1))
743.35/262.75	   U15(active(x0), x1)
743.35/262.75	   U15(x0, active(x1))
743.35/262.75	   U16(mark(x0))
743.35/262.75	   U16(active(x0))
743.35/262.75	   U21(mark(x0), x1)
743.35/262.75	   U21(x0, mark(x1))
743.35/262.75	   U21(active(x0), x1)
743.35/262.75	   U21(x0, active(x1))
743.35/262.75	   U22(mark(x0), x1)
743.35/262.75	   U22(x0, mark(x1))
743.35/262.75	   U22(active(x0), x1)
743.35/262.75	   U22(x0, active(x1))
743.35/262.75	   U23(mark(x0))
743.35/262.75	   U23(active(x0))
743.35/262.75	   U31(mark(x0), x1, x2)
743.35/262.75	   U31(x0, mark(x1), x2)
743.35/262.75	   U31(x0, x1, mark(x2))
743.35/262.75	   U31(active(x0), x1, x2)
743.35/262.75	   U31(x0, active(x1), x2)
743.35/262.75	   U31(x0, x1, active(x2))
743.35/262.75	   U32(mark(x0), x1, x2)
743.35/262.75	   U32(x0, mark(x1), x2)
743.35/262.75	   U32(x0, x1, mark(x2))
743.35/262.75	   U32(active(x0), x1, x2)
743.35/262.75	   U32(x0, active(x1), x2)
743.35/262.75	   U32(x0, x1, active(x2))
743.35/262.75	   U33(mark(x0), x1, x2)
743.35/262.75	   U33(x0, mark(x1), x2)
743.35/262.75	   U33(x0, x1, mark(x2))
743.35/262.75	   U33(active(x0), x1, x2)
743.35/262.75	   U33(x0, active(x1), x2)
743.35/262.75	   U33(x0, x1, active(x2))
743.35/262.75	   U34(mark(x0), x1, x2)
743.35/262.75	   U34(x0, mark(x1), x2)
743.35/262.75	   U34(x0, x1, mark(x2))
743.35/262.75	   U34(active(x0), x1, x2)
743.35/262.75	   U34(x0, active(x1), x2)
743.35/262.75	   U34(x0, x1, active(x2))
743.35/262.75	   U35(mark(x0), x1)
743.35/262.75	   U35(x0, mark(x1))
743.35/262.75	   U35(active(x0), x1)
743.35/262.75	   U35(x0, active(x1))
743.35/262.75	   U36(mark(x0))
743.35/262.75	   U36(active(x0))
743.35/262.75	   U41(mark(x0), x1)
743.35/262.75	   U41(x0, mark(x1))
743.35/262.75	   U41(active(x0), x1)
743.35/262.75	   U41(x0, active(x1))
743.35/262.75	   U42(mark(x0))
743.35/262.75	   U42(active(x0))
743.35/262.75	   U51(mark(x0))
743.35/262.75	   U51(active(x0))
743.35/262.75	   U61(mark(x0), x1)
743.35/262.75	   U61(x0, mark(x1))
743.35/262.75	   U61(active(x0), x1)
743.35/262.75	   U61(x0, active(x1))
743.35/262.75	   U62(mark(x0))
743.35/262.75	   U62(active(x0))
743.35/262.75	   U71(mark(x0), x1)
743.35/262.75	   U71(x0, mark(x1))
743.35/262.75	   U71(active(x0), x1)
743.35/262.75	   U71(x0, active(x1))
743.35/262.75	   U72(mark(x0), x1)
743.35/262.75	   U72(x0, mark(x1))
743.35/262.75	   U72(active(x0), x1)
743.35/262.75	   U72(x0, active(x1))
743.35/262.75	   U81(mark(x0), x1, x2)
743.35/262.75	   U81(x0, mark(x1), x2)
743.35/262.75	   U81(x0, x1, mark(x2))
743.35/262.75	   U81(active(x0), x1, x2)
743.35/262.75	   U81(x0, active(x1), x2)
743.35/262.75	   U81(x0, x1, active(x2))
743.35/262.75	   U82(mark(x0), x1, x2)
743.35/262.75	   U82(x0, mark(x1), x2)
743.35/262.75	   U82(x0, x1, mark(x2))
743.35/262.75	   U82(active(x0), x1, x2)
743.35/262.75	   U82(x0, active(x1), x2)
743.35/262.75	   U82(x0, x1, active(x2))
743.35/262.75	   U83(mark(x0), x1, x2)
743.35/262.75	   U83(x0, mark(x1), x2)
743.35/262.75	   U83(x0, x1, mark(x2))
743.35/262.75	   U83(active(x0), x1, x2)
743.35/262.75	   U83(x0, active(x1), x2)
743.35/262.75	   U83(x0, x1, active(x2))
743.35/262.75	   U84(mark(x0), x1, x2)
743.35/262.75	   U84(x0, mark(x1), x2)
743.35/262.75	   U84(x0, x1, mark(x2))
743.35/262.75	   U84(active(x0), x1, x2)
743.35/262.75	   U84(x0, active(x1), x2)
743.35/262.75	   U84(x0, x1, active(x2))
743.35/262.75	   s(mark(x0))
743.35/262.75	   s(active(x0))
743.35/262.75	   U91(mark(x0), x1)
743.35/262.76	   U91(x0, mark(x1))
743.35/262.76	   U91(active(x0), x1)
743.35/262.76	   U91(x0, active(x1))
743.35/262.76	   U92(mark(x0))
743.35/262.76	   U92(active(x0))
743.35/262.76	
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(16)
743.35/262.76	Obligation:
743.35/262.76	Q DP problem:
743.35/262.76	The TRS P consists of the following rules:
743.35/262.76	
743.35/262.76	   U91^1(X1, mark(X2)) -> U91^1(X1, X2)
743.35/262.76	   U91^1(mark(X1), X2) -> U91^1(X1, X2)
743.35/262.76	   U91^1(active(X1), X2) -> U91^1(X1, X2)
743.35/262.76	   U91^1(X1, active(X2)) -> U91^1(X1, X2)
743.35/262.76	
743.35/262.76	R is empty.
743.35/262.76	The set Q consists of the following terms:
743.35/262.76	
743.35/262.76	   active(U101(tt, x0, x1))
743.35/262.76	   active(U102(tt, x0, x1))
743.35/262.76	   active(U103(tt, x0, x1))
743.35/262.76	   active(U104(tt, x0, x1))
743.35/262.76	   active(U11(tt, x0, x1))
743.35/262.76	   active(U12(tt, x0, x1))
743.35/262.76	   active(U13(tt, x0, x1))
743.35/262.76	   active(U14(tt, x0, x1))
743.35/262.76	   active(U15(tt, x0))
743.35/262.76	   active(U16(tt))
743.35/262.76	   active(U21(tt, x0))
743.35/262.76	   active(U22(tt, x0))
743.35/262.76	   active(U23(tt))
743.35/262.76	   active(U31(tt, x0, x1))
743.35/262.76	   active(U32(tt, x0, x1))
743.35/262.76	   active(U33(tt, x0, x1))
743.35/262.76	   active(U34(tt, x0, x1))
743.35/262.76	   active(U35(tt, x0))
743.35/262.76	   active(U36(tt))
743.35/262.76	   active(U41(tt, x0))
743.35/262.76	   active(U42(tt))
743.35/262.76	   active(U51(tt))
743.35/262.76	   active(U61(tt, x0))
743.35/262.76	   active(U62(tt))
743.35/262.76	   active(U71(tt, x0))
743.35/262.76	   active(U72(tt, x0))
743.35/262.76	   active(U81(tt, x0, x1))
743.35/262.76	   active(U82(tt, x0, x1))
743.35/262.76	   active(U83(tt, x0, x1))
743.35/262.76	   active(U84(tt, x0, x1))
743.35/262.76	   active(U91(tt, x0))
743.35/262.76	   active(U92(tt))
743.35/262.76	   active(isNat(0))
743.35/262.76	   active(isNat(plus(x0, x1)))
743.35/262.76	   active(isNat(s(x0)))
743.35/262.76	   active(isNat(x(x0, x1)))
743.35/262.76	   active(isNatKind(0))
743.35/262.76	   active(isNatKind(plus(x0, x1)))
743.35/262.76	   active(isNatKind(s(x0)))
743.35/262.76	   active(isNatKind(x(x0, x1)))
743.35/262.76	   active(plus(x0, 0))
743.35/262.76	   active(plus(x0, s(x1)))
743.35/262.76	   active(x(x0, 0))
743.35/262.76	   active(x(x0, s(x1)))
743.35/262.76	   mark(U101(x0, x1, x2))
743.35/262.76	   mark(tt)
743.35/262.76	   mark(U102(x0, x1, x2))
743.35/262.76	   mark(isNatKind(x0))
743.35/262.76	   mark(U103(x0, x1, x2))
743.35/262.76	   mark(isNat(x0))
743.35/262.76	   mark(U104(x0, x1, x2))
743.35/262.76	   mark(plus(x0, x1))
743.35/262.76	   mark(x(x0, x1))
743.35/262.76	   mark(U11(x0, x1, x2))
743.35/262.76	   mark(U12(x0, x1, x2))
743.35/262.76	   mark(U13(x0, x1, x2))
743.35/262.76	   mark(U14(x0, x1, x2))
743.35/262.76	   mark(U15(x0, x1))
743.35/262.76	   mark(U16(x0))
743.35/262.76	   mark(U21(x0, x1))
743.35/262.76	   mark(U22(x0, x1))
743.35/262.76	   mark(U23(x0))
743.35/262.76	   mark(U31(x0, x1, x2))
743.35/262.76	   mark(U32(x0, x1, x2))
743.35/262.76	   mark(U33(x0, x1, x2))
743.35/262.76	   mark(U34(x0, x1, x2))
743.35/262.76	   mark(U35(x0, x1))
743.35/262.76	   mark(U36(x0))
743.35/262.76	   mark(U41(x0, x1))
743.35/262.76	   mark(U42(x0))
743.35/262.76	   mark(U51(x0))
743.35/262.76	   mark(U61(x0, x1))
743.35/262.76	   mark(U62(x0))
743.35/262.76	   mark(U71(x0, x1))
743.35/262.76	   mark(U72(x0, x1))
743.35/262.76	   mark(U81(x0, x1, x2))
743.35/262.76	   mark(U82(x0, x1, x2))
743.35/262.76	   mark(U83(x0, x1, x2))
743.35/262.76	   mark(U84(x0, x1, x2))
743.35/262.76	   mark(s(x0))
743.35/262.76	   mark(U91(x0, x1))
743.35/262.76	   mark(U92(x0))
743.35/262.76	   mark(0)
743.35/262.76	
743.35/262.76	We have to consider all minimal (P,Q,R)-chains.
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(17) QDPSizeChangeProof (EQUIVALENT)
743.35/262.76	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. 
743.35/262.76	
743.35/262.76	From the DPs we obtained the following set of size-change graphs:
743.35/262.76	*U91^1(X1, mark(X2)) -> U91^1(X1, X2)
743.35/262.76	The graph contains the following edges 1 >= 1, 2 > 2
743.35/262.76	
743.35/262.76	
743.35/262.76	*U91^1(mark(X1), X2) -> U91^1(X1, X2)
743.35/262.76	The graph contains the following edges 1 > 1, 2 >= 2
743.35/262.76	
743.35/262.76	
743.35/262.76	*U91^1(active(X1), X2) -> U91^1(X1, X2)
743.35/262.76	The graph contains the following edges 1 > 1, 2 >= 2
743.35/262.76	
743.35/262.76	
743.35/262.76	*U91^1(X1, active(X2)) -> U91^1(X1, X2)
743.35/262.76	The graph contains the following edges 1 >= 1, 2 > 2
743.35/262.76	
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(18)
743.35/262.76	YES
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(19)
743.35/262.76	Obligation:
743.35/262.76	Q DP problem:
743.35/262.76	The TRS P consists of the following rules:
743.35/262.76	
743.35/262.76	   S(active(X)) -> S(X)
743.35/262.76	   S(mark(X)) -> S(X)
743.35/262.76	
743.35/262.76	The TRS R consists of the following rules:
743.35/262.76	
743.35/262.76	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.76	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.76	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.76	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.76	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.76	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.76	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.76	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.76	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.76	   active(U16(tt)) -> mark(tt)
743.35/262.76	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.76	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.76	   active(U23(tt)) -> mark(tt)
743.35/262.76	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.76	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.76	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.76	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.76	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.76	   active(U36(tt)) -> mark(tt)
743.35/262.76	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.76	   active(U42(tt)) -> mark(tt)
743.35/262.76	   active(U51(tt)) -> mark(tt)
743.35/262.76	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.76	   active(U62(tt)) -> mark(tt)
743.35/262.76	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.76	   active(U72(tt, N)) -> mark(N)
743.35/262.76	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.76	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.76	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.76	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.76	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.76	   active(U92(tt)) -> mark(0)
743.35/262.76	   active(isNat(0)) -> mark(tt)
743.35/262.76	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.76	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.76	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.76	   active(isNatKind(0)) -> mark(tt)
743.35/262.76	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.76	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.76	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.76	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.76	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.76	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.76	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.76	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.76	   mark(tt) -> active(tt)
743.35/262.76	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.76	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.76	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.76	   mark(isNat(X)) -> active(isNat(X))
743.35/262.76	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.76	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.76	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.76	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.76	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.76	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.76	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.76	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.76	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.76	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.76	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.76	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.76	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.76	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.76	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.76	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.76	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.76	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.76	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.76	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.76	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.76	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.76	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.76	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.76	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.76	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.76	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.76	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.76	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.76	   mark(s(X)) -> active(s(mark(X)))
743.35/262.76	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.76	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.76	   mark(0) -> active(0)
743.35/262.76	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.76	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.76	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.76	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.76	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.76	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.76	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.76	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.76	   isNat(mark(X)) -> isNat(X)
743.35/262.76	   isNat(active(X)) -> isNat(X)
743.35/262.76	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.76	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.76	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.76	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.76	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.76	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.76	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.76	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.76	   x(active(X1), X2) -> x(X1, X2)
743.35/262.76	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.76	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.76	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.76	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.76	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.76	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.76	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.76	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.76	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.76	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.76	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.76	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.76	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.76	   U16(mark(X)) -> U16(X)
743.35/262.76	   U16(active(X)) -> U16(X)
743.35/262.76	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.76	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.76	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.76	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.76	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.76	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.76	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.76	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.76	   U23(mark(X)) -> U23(X)
743.35/262.76	   U23(active(X)) -> U23(X)
743.35/262.76	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.76	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.76	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.76	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.76	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.76	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.76	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.76	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.76	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.76	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.76	   U35(active(X1), X2) -> U35(X1, X2)
743.35/262.76	   U35(X1, active(X2)) -> U35(X1, X2)
743.35/262.76	   U36(mark(X)) -> U36(X)
743.35/262.76	   U36(active(X)) -> U36(X)
743.35/262.76	   U41(mark(X1), X2) -> U41(X1, X2)
743.35/262.76	   U41(X1, mark(X2)) -> U41(X1, X2)
743.35/262.76	   U41(active(X1), X2) -> U41(X1, X2)
743.35/262.76	   U41(X1, active(X2)) -> U41(X1, X2)
743.35/262.76	   U42(mark(X)) -> U42(X)
743.35/262.76	   U42(active(X)) -> U42(X)
743.35/262.76	   U51(mark(X)) -> U51(X)
743.35/262.76	   U51(active(X)) -> U51(X)
743.35/262.76	   U61(mark(X1), X2) -> U61(X1, X2)
743.35/262.76	   U61(X1, mark(X2)) -> U61(X1, X2)
743.35/262.76	   U61(active(X1), X2) -> U61(X1, X2)
743.35/262.76	   U61(X1, active(X2)) -> U61(X1, X2)
743.35/262.76	   U62(mark(X)) -> U62(X)
743.35/262.76	   U62(active(X)) -> U62(X)
743.35/262.76	   U71(mark(X1), X2) -> U71(X1, X2)
743.35/262.76	   U71(X1, mark(X2)) -> U71(X1, X2)
743.35/262.76	   U71(active(X1), X2) -> U71(X1, X2)
743.35/262.76	   U71(X1, active(X2)) -> U71(X1, X2)
743.35/262.76	   U72(mark(X1), X2) -> U72(X1, X2)
743.35/262.76	   U72(X1, mark(X2)) -> U72(X1, X2)
743.35/262.76	   U72(active(X1), X2) -> U72(X1, X2)
743.35/262.76	   U72(X1, active(X2)) -> U72(X1, X2)
743.35/262.76	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.76	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.35/262.76	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.35/262.76	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.35/262.76	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.35/262.76	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.35/262.76	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.76	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.35/262.76	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.35/262.76	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.35/262.76	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.35/262.76	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.35/262.76	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.76	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.35/262.76	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.35/262.76	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.35/262.76	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.35/262.76	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.35/262.76	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.76	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.35/262.76	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.35/262.76	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.35/262.76	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.35/262.76	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.35/262.76	   s(mark(X)) -> s(X)
743.35/262.76	   s(active(X)) -> s(X)
743.35/262.76	   U91(mark(X1), X2) -> U91(X1, X2)
743.35/262.76	   U91(X1, mark(X2)) -> U91(X1, X2)
743.35/262.76	   U91(active(X1), X2) -> U91(X1, X2)
743.35/262.76	   U91(X1, active(X2)) -> U91(X1, X2)
743.35/262.76	   U92(mark(X)) -> U92(X)
743.35/262.76	   U92(active(X)) -> U92(X)
743.35/262.76	
743.35/262.76	The set Q consists of the following terms:
743.35/262.76	
743.35/262.76	   active(U101(tt, x0, x1))
743.35/262.76	   active(U102(tt, x0, x1))
743.35/262.76	   active(U103(tt, x0, x1))
743.35/262.76	   active(U104(tt, x0, x1))
743.35/262.76	   active(U11(tt, x0, x1))
743.35/262.76	   active(U12(tt, x0, x1))
743.35/262.76	   active(U13(tt, x0, x1))
743.35/262.76	   active(U14(tt, x0, x1))
743.35/262.76	   active(U15(tt, x0))
743.35/262.76	   active(U16(tt))
743.35/262.76	   active(U21(tt, x0))
743.35/262.76	   active(U22(tt, x0))
743.35/262.76	   active(U23(tt))
743.35/262.76	   active(U31(tt, x0, x1))
743.35/262.76	   active(U32(tt, x0, x1))
743.35/262.76	   active(U33(tt, x0, x1))
743.35/262.76	   active(U34(tt, x0, x1))
743.35/262.76	   active(U35(tt, x0))
743.35/262.76	   active(U36(tt))
743.35/262.76	   active(U41(tt, x0))
743.35/262.76	   active(U42(tt))
743.35/262.76	   active(U51(tt))
743.35/262.76	   active(U61(tt, x0))
743.35/262.76	   active(U62(tt))
743.35/262.76	   active(U71(tt, x0))
743.35/262.76	   active(U72(tt, x0))
743.35/262.76	   active(U81(tt, x0, x1))
743.35/262.76	   active(U82(tt, x0, x1))
743.35/262.76	   active(U83(tt, x0, x1))
743.35/262.76	   active(U84(tt, x0, x1))
743.35/262.76	   active(U91(tt, x0))
743.35/262.76	   active(U92(tt))
743.35/262.76	   active(isNat(0))
743.35/262.76	   active(isNat(plus(x0, x1)))
743.35/262.76	   active(isNat(s(x0)))
743.35/262.76	   active(isNat(x(x0, x1)))
743.35/262.76	   active(isNatKind(0))
743.35/262.76	   active(isNatKind(plus(x0, x1)))
743.35/262.76	   active(isNatKind(s(x0)))
743.35/262.76	   active(isNatKind(x(x0, x1)))
743.35/262.76	   active(plus(x0, 0))
743.35/262.76	   active(plus(x0, s(x1)))
743.35/262.76	   active(x(x0, 0))
743.35/262.76	   active(x(x0, s(x1)))
743.35/262.76	   mark(U101(x0, x1, x2))
743.35/262.76	   mark(tt)
743.35/262.76	   mark(U102(x0, x1, x2))
743.35/262.76	   mark(isNatKind(x0))
743.35/262.76	   mark(U103(x0, x1, x2))
743.35/262.76	   mark(isNat(x0))
743.35/262.76	   mark(U104(x0, x1, x2))
743.35/262.76	   mark(plus(x0, x1))
743.35/262.76	   mark(x(x0, x1))
743.35/262.76	   mark(U11(x0, x1, x2))
743.35/262.76	   mark(U12(x0, x1, x2))
743.35/262.76	   mark(U13(x0, x1, x2))
743.35/262.76	   mark(U14(x0, x1, x2))
743.35/262.76	   mark(U15(x0, x1))
743.35/262.76	   mark(U16(x0))
743.35/262.76	   mark(U21(x0, x1))
743.35/262.76	   mark(U22(x0, x1))
743.35/262.76	   mark(U23(x0))
743.35/262.76	   mark(U31(x0, x1, x2))
743.35/262.76	   mark(U32(x0, x1, x2))
743.35/262.76	   mark(U33(x0, x1, x2))
743.35/262.76	   mark(U34(x0, x1, x2))
743.35/262.76	   mark(U35(x0, x1))
743.35/262.76	   mark(U36(x0))
743.35/262.76	   mark(U41(x0, x1))
743.35/262.76	   mark(U42(x0))
743.35/262.76	   mark(U51(x0))
743.35/262.76	   mark(U61(x0, x1))
743.35/262.76	   mark(U62(x0))
743.35/262.76	   mark(U71(x0, x1))
743.35/262.76	   mark(U72(x0, x1))
743.35/262.76	   mark(U81(x0, x1, x2))
743.35/262.76	   mark(U82(x0, x1, x2))
743.35/262.76	   mark(U83(x0, x1, x2))
743.35/262.76	   mark(U84(x0, x1, x2))
743.35/262.76	   mark(s(x0))
743.35/262.76	   mark(U91(x0, x1))
743.35/262.76	   mark(U92(x0))
743.35/262.76	   mark(0)
743.35/262.76	   U101(mark(x0), x1, x2)
743.35/262.76	   U101(x0, mark(x1), x2)
743.35/262.76	   U101(x0, x1, mark(x2))
743.35/262.76	   U101(active(x0), x1, x2)
743.35/262.76	   U101(x0, active(x1), x2)
743.35/262.76	   U101(x0, x1, active(x2))
743.35/262.76	   U102(mark(x0), x1, x2)
743.35/262.76	   U102(x0, mark(x1), x2)
743.35/262.76	   U102(x0, x1, mark(x2))
743.35/262.76	   U102(active(x0), x1, x2)
743.35/262.76	   U102(x0, active(x1), x2)
743.35/262.76	   U102(x0, x1, active(x2))
743.35/262.76	   isNatKind(mark(x0))
743.35/262.76	   isNatKind(active(x0))
743.35/262.76	   U103(mark(x0), x1, x2)
743.35/262.76	   U103(x0, mark(x1), x2)
743.35/262.76	   U103(x0, x1, mark(x2))
743.35/262.76	   U103(active(x0), x1, x2)
743.35/262.76	   U103(x0, active(x1), x2)
743.35/262.76	   U103(x0, x1, active(x2))
743.35/262.76	   isNat(mark(x0))
743.35/262.76	   isNat(active(x0))
743.35/262.76	   U104(mark(x0), x1, x2)
743.35/262.76	   U104(x0, mark(x1), x2)
743.35/262.76	   U104(x0, x1, mark(x2))
743.35/262.76	   U104(active(x0), x1, x2)
743.35/262.76	   U104(x0, active(x1), x2)
743.35/262.76	   U104(x0, x1, active(x2))
743.35/262.76	   plus(mark(x0), x1)
743.35/262.76	   plus(x0, mark(x1))
743.35/262.76	   plus(active(x0), x1)
743.35/262.76	   plus(x0, active(x1))
743.35/262.76	   x(mark(x0), x1)
743.35/262.76	   x(x0, mark(x1))
743.35/262.76	   x(active(x0), x1)
743.35/262.76	   x(x0, active(x1))
743.35/262.76	   U11(mark(x0), x1, x2)
743.35/262.76	   U11(x0, mark(x1), x2)
743.35/262.76	   U11(x0, x1, mark(x2))
743.35/262.76	   U11(active(x0), x1, x2)
743.35/262.76	   U11(x0, active(x1), x2)
743.35/262.76	   U11(x0, x1, active(x2))
743.35/262.76	   U12(mark(x0), x1, x2)
743.35/262.76	   U12(x0, mark(x1), x2)
743.35/262.76	   U12(x0, x1, mark(x2))
743.35/262.76	   U12(active(x0), x1, x2)
743.35/262.76	   U12(x0, active(x1), x2)
743.35/262.76	   U12(x0, x1, active(x2))
743.35/262.76	   U13(mark(x0), x1, x2)
743.35/262.76	   U13(x0, mark(x1), x2)
743.35/262.76	   U13(x0, x1, mark(x2))
743.35/262.76	   U13(active(x0), x1, x2)
743.35/262.76	   U13(x0, active(x1), x2)
743.35/262.76	   U13(x0, x1, active(x2))
743.35/262.76	   U14(mark(x0), x1, x2)
743.35/262.76	   U14(x0, mark(x1), x2)
743.35/262.76	   U14(x0, x1, mark(x2))
743.35/262.76	   U14(active(x0), x1, x2)
743.35/262.76	   U14(x0, active(x1), x2)
743.35/262.76	   U14(x0, x1, active(x2))
743.35/262.76	   U15(mark(x0), x1)
743.35/262.76	   U15(x0, mark(x1))
743.35/262.76	   U15(active(x0), x1)
743.35/262.76	   U15(x0, active(x1))
743.35/262.76	   U16(mark(x0))
743.35/262.76	   U16(active(x0))
743.35/262.76	   U21(mark(x0), x1)
743.35/262.76	   U21(x0, mark(x1))
743.35/262.76	   U21(active(x0), x1)
743.35/262.76	   U21(x0, active(x1))
743.35/262.76	   U22(mark(x0), x1)
743.35/262.76	   U22(x0, mark(x1))
743.35/262.76	   U22(active(x0), x1)
743.35/262.76	   U22(x0, active(x1))
743.35/262.76	   U23(mark(x0))
743.35/262.76	   U23(active(x0))
743.35/262.76	   U31(mark(x0), x1, x2)
743.35/262.76	   U31(x0, mark(x1), x2)
743.35/262.76	   U31(x0, x1, mark(x2))
743.35/262.76	   U31(active(x0), x1, x2)
743.35/262.76	   U31(x0, active(x1), x2)
743.35/262.76	   U31(x0, x1, active(x2))
743.35/262.76	   U32(mark(x0), x1, x2)
743.35/262.76	   U32(x0, mark(x1), x2)
743.35/262.76	   U32(x0, x1, mark(x2))
743.35/262.76	   U32(active(x0), x1, x2)
743.35/262.76	   U32(x0, active(x1), x2)
743.35/262.76	   U32(x0, x1, active(x2))
743.35/262.76	   U33(mark(x0), x1, x2)
743.35/262.76	   U33(x0, mark(x1), x2)
743.35/262.76	   U33(x0, x1, mark(x2))
743.35/262.76	   U33(active(x0), x1, x2)
743.35/262.76	   U33(x0, active(x1), x2)
743.35/262.76	   U33(x0, x1, active(x2))
743.35/262.76	   U34(mark(x0), x1, x2)
743.35/262.76	   U34(x0, mark(x1), x2)
743.35/262.76	   U34(x0, x1, mark(x2))
743.35/262.76	   U34(active(x0), x1, x2)
743.35/262.76	   U34(x0, active(x1), x2)
743.35/262.76	   U34(x0, x1, active(x2))
743.35/262.76	   U35(mark(x0), x1)
743.35/262.76	   U35(x0, mark(x1))
743.35/262.76	   U35(active(x0), x1)
743.35/262.76	   U35(x0, active(x1))
743.35/262.76	   U36(mark(x0))
743.35/262.76	   U36(active(x0))
743.35/262.76	   U41(mark(x0), x1)
743.35/262.76	   U41(x0, mark(x1))
743.35/262.76	   U41(active(x0), x1)
743.35/262.76	   U41(x0, active(x1))
743.35/262.76	   U42(mark(x0))
743.35/262.76	   U42(active(x0))
743.35/262.76	   U51(mark(x0))
743.35/262.76	   U51(active(x0))
743.35/262.76	   U61(mark(x0), x1)
743.35/262.76	   U61(x0, mark(x1))
743.35/262.76	   U61(active(x0), x1)
743.35/262.76	   U61(x0, active(x1))
743.35/262.76	   U62(mark(x0))
743.35/262.76	   U62(active(x0))
743.35/262.76	   U71(mark(x0), x1)
743.35/262.76	   U71(x0, mark(x1))
743.35/262.76	   U71(active(x0), x1)
743.35/262.76	   U71(x0, active(x1))
743.35/262.76	   U72(mark(x0), x1)
743.35/262.76	   U72(x0, mark(x1))
743.35/262.76	   U72(active(x0), x1)
743.35/262.76	   U72(x0, active(x1))
743.35/262.76	   U81(mark(x0), x1, x2)
743.35/262.76	   U81(x0, mark(x1), x2)
743.35/262.76	   U81(x0, x1, mark(x2))
743.35/262.76	   U81(active(x0), x1, x2)
743.35/262.76	   U81(x0, active(x1), x2)
743.35/262.76	   U81(x0, x1, active(x2))
743.35/262.76	   U82(mark(x0), x1, x2)
743.35/262.76	   U82(x0, mark(x1), x2)
743.35/262.76	   U82(x0, x1, mark(x2))
743.35/262.76	   U82(active(x0), x1, x2)
743.35/262.76	   U82(x0, active(x1), x2)
743.35/262.76	   U82(x0, x1, active(x2))
743.35/262.76	   U83(mark(x0), x1, x2)
743.35/262.76	   U83(x0, mark(x1), x2)
743.35/262.76	   U83(x0, x1, mark(x2))
743.35/262.76	   U83(active(x0), x1, x2)
743.35/262.76	   U83(x0, active(x1), x2)
743.35/262.76	   U83(x0, x1, active(x2))
743.35/262.76	   U84(mark(x0), x1, x2)
743.35/262.76	   U84(x0, mark(x1), x2)
743.35/262.76	   U84(x0, x1, mark(x2))
743.35/262.76	   U84(active(x0), x1, x2)
743.35/262.76	   U84(x0, active(x1), x2)
743.35/262.76	   U84(x0, x1, active(x2))
743.35/262.76	   s(mark(x0))
743.35/262.76	   s(active(x0))
743.35/262.76	   U91(mark(x0), x1)
743.35/262.76	   U91(x0, mark(x1))
743.35/262.76	   U91(active(x0), x1)
743.35/262.76	   U91(x0, active(x1))
743.35/262.76	   U92(mark(x0))
743.35/262.76	   U92(active(x0))
743.35/262.76	
743.35/262.76	We have to consider all minimal (P,Q,R)-chains.
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(20) UsableRulesProof (EQUIVALENT)
743.35/262.76	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.
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(21)
743.35/262.76	Obligation:
743.35/262.76	Q DP problem:
743.35/262.76	The TRS P consists of the following rules:
743.35/262.76	
743.35/262.76	   S(active(X)) -> S(X)
743.35/262.76	   S(mark(X)) -> S(X)
743.35/262.76	
743.35/262.76	R is empty.
743.35/262.76	The set Q consists of the following terms:
743.35/262.76	
743.35/262.76	   active(U101(tt, x0, x1))
743.35/262.76	   active(U102(tt, x0, x1))
743.35/262.76	   active(U103(tt, x0, x1))
743.35/262.76	   active(U104(tt, x0, x1))
743.35/262.76	   active(U11(tt, x0, x1))
743.35/262.76	   active(U12(tt, x0, x1))
743.35/262.76	   active(U13(tt, x0, x1))
743.35/262.76	   active(U14(tt, x0, x1))
743.35/262.76	   active(U15(tt, x0))
743.35/262.76	   active(U16(tt))
743.35/262.76	   active(U21(tt, x0))
743.35/262.76	   active(U22(tt, x0))
743.35/262.76	   active(U23(tt))
743.35/262.76	   active(U31(tt, x0, x1))
743.35/262.76	   active(U32(tt, x0, x1))
743.35/262.76	   active(U33(tt, x0, x1))
743.35/262.76	   active(U34(tt, x0, x1))
743.35/262.76	   active(U35(tt, x0))
743.35/262.76	   active(U36(tt))
743.35/262.76	   active(U41(tt, x0))
743.35/262.76	   active(U42(tt))
743.35/262.76	   active(U51(tt))
743.35/262.76	   active(U61(tt, x0))
743.35/262.76	   active(U62(tt))
743.35/262.76	   active(U71(tt, x0))
743.35/262.76	   active(U72(tt, x0))
743.35/262.76	   active(U81(tt, x0, x1))
743.35/262.76	   active(U82(tt, x0, x1))
743.35/262.76	   active(U83(tt, x0, x1))
743.35/262.76	   active(U84(tt, x0, x1))
743.35/262.76	   active(U91(tt, x0))
743.35/262.76	   active(U92(tt))
743.35/262.76	   active(isNat(0))
743.35/262.76	   active(isNat(plus(x0, x1)))
743.35/262.76	   active(isNat(s(x0)))
743.35/262.76	   active(isNat(x(x0, x1)))
743.35/262.76	   active(isNatKind(0))
743.35/262.76	   active(isNatKind(plus(x0, x1)))
743.35/262.76	   active(isNatKind(s(x0)))
743.35/262.76	   active(isNatKind(x(x0, x1)))
743.35/262.76	   active(plus(x0, 0))
743.35/262.76	   active(plus(x0, s(x1)))
743.35/262.76	   active(x(x0, 0))
743.35/262.76	   active(x(x0, s(x1)))
743.35/262.76	   mark(U101(x0, x1, x2))
743.35/262.76	   mark(tt)
743.35/262.76	   mark(U102(x0, x1, x2))
743.35/262.76	   mark(isNatKind(x0))
743.35/262.76	   mark(U103(x0, x1, x2))
743.35/262.76	   mark(isNat(x0))
743.35/262.76	   mark(U104(x0, x1, x2))
743.35/262.76	   mark(plus(x0, x1))
743.35/262.76	   mark(x(x0, x1))
743.35/262.76	   mark(U11(x0, x1, x2))
743.35/262.76	   mark(U12(x0, x1, x2))
743.35/262.76	   mark(U13(x0, x1, x2))
743.35/262.76	   mark(U14(x0, x1, x2))
743.35/262.76	   mark(U15(x0, x1))
743.35/262.76	   mark(U16(x0))
743.35/262.76	   mark(U21(x0, x1))
743.35/262.76	   mark(U22(x0, x1))
743.35/262.76	   mark(U23(x0))
743.35/262.76	   mark(U31(x0, x1, x2))
743.35/262.76	   mark(U32(x0, x1, x2))
743.35/262.76	   mark(U33(x0, x1, x2))
743.35/262.76	   mark(U34(x0, x1, x2))
743.35/262.76	   mark(U35(x0, x1))
743.35/262.76	   mark(U36(x0))
743.35/262.76	   mark(U41(x0, x1))
743.35/262.76	   mark(U42(x0))
743.35/262.76	   mark(U51(x0))
743.35/262.76	   mark(U61(x0, x1))
743.35/262.76	   mark(U62(x0))
743.35/262.76	   mark(U71(x0, x1))
743.35/262.76	   mark(U72(x0, x1))
743.35/262.76	   mark(U81(x0, x1, x2))
743.35/262.76	   mark(U82(x0, x1, x2))
743.35/262.76	   mark(U83(x0, x1, x2))
743.35/262.76	   mark(U84(x0, x1, x2))
743.35/262.76	   mark(s(x0))
743.35/262.76	   mark(U91(x0, x1))
743.35/262.76	   mark(U92(x0))
743.35/262.76	   mark(0)
743.35/262.76	   U101(mark(x0), x1, x2)
743.35/262.76	   U101(x0, mark(x1), x2)
743.35/262.76	   U101(x0, x1, mark(x2))
743.35/262.76	   U101(active(x0), x1, x2)
743.35/262.76	   U101(x0, active(x1), x2)
743.35/262.76	   U101(x0, x1, active(x2))
743.35/262.76	   U102(mark(x0), x1, x2)
743.35/262.76	   U102(x0, mark(x1), x2)
743.35/262.76	   U102(x0, x1, mark(x2))
743.35/262.76	   U102(active(x0), x1, x2)
743.35/262.76	   U102(x0, active(x1), x2)
743.35/262.76	   U102(x0, x1, active(x2))
743.35/262.76	   isNatKind(mark(x0))
743.35/262.76	   isNatKind(active(x0))
743.35/262.76	   U103(mark(x0), x1, x2)
743.35/262.76	   U103(x0, mark(x1), x2)
743.35/262.76	   U103(x0, x1, mark(x2))
743.35/262.76	   U103(active(x0), x1, x2)
743.35/262.76	   U103(x0, active(x1), x2)
743.35/262.76	   U103(x0, x1, active(x2))
743.35/262.76	   isNat(mark(x0))
743.35/262.76	   isNat(active(x0))
743.35/262.76	   U104(mark(x0), x1, x2)
743.35/262.76	   U104(x0, mark(x1), x2)
743.35/262.76	   U104(x0, x1, mark(x2))
743.35/262.76	   U104(active(x0), x1, x2)
743.35/262.76	   U104(x0, active(x1), x2)
743.35/262.76	   U104(x0, x1, active(x2))
743.35/262.76	   plus(mark(x0), x1)
743.35/262.76	   plus(x0, mark(x1))
743.35/262.76	   plus(active(x0), x1)
743.35/262.76	   plus(x0, active(x1))
743.35/262.76	   x(mark(x0), x1)
743.35/262.76	   x(x0, mark(x1))
743.35/262.76	   x(active(x0), x1)
743.35/262.76	   x(x0, active(x1))
743.35/262.76	   U11(mark(x0), x1, x2)
743.35/262.76	   U11(x0, mark(x1), x2)
743.35/262.76	   U11(x0, x1, mark(x2))
743.35/262.76	   U11(active(x0), x1, x2)
743.35/262.76	   U11(x0, active(x1), x2)
743.35/262.76	   U11(x0, x1, active(x2))
743.35/262.76	   U12(mark(x0), x1, x2)
743.35/262.76	   U12(x0, mark(x1), x2)
743.35/262.76	   U12(x0, x1, mark(x2))
743.35/262.76	   U12(active(x0), x1, x2)
743.35/262.76	   U12(x0, active(x1), x2)
743.35/262.76	   U12(x0, x1, active(x2))
743.35/262.76	   U13(mark(x0), x1, x2)
743.35/262.76	   U13(x0, mark(x1), x2)
743.35/262.76	   U13(x0, x1, mark(x2))
743.35/262.76	   U13(active(x0), x1, x2)
743.35/262.76	   U13(x0, active(x1), x2)
743.35/262.76	   U13(x0, x1, active(x2))
743.35/262.76	   U14(mark(x0), x1, x2)
743.35/262.76	   U14(x0, mark(x1), x2)
743.35/262.76	   U14(x0, x1, mark(x2))
743.35/262.76	   U14(active(x0), x1, x2)
743.35/262.76	   U14(x0, active(x1), x2)
743.35/262.76	   U14(x0, x1, active(x2))
743.35/262.76	   U15(mark(x0), x1)
743.35/262.76	   U15(x0, mark(x1))
743.35/262.76	   U15(active(x0), x1)
743.35/262.76	   U15(x0, active(x1))
743.35/262.76	   U16(mark(x0))
743.35/262.76	   U16(active(x0))
743.35/262.76	   U21(mark(x0), x1)
743.35/262.76	   U21(x0, mark(x1))
743.35/262.76	   U21(active(x0), x1)
743.35/262.76	   U21(x0, active(x1))
743.35/262.76	   U22(mark(x0), x1)
743.35/262.76	   U22(x0, mark(x1))
743.35/262.76	   U22(active(x0), x1)
743.35/262.76	   U22(x0, active(x1))
743.35/262.76	   U23(mark(x0))
743.35/262.76	   U23(active(x0))
743.35/262.76	   U31(mark(x0), x1, x2)
743.35/262.76	   U31(x0, mark(x1), x2)
743.35/262.76	   U31(x0, x1, mark(x2))
743.35/262.76	   U31(active(x0), x1, x2)
743.35/262.76	   U31(x0, active(x1), x2)
743.35/262.76	   U31(x0, x1, active(x2))
743.35/262.76	   U32(mark(x0), x1, x2)
743.35/262.76	   U32(x0, mark(x1), x2)
743.35/262.76	   U32(x0, x1, mark(x2))
743.35/262.76	   U32(active(x0), x1, x2)
743.35/262.76	   U32(x0, active(x1), x2)
743.35/262.76	   U32(x0, x1, active(x2))
743.35/262.76	   U33(mark(x0), x1, x2)
743.35/262.76	   U33(x0, mark(x1), x2)
743.35/262.76	   U33(x0, x1, mark(x2))
743.35/262.76	   U33(active(x0), x1, x2)
743.35/262.76	   U33(x0, active(x1), x2)
743.35/262.76	   U33(x0, x1, active(x2))
743.35/262.76	   U34(mark(x0), x1, x2)
743.35/262.76	   U34(x0, mark(x1), x2)
743.35/262.76	   U34(x0, x1, mark(x2))
743.35/262.76	   U34(active(x0), x1, x2)
743.35/262.76	   U34(x0, active(x1), x2)
743.35/262.76	   U34(x0, x1, active(x2))
743.35/262.76	   U35(mark(x0), x1)
743.35/262.76	   U35(x0, mark(x1))
743.35/262.76	   U35(active(x0), x1)
743.35/262.76	   U35(x0, active(x1))
743.35/262.76	   U36(mark(x0))
743.35/262.76	   U36(active(x0))
743.35/262.76	   U41(mark(x0), x1)
743.35/262.76	   U41(x0, mark(x1))
743.35/262.76	   U41(active(x0), x1)
743.35/262.76	   U41(x0, active(x1))
743.35/262.76	   U42(mark(x0))
743.35/262.76	   U42(active(x0))
743.35/262.76	   U51(mark(x0))
743.35/262.76	   U51(active(x0))
743.35/262.76	   U61(mark(x0), x1)
743.35/262.76	   U61(x0, mark(x1))
743.35/262.76	   U61(active(x0), x1)
743.35/262.76	   U61(x0, active(x1))
743.35/262.76	   U62(mark(x0))
743.35/262.76	   U62(active(x0))
743.35/262.76	   U71(mark(x0), x1)
743.35/262.76	   U71(x0, mark(x1))
743.35/262.76	   U71(active(x0), x1)
743.35/262.76	   U71(x0, active(x1))
743.35/262.76	   U72(mark(x0), x1)
743.35/262.76	   U72(x0, mark(x1))
743.35/262.76	   U72(active(x0), x1)
743.35/262.76	   U72(x0, active(x1))
743.35/262.76	   U81(mark(x0), x1, x2)
743.35/262.76	   U81(x0, mark(x1), x2)
743.35/262.76	   U81(x0, x1, mark(x2))
743.35/262.76	   U81(active(x0), x1, x2)
743.35/262.76	   U81(x0, active(x1), x2)
743.35/262.76	   U81(x0, x1, active(x2))
743.35/262.76	   U82(mark(x0), x1, x2)
743.35/262.76	   U82(x0, mark(x1), x2)
743.35/262.76	   U82(x0, x1, mark(x2))
743.35/262.76	   U82(active(x0), x1, x2)
743.35/262.76	   U82(x0, active(x1), x2)
743.35/262.76	   U82(x0, x1, active(x2))
743.35/262.76	   U83(mark(x0), x1, x2)
743.35/262.76	   U83(x0, mark(x1), x2)
743.35/262.76	   U83(x0, x1, mark(x2))
743.35/262.76	   U83(active(x0), x1, x2)
743.35/262.76	   U83(x0, active(x1), x2)
743.35/262.76	   U83(x0, x1, active(x2))
743.35/262.76	   U84(mark(x0), x1, x2)
743.35/262.76	   U84(x0, mark(x1), x2)
743.35/262.76	   U84(x0, x1, mark(x2))
743.35/262.76	   U84(active(x0), x1, x2)
743.35/262.76	   U84(x0, active(x1), x2)
743.35/262.76	   U84(x0, x1, active(x2))
743.35/262.76	   s(mark(x0))
743.35/262.76	   s(active(x0))
743.35/262.76	   U91(mark(x0), x1)
743.35/262.76	   U91(x0, mark(x1))
743.35/262.76	   U91(active(x0), x1)
743.35/262.76	   U91(x0, active(x1))
743.35/262.76	   U92(mark(x0))
743.35/262.76	   U92(active(x0))
743.35/262.76	
743.35/262.76	We have to consider all minimal (P,Q,R)-chains.
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(22) QReductionProof (EQUIVALENT)
743.35/262.76	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.35/262.76	
743.35/262.76	   U101(mark(x0), x1, x2)
743.35/262.76	   U101(x0, mark(x1), x2)
743.35/262.76	   U101(x0, x1, mark(x2))
743.35/262.76	   U101(active(x0), x1, x2)
743.35/262.76	   U101(x0, active(x1), x2)
743.35/262.76	   U101(x0, x1, active(x2))
743.35/262.76	   U102(mark(x0), x1, x2)
743.35/262.76	   U102(x0, mark(x1), x2)
743.35/262.76	   U102(x0, x1, mark(x2))
743.35/262.76	   U102(active(x0), x1, x2)
743.35/262.76	   U102(x0, active(x1), x2)
743.35/262.76	   U102(x0, x1, active(x2))
743.35/262.76	   isNatKind(mark(x0))
743.35/262.76	   isNatKind(active(x0))
743.35/262.76	   U103(mark(x0), x1, x2)
743.35/262.76	   U103(x0, mark(x1), x2)
743.35/262.76	   U103(x0, x1, mark(x2))
743.35/262.76	   U103(active(x0), x1, x2)
743.35/262.76	   U103(x0, active(x1), x2)
743.35/262.76	   U103(x0, x1, active(x2))
743.35/262.76	   isNat(mark(x0))
743.35/262.76	   isNat(active(x0))
743.35/262.76	   U104(mark(x0), x1, x2)
743.35/262.76	   U104(x0, mark(x1), x2)
743.35/262.76	   U104(x0, x1, mark(x2))
743.35/262.76	   U104(active(x0), x1, x2)
743.35/262.76	   U104(x0, active(x1), x2)
743.35/262.76	   U104(x0, x1, active(x2))
743.35/262.76	   plus(mark(x0), x1)
743.35/262.76	   plus(x0, mark(x1))
743.35/262.76	   plus(active(x0), x1)
743.35/262.76	   plus(x0, active(x1))
743.35/262.76	   x(mark(x0), x1)
743.35/262.76	   x(x0, mark(x1))
743.35/262.76	   x(active(x0), x1)
743.35/262.76	   x(x0, active(x1))
743.35/262.76	   U11(mark(x0), x1, x2)
743.35/262.76	   U11(x0, mark(x1), x2)
743.35/262.76	   U11(x0, x1, mark(x2))
743.35/262.76	   U11(active(x0), x1, x2)
743.35/262.76	   U11(x0, active(x1), x2)
743.35/262.76	   U11(x0, x1, active(x2))
743.35/262.76	   U12(mark(x0), x1, x2)
743.35/262.76	   U12(x0, mark(x1), x2)
743.35/262.76	   U12(x0, x1, mark(x2))
743.35/262.76	   U12(active(x0), x1, x2)
743.35/262.76	   U12(x0, active(x1), x2)
743.35/262.76	   U12(x0, x1, active(x2))
743.35/262.76	   U13(mark(x0), x1, x2)
743.35/262.76	   U13(x0, mark(x1), x2)
743.35/262.76	   U13(x0, x1, mark(x2))
743.35/262.76	   U13(active(x0), x1, x2)
743.35/262.76	   U13(x0, active(x1), x2)
743.35/262.76	   U13(x0, x1, active(x2))
743.35/262.76	   U14(mark(x0), x1, x2)
743.35/262.76	   U14(x0, mark(x1), x2)
743.35/262.76	   U14(x0, x1, mark(x2))
743.35/262.76	   U14(active(x0), x1, x2)
743.35/262.76	   U14(x0, active(x1), x2)
743.35/262.76	   U14(x0, x1, active(x2))
743.35/262.76	   U15(mark(x0), x1)
743.35/262.76	   U15(x0, mark(x1))
743.35/262.76	   U15(active(x0), x1)
743.35/262.76	   U15(x0, active(x1))
743.35/262.76	   U16(mark(x0))
743.35/262.76	   U16(active(x0))
743.35/262.76	   U21(mark(x0), x1)
743.35/262.76	   U21(x0, mark(x1))
743.35/262.76	   U21(active(x0), x1)
743.35/262.76	   U21(x0, active(x1))
743.35/262.76	   U22(mark(x0), x1)
743.35/262.76	   U22(x0, mark(x1))
743.35/262.76	   U22(active(x0), x1)
743.35/262.76	   U22(x0, active(x1))
743.35/262.76	   U23(mark(x0))
743.35/262.76	   U23(active(x0))
743.35/262.76	   U31(mark(x0), x1, x2)
743.35/262.76	   U31(x0, mark(x1), x2)
743.35/262.76	   U31(x0, x1, mark(x2))
743.35/262.76	   U31(active(x0), x1, x2)
743.35/262.76	   U31(x0, active(x1), x2)
743.35/262.76	   U31(x0, x1, active(x2))
743.35/262.76	   U32(mark(x0), x1, x2)
743.35/262.76	   U32(x0, mark(x1), x2)
743.35/262.76	   U32(x0, x1, mark(x2))
743.35/262.76	   U32(active(x0), x1, x2)
743.35/262.76	   U32(x0, active(x1), x2)
743.35/262.76	   U32(x0, x1, active(x2))
743.35/262.76	   U33(mark(x0), x1, x2)
743.35/262.76	   U33(x0, mark(x1), x2)
743.35/262.76	   U33(x0, x1, mark(x2))
743.35/262.76	   U33(active(x0), x1, x2)
743.35/262.76	   U33(x0, active(x1), x2)
743.35/262.76	   U33(x0, x1, active(x2))
743.35/262.76	   U34(mark(x0), x1, x2)
743.35/262.76	   U34(x0, mark(x1), x2)
743.35/262.76	   U34(x0, x1, mark(x2))
743.35/262.76	   U34(active(x0), x1, x2)
743.35/262.76	   U34(x0, active(x1), x2)
743.35/262.76	   U34(x0, x1, active(x2))
743.35/262.76	   U35(mark(x0), x1)
743.35/262.76	   U35(x0, mark(x1))
743.35/262.76	   U35(active(x0), x1)
743.35/262.76	   U35(x0, active(x1))
743.35/262.76	   U36(mark(x0))
743.35/262.76	   U36(active(x0))
743.35/262.76	   U41(mark(x0), x1)
743.35/262.76	   U41(x0, mark(x1))
743.35/262.76	   U41(active(x0), x1)
743.35/262.76	   U41(x0, active(x1))
743.35/262.76	   U42(mark(x0))
743.35/262.76	   U42(active(x0))
743.35/262.76	   U51(mark(x0))
743.35/262.76	   U51(active(x0))
743.35/262.76	   U61(mark(x0), x1)
743.35/262.76	   U61(x0, mark(x1))
743.35/262.76	   U61(active(x0), x1)
743.35/262.76	   U61(x0, active(x1))
743.35/262.76	   U62(mark(x0))
743.35/262.76	   U62(active(x0))
743.35/262.76	   U71(mark(x0), x1)
743.35/262.76	   U71(x0, mark(x1))
743.35/262.76	   U71(active(x0), x1)
743.35/262.76	   U71(x0, active(x1))
743.35/262.76	   U72(mark(x0), x1)
743.35/262.76	   U72(x0, mark(x1))
743.35/262.76	   U72(active(x0), x1)
743.35/262.76	   U72(x0, active(x1))
743.35/262.76	   U81(mark(x0), x1, x2)
743.35/262.76	   U81(x0, mark(x1), x2)
743.35/262.76	   U81(x0, x1, mark(x2))
743.35/262.76	   U81(active(x0), x1, x2)
743.35/262.76	   U81(x0, active(x1), x2)
743.35/262.76	   U81(x0, x1, active(x2))
743.35/262.76	   U82(mark(x0), x1, x2)
743.35/262.76	   U82(x0, mark(x1), x2)
743.35/262.76	   U82(x0, x1, mark(x2))
743.35/262.76	   U82(active(x0), x1, x2)
743.35/262.76	   U82(x0, active(x1), x2)
743.35/262.76	   U82(x0, x1, active(x2))
743.35/262.76	   U83(mark(x0), x1, x2)
743.35/262.76	   U83(x0, mark(x1), x2)
743.35/262.76	   U83(x0, x1, mark(x2))
743.35/262.76	   U83(active(x0), x1, x2)
743.35/262.76	   U83(x0, active(x1), x2)
743.35/262.76	   U83(x0, x1, active(x2))
743.35/262.76	   U84(mark(x0), x1, x2)
743.35/262.76	   U84(x0, mark(x1), x2)
743.35/262.76	   U84(x0, x1, mark(x2))
743.35/262.76	   U84(active(x0), x1, x2)
743.35/262.76	   U84(x0, active(x1), x2)
743.35/262.76	   U84(x0, x1, active(x2))
743.35/262.76	   s(mark(x0))
743.35/262.76	   s(active(x0))
743.35/262.76	   U91(mark(x0), x1)
743.35/262.76	   U91(x0, mark(x1))
743.35/262.76	   U91(active(x0), x1)
743.35/262.76	   U91(x0, active(x1))
743.35/262.76	   U92(mark(x0))
743.35/262.76	   U92(active(x0))
743.35/262.76	
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(23)
743.35/262.76	Obligation:
743.35/262.76	Q DP problem:
743.35/262.76	The TRS P consists of the following rules:
743.35/262.76	
743.35/262.76	   S(active(X)) -> S(X)
743.35/262.76	   S(mark(X)) -> S(X)
743.35/262.76	
743.35/262.76	R is empty.
743.35/262.76	The set Q consists of the following terms:
743.35/262.76	
743.35/262.76	   active(U101(tt, x0, x1))
743.35/262.76	   active(U102(tt, x0, x1))
743.35/262.76	   active(U103(tt, x0, x1))
743.35/262.76	   active(U104(tt, x0, x1))
743.35/262.76	   active(U11(tt, x0, x1))
743.35/262.76	   active(U12(tt, x0, x1))
743.35/262.76	   active(U13(tt, x0, x1))
743.35/262.76	   active(U14(tt, x0, x1))
743.35/262.76	   active(U15(tt, x0))
743.35/262.76	   active(U16(tt))
743.35/262.76	   active(U21(tt, x0))
743.35/262.76	   active(U22(tt, x0))
743.35/262.76	   active(U23(tt))
743.35/262.76	   active(U31(tt, x0, x1))
743.35/262.76	   active(U32(tt, x0, x1))
743.35/262.76	   active(U33(tt, x0, x1))
743.35/262.76	   active(U34(tt, x0, x1))
743.35/262.76	   active(U35(tt, x0))
743.35/262.76	   active(U36(tt))
743.35/262.76	   active(U41(tt, x0))
743.35/262.76	   active(U42(tt))
743.35/262.76	   active(U51(tt))
743.35/262.76	   active(U61(tt, x0))
743.35/262.76	   active(U62(tt))
743.35/262.76	   active(U71(tt, x0))
743.35/262.76	   active(U72(tt, x0))
743.35/262.76	   active(U81(tt, x0, x1))
743.35/262.76	   active(U82(tt, x0, x1))
743.35/262.76	   active(U83(tt, x0, x1))
743.35/262.76	   active(U84(tt, x0, x1))
743.35/262.76	   active(U91(tt, x0))
743.35/262.76	   active(U92(tt))
743.35/262.76	   active(isNat(0))
743.35/262.76	   active(isNat(plus(x0, x1)))
743.35/262.76	   active(isNat(s(x0)))
743.35/262.76	   active(isNat(x(x0, x1)))
743.35/262.76	   active(isNatKind(0))
743.35/262.76	   active(isNatKind(plus(x0, x1)))
743.35/262.76	   active(isNatKind(s(x0)))
743.35/262.76	   active(isNatKind(x(x0, x1)))
743.35/262.76	   active(plus(x0, 0))
743.35/262.76	   active(plus(x0, s(x1)))
743.35/262.76	   active(x(x0, 0))
743.35/262.76	   active(x(x0, s(x1)))
743.35/262.76	   mark(U101(x0, x1, x2))
743.35/262.76	   mark(tt)
743.35/262.76	   mark(U102(x0, x1, x2))
743.35/262.76	   mark(isNatKind(x0))
743.35/262.76	   mark(U103(x0, x1, x2))
743.35/262.76	   mark(isNat(x0))
743.35/262.76	   mark(U104(x0, x1, x2))
743.35/262.76	   mark(plus(x0, x1))
743.35/262.76	   mark(x(x0, x1))
743.35/262.76	   mark(U11(x0, x1, x2))
743.35/262.76	   mark(U12(x0, x1, x2))
743.35/262.76	   mark(U13(x0, x1, x2))
743.35/262.76	   mark(U14(x0, x1, x2))
743.35/262.76	   mark(U15(x0, x1))
743.35/262.76	   mark(U16(x0))
743.35/262.76	   mark(U21(x0, x1))
743.35/262.76	   mark(U22(x0, x1))
743.35/262.76	   mark(U23(x0))
743.35/262.76	   mark(U31(x0, x1, x2))
743.35/262.76	   mark(U32(x0, x1, x2))
743.35/262.76	   mark(U33(x0, x1, x2))
743.35/262.76	   mark(U34(x0, x1, x2))
743.35/262.76	   mark(U35(x0, x1))
743.35/262.76	   mark(U36(x0))
743.35/262.76	   mark(U41(x0, x1))
743.35/262.76	   mark(U42(x0))
743.35/262.76	   mark(U51(x0))
743.35/262.76	   mark(U61(x0, x1))
743.35/262.76	   mark(U62(x0))
743.35/262.76	   mark(U71(x0, x1))
743.35/262.76	   mark(U72(x0, x1))
743.35/262.76	   mark(U81(x0, x1, x2))
743.35/262.76	   mark(U82(x0, x1, x2))
743.35/262.76	   mark(U83(x0, x1, x2))
743.35/262.76	   mark(U84(x0, x1, x2))
743.35/262.76	   mark(s(x0))
743.35/262.76	   mark(U91(x0, x1))
743.35/262.76	   mark(U92(x0))
743.35/262.76	   mark(0)
743.35/262.76	
743.35/262.76	We have to consider all minimal (P,Q,R)-chains.
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(24) QDPSizeChangeProof (EQUIVALENT)
743.35/262.76	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. 
743.35/262.76	
743.35/262.76	From the DPs we obtained the following set of size-change graphs:
743.35/262.76	*S(active(X)) -> S(X)
743.35/262.76	The graph contains the following edges 1 > 1
743.35/262.76	
743.35/262.76	
743.35/262.76	*S(mark(X)) -> S(X)
743.35/262.76	The graph contains the following edges 1 > 1
743.35/262.76	
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(25)
743.35/262.76	YES
743.35/262.76	
743.35/262.76	----------------------------------------
743.35/262.76	
743.35/262.76	(26)
743.35/262.76	Obligation:
743.35/262.76	Q DP problem:
743.35/262.76	The TRS P consists of the following rules:
743.35/262.76	
743.35/262.76	   U84^1(X1, mark(X2), X3) -> U84^1(X1, X2, X3)
743.35/262.76	   U84^1(mark(X1), X2, X3) -> U84^1(X1, X2, X3)
743.35/262.76	   U84^1(X1, X2, mark(X3)) -> U84^1(X1, X2, X3)
743.35/262.76	   U84^1(active(X1), X2, X3) -> U84^1(X1, X2, X3)
743.35/262.76	   U84^1(X1, active(X2), X3) -> U84^1(X1, X2, X3)
743.35/262.76	   U84^1(X1, X2, active(X3)) -> U84^1(X1, X2, X3)
743.35/262.76	
743.35/262.76	The TRS R consists of the following rules:
743.35/262.76	
743.35/262.76	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.35/262.76	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.35/262.76	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.35/262.76	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.35/262.76	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.35/262.76	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.35/262.76	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.35/262.76	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.35/262.76	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.35/262.76	   active(U16(tt)) -> mark(tt)
743.35/262.76	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.35/262.76	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.35/262.76	   active(U23(tt)) -> mark(tt)
743.35/262.76	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.35/262.76	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.35/262.76	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.35/262.76	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.35/262.76	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.35/262.76	   active(U36(tt)) -> mark(tt)
743.35/262.76	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.35/262.76	   active(U42(tt)) -> mark(tt)
743.35/262.76	   active(U51(tt)) -> mark(tt)
743.35/262.76	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.35/262.76	   active(U62(tt)) -> mark(tt)
743.35/262.76	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.35/262.76	   active(U72(tt, N)) -> mark(N)
743.35/262.76	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.35/262.76	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.35/262.76	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.35/262.76	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.35/262.76	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.35/262.76	   active(U92(tt)) -> mark(0)
743.35/262.76	   active(isNat(0)) -> mark(tt)
743.35/262.76	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.35/262.76	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.35/262.76	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.35/262.76	   active(isNatKind(0)) -> mark(tt)
743.35/262.76	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.35/262.76	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.35/262.76	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.35/262.76	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.35/262.76	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.35/262.76	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.35/262.76	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.35/262.76	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.35/262.76	   mark(tt) -> active(tt)
743.35/262.76	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.35/262.76	   mark(isNatKind(X)) -> active(isNatKind(X))
743.35/262.76	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.35/262.76	   mark(isNat(X)) -> active(isNat(X))
743.35/262.76	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.35/262.76	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.35/262.76	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.35/262.76	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.35/262.76	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.35/262.76	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.35/262.76	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.35/262.76	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.35/262.76	   mark(U16(X)) -> active(U16(mark(X)))
743.35/262.76	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.35/262.76	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.35/262.76	   mark(U23(X)) -> active(U23(mark(X)))
743.35/262.76	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.35/262.76	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.35/262.76	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.35/262.76	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.35/262.76	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.35/262.76	   mark(U36(X)) -> active(U36(mark(X)))
743.35/262.76	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.35/262.76	   mark(U42(X)) -> active(U42(mark(X)))
743.35/262.76	   mark(U51(X)) -> active(U51(mark(X)))
743.35/262.76	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.35/262.76	   mark(U62(X)) -> active(U62(mark(X)))
743.35/262.76	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.35/262.76	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.35/262.76	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.35/262.76	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.35/262.76	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.35/262.76	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.35/262.76	   mark(s(X)) -> active(s(mark(X)))
743.35/262.76	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.35/262.76	   mark(U92(X)) -> active(U92(mark(X)))
743.35/262.76	   mark(0) -> active(0)
743.35/262.76	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.35/262.76	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.35/262.76	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.35/262.76	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.35/262.76	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.35/262.76	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.35/262.76	   isNatKind(mark(X)) -> isNatKind(X)
743.35/262.76	   isNatKind(active(X)) -> isNatKind(X)
743.35/262.76	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.35/262.76	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.35/262.76	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.35/262.76	   isNat(mark(X)) -> isNat(X)
743.35/262.76	   isNat(active(X)) -> isNat(X)
743.35/262.76	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.35/262.76	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.35/262.76	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.35/262.76	   plus(mark(X1), X2) -> plus(X1, X2)
743.35/262.76	   plus(X1, mark(X2)) -> plus(X1, X2)
743.35/262.76	   plus(active(X1), X2) -> plus(X1, X2)
743.35/262.76	   plus(X1, active(X2)) -> plus(X1, X2)
743.35/262.76	   x(mark(X1), X2) -> x(X1, X2)
743.35/262.76	   x(X1, mark(X2)) -> x(X1, X2)
743.35/262.76	   x(active(X1), X2) -> x(X1, X2)
743.35/262.76	   x(X1, active(X2)) -> x(X1, X2)
743.35/262.76	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.35/262.76	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.35/262.76	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.35/262.76	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.35/262.76	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.35/262.76	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.35/262.76	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.35/262.76	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.35/262.76	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.35/262.76	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.35/262.76	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.35/262.76	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.35/262.76	   U15(mark(X1), X2) -> U15(X1, X2)
743.35/262.76	   U15(X1, mark(X2)) -> U15(X1, X2)
743.35/262.76	   U15(active(X1), X2) -> U15(X1, X2)
743.35/262.76	   U15(X1, active(X2)) -> U15(X1, X2)
743.35/262.76	   U16(mark(X)) -> U16(X)
743.35/262.76	   U16(active(X)) -> U16(X)
743.35/262.76	   U21(mark(X1), X2) -> U21(X1, X2)
743.35/262.76	   U21(X1, mark(X2)) -> U21(X1, X2)
743.35/262.76	   U21(active(X1), X2) -> U21(X1, X2)
743.35/262.76	   U21(X1, active(X2)) -> U21(X1, X2)
743.35/262.76	   U22(mark(X1), X2) -> U22(X1, X2)
743.35/262.76	   U22(X1, mark(X2)) -> U22(X1, X2)
743.35/262.76	   U22(active(X1), X2) -> U22(X1, X2)
743.35/262.76	   U22(X1, active(X2)) -> U22(X1, X2)
743.35/262.76	   U23(mark(X)) -> U23(X)
743.35/262.76	   U23(active(X)) -> U23(X)
743.35/262.76	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.35/262.76	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.35/262.76	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.35/262.76	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.35/262.76	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.35/262.76	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.35/262.76	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.35/262.76	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.35/262.76	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.35/262.76	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.35/262.76	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.35/262.76	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.35/262.76	   U35(mark(X1), X2) -> U35(X1, X2)
743.35/262.76	   U35(X1, mark(X2)) -> U35(X1, X2)
743.35/262.76	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.76	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.76	   U36(mark(X)) -> U36(X)
743.71/262.76	   U36(active(X)) -> U36(X)
743.71/262.76	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.76	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.76	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.76	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.76	   U42(mark(X)) -> U42(X)
743.71/262.76	   U42(active(X)) -> U42(X)
743.71/262.76	   U51(mark(X)) -> U51(X)
743.71/262.76	   U51(active(X)) -> U51(X)
743.71/262.76	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.76	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.76	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.76	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.76	   U62(mark(X)) -> U62(X)
743.71/262.76	   U62(active(X)) -> U62(X)
743.71/262.76	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.76	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.76	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.76	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.76	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.76	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.76	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.76	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.76	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.76	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.76	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.76	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.76	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.76	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.76	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.76	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.76	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.76	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.76	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.76	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.76	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.76	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.76	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.76	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.76	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.76	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.76	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.76	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.76	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.76	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.76	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.76	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.76	   s(mark(X)) -> s(X)
743.71/262.76	   s(active(X)) -> s(X)
743.71/262.76	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.76	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.76	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.76	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.76	   U92(mark(X)) -> U92(X)
743.71/262.76	   U92(active(X)) -> U92(X)
743.71/262.76	
743.71/262.76	The set Q consists of the following terms:
743.71/262.76	
743.71/262.76	   active(U101(tt, x0, x1))
743.71/262.76	   active(U102(tt, x0, x1))
743.71/262.76	   active(U103(tt, x0, x1))
743.71/262.76	   active(U104(tt, x0, x1))
743.71/262.76	   active(U11(tt, x0, x1))
743.71/262.76	   active(U12(tt, x0, x1))
743.71/262.76	   active(U13(tt, x0, x1))
743.71/262.76	   active(U14(tt, x0, x1))
743.71/262.76	   active(U15(tt, x0))
743.71/262.76	   active(U16(tt))
743.71/262.76	   active(U21(tt, x0))
743.71/262.76	   active(U22(tt, x0))
743.71/262.76	   active(U23(tt))
743.71/262.76	   active(U31(tt, x0, x1))
743.71/262.76	   active(U32(tt, x0, x1))
743.71/262.76	   active(U33(tt, x0, x1))
743.71/262.76	   active(U34(tt, x0, x1))
743.71/262.76	   active(U35(tt, x0))
743.71/262.76	   active(U36(tt))
743.71/262.76	   active(U41(tt, x0))
743.71/262.76	   active(U42(tt))
743.71/262.76	   active(U51(tt))
743.71/262.76	   active(U61(tt, x0))
743.71/262.76	   active(U62(tt))
743.71/262.76	   active(U71(tt, x0))
743.71/262.76	   active(U72(tt, x0))
743.71/262.76	   active(U81(tt, x0, x1))
743.71/262.76	   active(U82(tt, x0, x1))
743.71/262.76	   active(U83(tt, x0, x1))
743.71/262.76	   active(U84(tt, x0, x1))
743.71/262.76	   active(U91(tt, x0))
743.71/262.76	   active(U92(tt))
743.71/262.76	   active(isNat(0))
743.71/262.76	   active(isNat(plus(x0, x1)))
743.71/262.76	   active(isNat(s(x0)))
743.71/262.76	   active(isNat(x(x0, x1)))
743.71/262.76	   active(isNatKind(0))
743.71/262.76	   active(isNatKind(plus(x0, x1)))
743.71/262.76	   active(isNatKind(s(x0)))
743.71/262.76	   active(isNatKind(x(x0, x1)))
743.71/262.76	   active(plus(x0, 0))
743.71/262.76	   active(plus(x0, s(x1)))
743.71/262.76	   active(x(x0, 0))
743.71/262.76	   active(x(x0, s(x1)))
743.71/262.76	   mark(U101(x0, x1, x2))
743.71/262.76	   mark(tt)
743.71/262.76	   mark(U102(x0, x1, x2))
743.71/262.76	   mark(isNatKind(x0))
743.71/262.76	   mark(U103(x0, x1, x2))
743.71/262.76	   mark(isNat(x0))
743.71/262.76	   mark(U104(x0, x1, x2))
743.71/262.76	   mark(plus(x0, x1))
743.71/262.76	   mark(x(x0, x1))
743.71/262.76	   mark(U11(x0, x1, x2))
743.71/262.76	   mark(U12(x0, x1, x2))
743.71/262.76	   mark(U13(x0, x1, x2))
743.71/262.76	   mark(U14(x0, x1, x2))
743.71/262.76	   mark(U15(x0, x1))
743.71/262.76	   mark(U16(x0))
743.71/262.76	   mark(U21(x0, x1))
743.71/262.76	   mark(U22(x0, x1))
743.71/262.76	   mark(U23(x0))
743.71/262.76	   mark(U31(x0, x1, x2))
743.71/262.76	   mark(U32(x0, x1, x2))
743.71/262.76	   mark(U33(x0, x1, x2))
743.71/262.76	   mark(U34(x0, x1, x2))
743.71/262.76	   mark(U35(x0, x1))
743.71/262.76	   mark(U36(x0))
743.71/262.76	   mark(U41(x0, x1))
743.71/262.76	   mark(U42(x0))
743.71/262.76	   mark(U51(x0))
743.71/262.76	   mark(U61(x0, x1))
743.71/262.76	   mark(U62(x0))
743.71/262.76	   mark(U71(x0, x1))
743.71/262.76	   mark(U72(x0, x1))
743.71/262.76	   mark(U81(x0, x1, x2))
743.71/262.76	   mark(U82(x0, x1, x2))
743.71/262.76	   mark(U83(x0, x1, x2))
743.71/262.76	   mark(U84(x0, x1, x2))
743.71/262.76	   mark(s(x0))
743.71/262.76	   mark(U91(x0, x1))
743.71/262.76	   mark(U92(x0))
743.71/262.76	   mark(0)
743.71/262.76	   U101(mark(x0), x1, x2)
743.71/262.76	   U101(x0, mark(x1), x2)
743.71/262.76	   U101(x0, x1, mark(x2))
743.71/262.76	   U101(active(x0), x1, x2)
743.71/262.76	   U101(x0, active(x1), x2)
743.71/262.76	   U101(x0, x1, active(x2))
743.71/262.76	   U102(mark(x0), x1, x2)
743.71/262.76	   U102(x0, mark(x1), x2)
743.71/262.76	   U102(x0, x1, mark(x2))
743.71/262.76	   U102(active(x0), x1, x2)
743.71/262.76	   U102(x0, active(x1), x2)
743.71/262.76	   U102(x0, x1, active(x2))
743.71/262.76	   isNatKind(mark(x0))
743.71/262.76	   isNatKind(active(x0))
743.71/262.76	   U103(mark(x0), x1, x2)
743.71/262.76	   U103(x0, mark(x1), x2)
743.71/262.76	   U103(x0, x1, mark(x2))
743.71/262.76	   U103(active(x0), x1, x2)
743.71/262.76	   U103(x0, active(x1), x2)
743.71/262.76	   U103(x0, x1, active(x2))
743.71/262.76	   isNat(mark(x0))
743.71/262.76	   isNat(active(x0))
743.71/262.76	   U104(mark(x0), x1, x2)
743.71/262.76	   U104(x0, mark(x1), x2)
743.71/262.76	   U104(x0, x1, mark(x2))
743.71/262.76	   U104(active(x0), x1, x2)
743.71/262.76	   U104(x0, active(x1), x2)
743.71/262.76	   U104(x0, x1, active(x2))
743.71/262.76	   plus(mark(x0), x1)
743.71/262.76	   plus(x0, mark(x1))
743.71/262.76	   plus(active(x0), x1)
743.71/262.76	   plus(x0, active(x1))
743.71/262.76	   x(mark(x0), x1)
743.71/262.76	   x(x0, mark(x1))
743.71/262.76	   x(active(x0), x1)
743.71/262.76	   x(x0, active(x1))
743.71/262.76	   U11(mark(x0), x1, x2)
743.71/262.76	   U11(x0, mark(x1), x2)
743.71/262.76	   U11(x0, x1, mark(x2))
743.71/262.76	   U11(active(x0), x1, x2)
743.71/262.76	   U11(x0, active(x1), x2)
743.71/262.76	   U11(x0, x1, active(x2))
743.71/262.76	   U12(mark(x0), x1, x2)
743.71/262.76	   U12(x0, mark(x1), x2)
743.71/262.76	   U12(x0, x1, mark(x2))
743.71/262.76	   U12(active(x0), x1, x2)
743.71/262.76	   U12(x0, active(x1), x2)
743.71/262.76	   U12(x0, x1, active(x2))
743.71/262.76	   U13(mark(x0), x1, x2)
743.71/262.76	   U13(x0, mark(x1), x2)
743.71/262.76	   U13(x0, x1, mark(x2))
743.71/262.76	   U13(active(x0), x1, x2)
743.71/262.76	   U13(x0, active(x1), x2)
743.71/262.76	   U13(x0, x1, active(x2))
743.71/262.76	   U14(mark(x0), x1, x2)
743.71/262.76	   U14(x0, mark(x1), x2)
743.71/262.76	   U14(x0, x1, mark(x2))
743.71/262.76	   U14(active(x0), x1, x2)
743.71/262.76	   U14(x0, active(x1), x2)
743.71/262.76	   U14(x0, x1, active(x2))
743.71/262.76	   U15(mark(x0), x1)
743.71/262.76	   U15(x0, mark(x1))
743.71/262.76	   U15(active(x0), x1)
743.71/262.76	   U15(x0, active(x1))
743.71/262.76	   U16(mark(x0))
743.71/262.76	   U16(active(x0))
743.71/262.76	   U21(mark(x0), x1)
743.71/262.76	   U21(x0, mark(x1))
743.71/262.76	   U21(active(x0), x1)
743.71/262.76	   U21(x0, active(x1))
743.71/262.76	   U22(mark(x0), x1)
743.71/262.76	   U22(x0, mark(x1))
743.71/262.76	   U22(active(x0), x1)
743.71/262.76	   U22(x0, active(x1))
743.71/262.76	   U23(mark(x0))
743.71/262.76	   U23(active(x0))
743.71/262.76	   U31(mark(x0), x1, x2)
743.71/262.76	   U31(x0, mark(x1), x2)
743.71/262.76	   U31(x0, x1, mark(x2))
743.71/262.76	   U31(active(x0), x1, x2)
743.71/262.76	   U31(x0, active(x1), x2)
743.71/262.76	   U31(x0, x1, active(x2))
743.71/262.76	   U32(mark(x0), x1, x2)
743.71/262.76	   U32(x0, mark(x1), x2)
743.71/262.76	   U32(x0, x1, mark(x2))
743.71/262.76	   U32(active(x0), x1, x2)
743.71/262.76	   U32(x0, active(x1), x2)
743.71/262.76	   U32(x0, x1, active(x2))
743.71/262.76	   U33(mark(x0), x1, x2)
743.71/262.76	   U33(x0, mark(x1), x2)
743.71/262.76	   U33(x0, x1, mark(x2))
743.71/262.76	   U33(active(x0), x1, x2)
743.71/262.76	   U33(x0, active(x1), x2)
743.71/262.76	   U33(x0, x1, active(x2))
743.71/262.76	   U34(mark(x0), x1, x2)
743.71/262.76	   U34(x0, mark(x1), x2)
743.71/262.76	   U34(x0, x1, mark(x2))
743.71/262.76	   U34(active(x0), x1, x2)
743.71/262.76	   U34(x0, active(x1), x2)
743.71/262.76	   U34(x0, x1, active(x2))
743.71/262.76	   U35(mark(x0), x1)
743.71/262.76	   U35(x0, mark(x1))
743.71/262.76	   U35(active(x0), x1)
743.71/262.76	   U35(x0, active(x1))
743.71/262.76	   U36(mark(x0))
743.71/262.76	   U36(active(x0))
743.71/262.76	   U41(mark(x0), x1)
743.71/262.76	   U41(x0, mark(x1))
743.71/262.76	   U41(active(x0), x1)
743.71/262.76	   U41(x0, active(x1))
743.71/262.76	   U42(mark(x0))
743.71/262.76	   U42(active(x0))
743.71/262.76	   U51(mark(x0))
743.71/262.76	   U51(active(x0))
743.71/262.76	   U61(mark(x0), x1)
743.71/262.76	   U61(x0, mark(x1))
743.71/262.76	   U61(active(x0), x1)
743.71/262.76	   U61(x0, active(x1))
743.71/262.76	   U62(mark(x0))
743.71/262.76	   U62(active(x0))
743.71/262.76	   U71(mark(x0), x1)
743.71/262.76	   U71(x0, mark(x1))
743.71/262.76	   U71(active(x0), x1)
743.71/262.76	   U71(x0, active(x1))
743.71/262.76	   U72(mark(x0), x1)
743.71/262.76	   U72(x0, mark(x1))
743.71/262.76	   U72(active(x0), x1)
743.71/262.76	   U72(x0, active(x1))
743.71/262.76	   U81(mark(x0), x1, x2)
743.71/262.76	   U81(x0, mark(x1), x2)
743.71/262.76	   U81(x0, x1, mark(x2))
743.71/262.76	   U81(active(x0), x1, x2)
743.71/262.76	   U81(x0, active(x1), x2)
743.71/262.76	   U81(x0, x1, active(x2))
743.71/262.76	   U82(mark(x0), x1, x2)
743.71/262.76	   U82(x0, mark(x1), x2)
743.71/262.76	   U82(x0, x1, mark(x2))
743.71/262.76	   U82(active(x0), x1, x2)
743.71/262.76	   U82(x0, active(x1), x2)
743.71/262.76	   U82(x0, x1, active(x2))
743.71/262.76	   U83(mark(x0), x1, x2)
743.71/262.76	   U83(x0, mark(x1), x2)
743.71/262.76	   U83(x0, x1, mark(x2))
743.71/262.76	   U83(active(x0), x1, x2)
743.71/262.76	   U83(x0, active(x1), x2)
743.71/262.76	   U83(x0, x1, active(x2))
743.71/262.76	   U84(mark(x0), x1, x2)
743.71/262.76	   U84(x0, mark(x1), x2)
743.71/262.76	   U84(x0, x1, mark(x2))
743.71/262.76	   U84(active(x0), x1, x2)
743.71/262.76	   U84(x0, active(x1), x2)
743.71/262.76	   U84(x0, x1, active(x2))
743.71/262.76	   s(mark(x0))
743.71/262.76	   s(active(x0))
743.71/262.76	   U91(mark(x0), x1)
743.71/262.76	   U91(x0, mark(x1))
743.71/262.76	   U91(active(x0), x1)
743.71/262.76	   U91(x0, active(x1))
743.71/262.76	   U92(mark(x0))
743.71/262.76	   U92(active(x0))
743.71/262.76	
743.71/262.76	We have to consider all minimal (P,Q,R)-chains.
743.71/262.76	----------------------------------------
743.71/262.76	
743.71/262.76	(27) UsableRulesProof (EQUIVALENT)
743.71/262.76	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.
743.71/262.76	----------------------------------------
743.71/262.76	
743.71/262.76	(28)
743.71/262.76	Obligation:
743.71/262.76	Q DP problem:
743.71/262.76	The TRS P consists of the following rules:
743.71/262.76	
743.71/262.76	   U84^1(X1, mark(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.76	   U84^1(mark(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.76	   U84^1(X1, X2, mark(X3)) -> U84^1(X1, X2, X3)
743.71/262.76	   U84^1(active(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.76	   U84^1(X1, active(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.76	   U84^1(X1, X2, active(X3)) -> U84^1(X1, X2, X3)
743.71/262.76	
743.71/262.76	R is empty.
743.71/262.76	The set Q consists of the following terms:
743.71/262.76	
743.71/262.76	   active(U101(tt, x0, x1))
743.71/262.76	   active(U102(tt, x0, x1))
743.71/262.76	   active(U103(tt, x0, x1))
743.71/262.76	   active(U104(tt, x0, x1))
743.71/262.76	   active(U11(tt, x0, x1))
743.71/262.76	   active(U12(tt, x0, x1))
743.71/262.76	   active(U13(tt, x0, x1))
743.71/262.76	   active(U14(tt, x0, x1))
743.71/262.76	   active(U15(tt, x0))
743.71/262.76	   active(U16(tt))
743.71/262.76	   active(U21(tt, x0))
743.71/262.76	   active(U22(tt, x0))
743.71/262.76	   active(U23(tt))
743.71/262.76	   active(U31(tt, x0, x1))
743.71/262.76	   active(U32(tt, x0, x1))
743.71/262.76	   active(U33(tt, x0, x1))
743.71/262.76	   active(U34(tt, x0, x1))
743.71/262.76	   active(U35(tt, x0))
743.71/262.76	   active(U36(tt))
743.71/262.76	   active(U41(tt, x0))
743.71/262.76	   active(U42(tt))
743.71/262.76	   active(U51(tt))
743.71/262.76	   active(U61(tt, x0))
743.71/262.76	   active(U62(tt))
743.71/262.76	   active(U71(tt, x0))
743.71/262.76	   active(U72(tt, x0))
743.71/262.76	   active(U81(tt, x0, x1))
743.71/262.76	   active(U82(tt, x0, x1))
743.71/262.76	   active(U83(tt, x0, x1))
743.71/262.76	   active(U84(tt, x0, x1))
743.71/262.76	   active(U91(tt, x0))
743.71/262.76	   active(U92(tt))
743.71/262.76	   active(isNat(0))
743.71/262.76	   active(isNat(plus(x0, x1)))
743.71/262.76	   active(isNat(s(x0)))
743.71/262.76	   active(isNat(x(x0, x1)))
743.71/262.76	   active(isNatKind(0))
743.71/262.76	   active(isNatKind(plus(x0, x1)))
743.71/262.76	   active(isNatKind(s(x0)))
743.71/262.76	   active(isNatKind(x(x0, x1)))
743.71/262.76	   active(plus(x0, 0))
743.71/262.76	   active(plus(x0, s(x1)))
743.71/262.76	   active(x(x0, 0))
743.71/262.76	   active(x(x0, s(x1)))
743.71/262.76	   mark(U101(x0, x1, x2))
743.71/262.76	   mark(tt)
743.71/262.76	   mark(U102(x0, x1, x2))
743.71/262.76	   mark(isNatKind(x0))
743.71/262.76	   mark(U103(x0, x1, x2))
743.71/262.76	   mark(isNat(x0))
743.71/262.76	   mark(U104(x0, x1, x2))
743.71/262.76	   mark(plus(x0, x1))
743.71/262.76	   mark(x(x0, x1))
743.71/262.76	   mark(U11(x0, x1, x2))
743.71/262.76	   mark(U12(x0, x1, x2))
743.71/262.76	   mark(U13(x0, x1, x2))
743.71/262.76	   mark(U14(x0, x1, x2))
743.71/262.76	   mark(U15(x0, x1))
743.71/262.76	   mark(U16(x0))
743.71/262.76	   mark(U21(x0, x1))
743.71/262.76	   mark(U22(x0, x1))
743.71/262.76	   mark(U23(x0))
743.71/262.76	   mark(U31(x0, x1, x2))
743.71/262.76	   mark(U32(x0, x1, x2))
743.71/262.76	   mark(U33(x0, x1, x2))
743.71/262.76	   mark(U34(x0, x1, x2))
743.71/262.76	   mark(U35(x0, x1))
743.71/262.76	   mark(U36(x0))
743.71/262.76	   mark(U41(x0, x1))
743.71/262.76	   mark(U42(x0))
743.71/262.76	   mark(U51(x0))
743.71/262.76	   mark(U61(x0, x1))
743.71/262.76	   mark(U62(x0))
743.71/262.76	   mark(U71(x0, x1))
743.71/262.76	   mark(U72(x0, x1))
743.71/262.76	   mark(U81(x0, x1, x2))
743.71/262.76	   mark(U82(x0, x1, x2))
743.71/262.76	   mark(U83(x0, x1, x2))
743.71/262.76	   mark(U84(x0, x1, x2))
743.71/262.76	   mark(s(x0))
743.71/262.76	   mark(U91(x0, x1))
743.71/262.76	   mark(U92(x0))
743.71/262.76	   mark(0)
743.71/262.76	   U101(mark(x0), x1, x2)
743.71/262.76	   U101(x0, mark(x1), x2)
743.71/262.76	   U101(x0, x1, mark(x2))
743.71/262.76	   U101(active(x0), x1, x2)
743.71/262.76	   U101(x0, active(x1), x2)
743.71/262.76	   U101(x0, x1, active(x2))
743.71/262.76	   U102(mark(x0), x1, x2)
743.71/262.76	   U102(x0, mark(x1), x2)
743.71/262.76	   U102(x0, x1, mark(x2))
743.71/262.76	   U102(active(x0), x1, x2)
743.71/262.76	   U102(x0, active(x1), x2)
743.71/262.76	   U102(x0, x1, active(x2))
743.71/262.76	   isNatKind(mark(x0))
743.71/262.76	   isNatKind(active(x0))
743.71/262.76	   U103(mark(x0), x1, x2)
743.71/262.76	   U103(x0, mark(x1), x2)
743.71/262.76	   U103(x0, x1, mark(x2))
743.71/262.76	   U103(active(x0), x1, x2)
743.71/262.76	   U103(x0, active(x1), x2)
743.71/262.76	   U103(x0, x1, active(x2))
743.71/262.76	   isNat(mark(x0))
743.71/262.76	   isNat(active(x0))
743.71/262.76	   U104(mark(x0), x1, x2)
743.71/262.76	   U104(x0, mark(x1), x2)
743.71/262.76	   U104(x0, x1, mark(x2))
743.71/262.76	   U104(active(x0), x1, x2)
743.71/262.76	   U104(x0, active(x1), x2)
743.71/262.76	   U104(x0, x1, active(x2))
743.71/262.76	   plus(mark(x0), x1)
743.71/262.76	   plus(x0, mark(x1))
743.71/262.76	   plus(active(x0), x1)
743.71/262.76	   plus(x0, active(x1))
743.71/262.76	   x(mark(x0), x1)
743.71/262.76	   x(x0, mark(x1))
743.71/262.76	   x(active(x0), x1)
743.71/262.76	   x(x0, active(x1))
743.71/262.76	   U11(mark(x0), x1, x2)
743.71/262.76	   U11(x0, mark(x1), x2)
743.71/262.76	   U11(x0, x1, mark(x2))
743.71/262.76	   U11(active(x0), x1, x2)
743.71/262.76	   U11(x0, active(x1), x2)
743.71/262.76	   U11(x0, x1, active(x2))
743.71/262.76	   U12(mark(x0), x1, x2)
743.71/262.76	   U12(x0, mark(x1), x2)
743.71/262.76	   U12(x0, x1, mark(x2))
743.71/262.76	   U12(active(x0), x1, x2)
743.71/262.76	   U12(x0, active(x1), x2)
743.71/262.76	   U12(x0, x1, active(x2))
743.71/262.76	   U13(mark(x0), x1, x2)
743.71/262.76	   U13(x0, mark(x1), x2)
743.71/262.76	   U13(x0, x1, mark(x2))
743.71/262.76	   U13(active(x0), x1, x2)
743.71/262.76	   U13(x0, active(x1), x2)
743.71/262.76	   U13(x0, x1, active(x2))
743.71/262.76	   U14(mark(x0), x1, x2)
743.71/262.76	   U14(x0, mark(x1), x2)
743.71/262.76	   U14(x0, x1, mark(x2))
743.71/262.76	   U14(active(x0), x1, x2)
743.71/262.76	   U14(x0, active(x1), x2)
743.71/262.76	   U14(x0, x1, active(x2))
743.71/262.76	   U15(mark(x0), x1)
743.71/262.76	   U15(x0, mark(x1))
743.71/262.76	   U15(active(x0), x1)
743.71/262.76	   U15(x0, active(x1))
743.71/262.76	   U16(mark(x0))
743.71/262.76	   U16(active(x0))
743.71/262.76	   U21(mark(x0), x1)
743.71/262.76	   U21(x0, mark(x1))
743.71/262.76	   U21(active(x0), x1)
743.71/262.76	   U21(x0, active(x1))
743.71/262.76	   U22(mark(x0), x1)
743.71/262.76	   U22(x0, mark(x1))
743.71/262.76	   U22(active(x0), x1)
743.71/262.76	   U22(x0, active(x1))
743.71/262.76	   U23(mark(x0))
743.71/262.76	   U23(active(x0))
743.71/262.76	   U31(mark(x0), x1, x2)
743.71/262.76	   U31(x0, mark(x1), x2)
743.71/262.76	   U31(x0, x1, mark(x2))
743.71/262.76	   U31(active(x0), x1, x2)
743.71/262.76	   U31(x0, active(x1), x2)
743.71/262.76	   U31(x0, x1, active(x2))
743.71/262.76	   U32(mark(x0), x1, x2)
743.71/262.76	   U32(x0, mark(x1), x2)
743.71/262.76	   U32(x0, x1, mark(x2))
743.71/262.76	   U32(active(x0), x1, x2)
743.71/262.76	   U32(x0, active(x1), x2)
743.71/262.76	   U32(x0, x1, active(x2))
743.71/262.76	   U33(mark(x0), x1, x2)
743.71/262.76	   U33(x0, mark(x1), x2)
743.71/262.76	   U33(x0, x1, mark(x2))
743.71/262.76	   U33(active(x0), x1, x2)
743.71/262.76	   U33(x0, active(x1), x2)
743.71/262.76	   U33(x0, x1, active(x2))
743.71/262.76	   U34(mark(x0), x1, x2)
743.71/262.76	   U34(x0, mark(x1), x2)
743.71/262.76	   U34(x0, x1, mark(x2))
743.71/262.76	   U34(active(x0), x1, x2)
743.71/262.76	   U34(x0, active(x1), x2)
743.71/262.76	   U34(x0, x1, active(x2))
743.71/262.76	   U35(mark(x0), x1)
743.71/262.76	   U35(x0, mark(x1))
743.71/262.76	   U35(active(x0), x1)
743.71/262.76	   U35(x0, active(x1))
743.71/262.76	   U36(mark(x0))
743.71/262.76	   U36(active(x0))
743.71/262.76	   U41(mark(x0), x1)
743.71/262.76	   U41(x0, mark(x1))
743.71/262.76	   U41(active(x0), x1)
743.71/262.76	   U41(x0, active(x1))
743.71/262.76	   U42(mark(x0))
743.71/262.76	   U42(active(x0))
743.71/262.76	   U51(mark(x0))
743.71/262.76	   U51(active(x0))
743.71/262.76	   U61(mark(x0), x1)
743.71/262.76	   U61(x0, mark(x1))
743.71/262.76	   U61(active(x0), x1)
743.71/262.76	   U61(x0, active(x1))
743.71/262.76	   U62(mark(x0))
743.71/262.76	   U62(active(x0))
743.71/262.76	   U71(mark(x0), x1)
743.71/262.76	   U71(x0, mark(x1))
743.71/262.76	   U71(active(x0), x1)
743.71/262.76	   U71(x0, active(x1))
743.71/262.76	   U72(mark(x0), x1)
743.71/262.76	   U72(x0, mark(x1))
743.71/262.76	   U72(active(x0), x1)
743.71/262.76	   U72(x0, active(x1))
743.71/262.76	   U81(mark(x0), x1, x2)
743.71/262.76	   U81(x0, mark(x1), x2)
743.71/262.76	   U81(x0, x1, mark(x2))
743.71/262.76	   U81(active(x0), x1, x2)
743.71/262.76	   U81(x0, active(x1), x2)
743.71/262.76	   U81(x0, x1, active(x2))
743.71/262.76	   U82(mark(x0), x1, x2)
743.71/262.76	   U82(x0, mark(x1), x2)
743.71/262.76	   U82(x0, x1, mark(x2))
743.71/262.76	   U82(active(x0), x1, x2)
743.71/262.76	   U82(x0, active(x1), x2)
743.71/262.76	   U82(x0, x1, active(x2))
743.71/262.76	   U83(mark(x0), x1, x2)
743.71/262.76	   U83(x0, mark(x1), x2)
743.71/262.76	   U83(x0, x1, mark(x2))
743.71/262.76	   U83(active(x0), x1, x2)
743.71/262.76	   U83(x0, active(x1), x2)
743.71/262.76	   U83(x0, x1, active(x2))
743.71/262.76	   U84(mark(x0), x1, x2)
743.71/262.76	   U84(x0, mark(x1), x2)
743.71/262.76	   U84(x0, x1, mark(x2))
743.71/262.76	   U84(active(x0), x1, x2)
743.71/262.76	   U84(x0, active(x1), x2)
743.71/262.76	   U84(x0, x1, active(x2))
743.71/262.76	   s(mark(x0))
743.71/262.76	   s(active(x0))
743.71/262.76	   U91(mark(x0), x1)
743.71/262.76	   U91(x0, mark(x1))
743.71/262.76	   U91(active(x0), x1)
743.71/262.76	   U91(x0, active(x1))
743.71/262.76	   U92(mark(x0))
743.71/262.76	   U92(active(x0))
743.71/262.76	
743.71/262.76	We have to consider all minimal (P,Q,R)-chains.
743.71/262.76	----------------------------------------
743.71/262.76	
743.71/262.76	(29) QReductionProof (EQUIVALENT)
743.71/262.76	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.76	
743.71/262.76	   U101(mark(x0), x1, x2)
743.71/262.76	   U101(x0, mark(x1), x2)
743.71/262.76	   U101(x0, x1, mark(x2))
743.71/262.76	   U101(active(x0), x1, x2)
743.71/262.76	   U101(x0, active(x1), x2)
743.71/262.76	   U101(x0, x1, active(x2))
743.71/262.76	   U102(mark(x0), x1, x2)
743.71/262.76	   U102(x0, mark(x1), x2)
743.71/262.76	   U102(x0, x1, mark(x2))
743.71/262.76	   U102(active(x0), x1, x2)
743.71/262.76	   U102(x0, active(x1), x2)
743.71/262.76	   U102(x0, x1, active(x2))
743.71/262.76	   isNatKind(mark(x0))
743.71/262.76	   isNatKind(active(x0))
743.71/262.76	   U103(mark(x0), x1, x2)
743.71/262.76	   U103(x0, mark(x1), x2)
743.71/262.76	   U103(x0, x1, mark(x2))
743.71/262.76	   U103(active(x0), x1, x2)
743.71/262.76	   U103(x0, active(x1), x2)
743.71/262.76	   U103(x0, x1, active(x2))
743.71/262.76	   isNat(mark(x0))
743.71/262.76	   isNat(active(x0))
743.71/262.76	   U104(mark(x0), x1, x2)
743.71/262.76	   U104(x0, mark(x1), x2)
743.71/262.76	   U104(x0, x1, mark(x2))
743.71/262.76	   U104(active(x0), x1, x2)
743.71/262.76	   U104(x0, active(x1), x2)
743.71/262.76	   U104(x0, x1, active(x2))
743.71/262.76	   plus(mark(x0), x1)
743.71/262.76	   plus(x0, mark(x1))
743.71/262.76	   plus(active(x0), x1)
743.71/262.76	   plus(x0, active(x1))
743.71/262.76	   x(mark(x0), x1)
743.71/262.76	   x(x0, mark(x1))
743.71/262.76	   x(active(x0), x1)
743.71/262.76	   x(x0, active(x1))
743.71/262.76	   U11(mark(x0), x1, x2)
743.71/262.76	   U11(x0, mark(x1), x2)
743.71/262.76	   U11(x0, x1, mark(x2))
743.71/262.76	   U11(active(x0), x1, x2)
743.71/262.76	   U11(x0, active(x1), x2)
743.71/262.76	   U11(x0, x1, active(x2))
743.71/262.76	   U12(mark(x0), x1, x2)
743.71/262.76	   U12(x0, mark(x1), x2)
743.71/262.76	   U12(x0, x1, mark(x2))
743.71/262.76	   U12(active(x0), x1, x2)
743.71/262.76	   U12(x0, active(x1), x2)
743.71/262.76	   U12(x0, x1, active(x2))
743.71/262.76	   U13(mark(x0), x1, x2)
743.71/262.76	   U13(x0, mark(x1), x2)
743.71/262.76	   U13(x0, x1, mark(x2))
743.71/262.76	   U13(active(x0), x1, x2)
743.71/262.76	   U13(x0, active(x1), x2)
743.71/262.76	   U13(x0, x1, active(x2))
743.71/262.76	   U14(mark(x0), x1, x2)
743.71/262.76	   U14(x0, mark(x1), x2)
743.71/262.76	   U14(x0, x1, mark(x2))
743.71/262.76	   U14(active(x0), x1, x2)
743.71/262.76	   U14(x0, active(x1), x2)
743.71/262.76	   U14(x0, x1, active(x2))
743.71/262.76	   U15(mark(x0), x1)
743.71/262.76	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.77	   U22(active(x0), x1)
743.71/262.77	   U22(x0, active(x1))
743.71/262.77	   U23(mark(x0))
743.71/262.77	   U23(active(x0))
743.71/262.77	   U31(mark(x0), x1, x2)
743.71/262.77	   U31(x0, mark(x1), x2)
743.71/262.77	   U31(x0, x1, mark(x2))
743.71/262.77	   U31(active(x0), x1, x2)
743.71/262.77	   U31(x0, active(x1), x2)
743.71/262.77	   U31(x0, x1, active(x2))
743.71/262.77	   U32(mark(x0), x1, x2)
743.71/262.77	   U32(x0, mark(x1), x2)
743.71/262.77	   U32(x0, x1, mark(x2))
743.71/262.77	   U32(active(x0), x1, x2)
743.71/262.77	   U32(x0, active(x1), x2)
743.71/262.77	   U32(x0, x1, active(x2))
743.71/262.77	   U33(mark(x0), x1, x2)
743.71/262.77	   U33(x0, mark(x1), x2)
743.71/262.77	   U33(x0, x1, mark(x2))
743.71/262.77	   U33(active(x0), x1, x2)
743.71/262.77	   U33(x0, active(x1), x2)
743.71/262.77	   U33(x0, x1, active(x2))
743.71/262.77	   U34(mark(x0), x1, x2)
743.71/262.77	   U34(x0, mark(x1), x2)
743.71/262.77	   U34(x0, x1, mark(x2))
743.71/262.77	   U34(active(x0), x1, x2)
743.71/262.77	   U34(x0, active(x1), x2)
743.71/262.77	   U34(x0, x1, active(x2))
743.71/262.77	   U35(mark(x0), x1)
743.71/262.77	   U35(x0, mark(x1))
743.71/262.77	   U35(active(x0), x1)
743.71/262.77	   U35(x0, active(x1))
743.71/262.77	   U36(mark(x0))
743.71/262.77	   U36(active(x0))
743.71/262.77	   U41(mark(x0), x1)
743.71/262.77	   U41(x0, mark(x1))
743.71/262.77	   U41(active(x0), x1)
743.71/262.77	   U41(x0, active(x1))
743.71/262.77	   U42(mark(x0))
743.71/262.77	   U42(active(x0))
743.71/262.77	   U51(mark(x0))
743.71/262.77	   U51(active(x0))
743.71/262.77	   U61(mark(x0), x1)
743.71/262.77	   U61(x0, mark(x1))
743.71/262.77	   U61(active(x0), x1)
743.71/262.77	   U61(x0, active(x1))
743.71/262.77	   U62(mark(x0))
743.71/262.77	   U62(active(x0))
743.71/262.77	   U71(mark(x0), x1)
743.71/262.77	   U71(x0, mark(x1))
743.71/262.77	   U71(active(x0), x1)
743.71/262.77	   U71(x0, active(x1))
743.71/262.77	   U72(mark(x0), x1)
743.71/262.77	   U72(x0, mark(x1))
743.71/262.77	   U72(active(x0), x1)
743.71/262.77	   U72(x0, active(x1))
743.71/262.77	   U81(mark(x0), x1, x2)
743.71/262.77	   U81(x0, mark(x1), x2)
743.71/262.77	   U81(x0, x1, mark(x2))
743.71/262.77	   U81(active(x0), x1, x2)
743.71/262.77	   U81(x0, active(x1), x2)
743.71/262.77	   U81(x0, x1, active(x2))
743.71/262.77	   U82(mark(x0), x1, x2)
743.71/262.77	   U82(x0, mark(x1), x2)
743.71/262.77	   U82(x0, x1, mark(x2))
743.71/262.77	   U82(active(x0), x1, x2)
743.71/262.77	   U82(x0, active(x1), x2)
743.71/262.77	   U82(x0, x1, active(x2))
743.71/262.77	   U83(mark(x0), x1, x2)
743.71/262.77	   U83(x0, mark(x1), x2)
743.71/262.77	   U83(x0, x1, mark(x2))
743.71/262.77	   U83(active(x0), x1, x2)
743.71/262.77	   U83(x0, active(x1), x2)
743.71/262.77	   U83(x0, x1, active(x2))
743.71/262.77	   U84(mark(x0), x1, x2)
743.71/262.77	   U84(x0, mark(x1), x2)
743.71/262.77	   U84(x0, x1, mark(x2))
743.71/262.77	   U84(active(x0), x1, x2)
743.71/262.77	   U84(x0, active(x1), x2)
743.71/262.77	   U84(x0, x1, active(x2))
743.71/262.77	   s(mark(x0))
743.71/262.77	   s(active(x0))
743.71/262.77	   U91(mark(x0), x1)
743.71/262.77	   U91(x0, mark(x1))
743.71/262.77	   U91(active(x0), x1)
743.71/262.77	   U91(x0, active(x1))
743.71/262.77	   U92(mark(x0))
743.71/262.77	   U92(active(x0))
743.71/262.77	
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(30)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U84^1(X1, mark(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.77	   U84^1(mark(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.77	   U84^1(X1, X2, mark(X3)) -> U84^1(X1, X2, X3)
743.71/262.77	   U84^1(active(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.77	   U84^1(X1, active(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.77	   U84^1(X1, X2, active(X3)) -> U84^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	R is empty.
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	
743.71/262.77	We have to consider all minimal (P,Q,R)-chains.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(31) QDPSizeChangeProof (EQUIVALENT)
743.71/262.77	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. 
743.71/262.77	
743.71/262.77	From the DPs we obtained the following set of size-change graphs:
743.71/262.77	*U84^1(X1, mark(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U84^1(mark(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U84^1(X1, X2, mark(X3)) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U84^1(active(X1), X2, X3) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U84^1(X1, active(X2), X3) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U84^1(X1, X2, active(X3)) -> U84^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.77	
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(32)
743.71/262.77	YES
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(33)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U83^1(X1, mark(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(mark(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, mark(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(active(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, active(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, active(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	The TRS R consists of the following rules:
743.71/262.77	
743.71/262.77	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.77	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.77	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.77	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.77	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.77	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.77	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.77	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.77	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.77	   active(U16(tt)) -> mark(tt)
743.71/262.77	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.77	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.77	   active(U23(tt)) -> mark(tt)
743.71/262.77	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.77	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.77	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.77	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.77	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.77	   active(U36(tt)) -> mark(tt)
743.71/262.77	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.77	   active(U42(tt)) -> mark(tt)
743.71/262.77	   active(U51(tt)) -> mark(tt)
743.71/262.77	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.77	   active(U62(tt)) -> mark(tt)
743.71/262.77	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.77	   active(U72(tt, N)) -> mark(N)
743.71/262.77	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.77	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.77	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.77	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.77	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.77	   active(U92(tt)) -> mark(0)
743.71/262.77	   active(isNat(0)) -> mark(tt)
743.71/262.77	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.77	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.77	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.77	   active(isNatKind(0)) -> mark(tt)
743.71/262.77	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.77	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.77	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.77	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.77	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.77	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.77	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.77	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.77	   mark(tt) -> active(tt)
743.71/262.77	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.77	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.77	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.77	   mark(isNat(X)) -> active(isNat(X))
743.71/262.77	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.77	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.77	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.77	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.77	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.77	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.77	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.77	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.77	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.77	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.77	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.77	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.77	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.77	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.77	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.77	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.77	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.77	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.77	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.77	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.77	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.77	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.77	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.77	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.77	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.77	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.77	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.77	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.77	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.77	   mark(s(X)) -> active(s(mark(X)))
743.71/262.77	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.77	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.77	   mark(0) -> active(0)
743.71/262.77	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.77	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.77	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.77	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.77	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.77	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.77	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.77	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.77	   isNat(mark(X)) -> isNat(X)
743.71/262.77	   isNat(active(X)) -> isNat(X)
743.71/262.77	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.77	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.77	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.77	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.77	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.77	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.77	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.77	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.77	   x(active(X1), X2) -> x(X1, X2)
743.71/262.77	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.77	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.77	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.77	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.77	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.77	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.77	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.77	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.77	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.77	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.77	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.77	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.77	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.77	   U16(mark(X)) -> U16(X)
743.71/262.77	   U16(active(X)) -> U16(X)
743.71/262.77	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.77	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.77	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.77	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.77	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.77	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.77	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.77	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.77	   U23(mark(X)) -> U23(X)
743.71/262.77	   U23(active(X)) -> U23(X)
743.71/262.77	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.77	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.77	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.77	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.77	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.77	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.77	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.77	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.77	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.77	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.77	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.77	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.77	   U36(mark(X)) -> U36(X)
743.71/262.77	   U36(active(X)) -> U36(X)
743.71/262.77	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.77	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.77	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.77	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.77	   U42(mark(X)) -> U42(X)
743.71/262.77	   U42(active(X)) -> U42(X)
743.71/262.77	   U51(mark(X)) -> U51(X)
743.71/262.77	   U51(active(X)) -> U51(X)
743.71/262.77	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.77	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.77	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.77	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.77	   U62(mark(X)) -> U62(X)
743.71/262.77	   U62(active(X)) -> U62(X)
743.71/262.77	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.77	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.77	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.77	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.77	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.77	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.77	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.77	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.77	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.77	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.77	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.77	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.77	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.77	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.77	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.77	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.77	   s(mark(X)) -> s(X)
743.71/262.77	   s(active(X)) -> s(X)
743.71/262.77	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.77	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.77	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.77	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.77	   U92(mark(X)) -> U92(X)
743.71/262.77	   U92(active(X)) -> U92(X)
743.71/262.77	
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	   U101(mark(x0), x1, x2)
743.71/262.77	   U101(x0, mark(x1), x2)
743.71/262.77	   U101(x0, x1, mark(x2))
743.71/262.77	   U101(active(x0), x1, x2)
743.71/262.77	   U101(x0, active(x1), x2)
743.71/262.77	   U101(x0, x1, active(x2))
743.71/262.77	   U102(mark(x0), x1, x2)
743.71/262.77	   U102(x0, mark(x1), x2)
743.71/262.77	   U102(x0, x1, mark(x2))
743.71/262.77	   U102(active(x0), x1, x2)
743.71/262.77	   U102(x0, active(x1), x2)
743.71/262.77	   U102(x0, x1, active(x2))
743.71/262.77	   isNatKind(mark(x0))
743.71/262.77	   isNatKind(active(x0))
743.71/262.77	   U103(mark(x0), x1, x2)
743.71/262.77	   U103(x0, mark(x1), x2)
743.71/262.77	   U103(x0, x1, mark(x2))
743.71/262.77	   U103(active(x0), x1, x2)
743.71/262.77	   U103(x0, active(x1), x2)
743.71/262.77	   U103(x0, x1, active(x2))
743.71/262.77	   isNat(mark(x0))
743.71/262.77	   isNat(active(x0))
743.71/262.77	   U104(mark(x0), x1, x2)
743.71/262.77	   U104(x0, mark(x1), x2)
743.71/262.77	   U104(x0, x1, mark(x2))
743.71/262.77	   U104(active(x0), x1, x2)
743.71/262.77	   U104(x0, active(x1), x2)
743.71/262.77	   U104(x0, x1, active(x2))
743.71/262.77	   plus(mark(x0), x1)
743.71/262.77	   plus(x0, mark(x1))
743.71/262.77	   plus(active(x0), x1)
743.71/262.77	   plus(x0, active(x1))
743.71/262.77	   x(mark(x0), x1)
743.71/262.77	   x(x0, mark(x1))
743.71/262.77	   x(active(x0), x1)
743.71/262.77	   x(x0, active(x1))
743.71/262.77	   U11(mark(x0), x1, x2)
743.71/262.77	   U11(x0, mark(x1), x2)
743.71/262.77	   U11(x0, x1, mark(x2))
743.71/262.77	   U11(active(x0), x1, x2)
743.71/262.77	   U11(x0, active(x1), x2)
743.71/262.77	   U11(x0, x1, active(x2))
743.71/262.77	   U12(mark(x0), x1, x2)
743.71/262.77	   U12(x0, mark(x1), x2)
743.71/262.77	   U12(x0, x1, mark(x2))
743.71/262.77	   U12(active(x0), x1, x2)
743.71/262.77	   U12(x0, active(x1), x2)
743.71/262.77	   U12(x0, x1, active(x2))
743.71/262.77	   U13(mark(x0), x1, x2)
743.71/262.77	   U13(x0, mark(x1), x2)
743.71/262.77	   U13(x0, x1, mark(x2))
743.71/262.77	   U13(active(x0), x1, x2)
743.71/262.77	   U13(x0, active(x1), x2)
743.71/262.77	   U13(x0, x1, active(x2))
743.71/262.77	   U14(mark(x0), x1, x2)
743.71/262.77	   U14(x0, mark(x1), x2)
743.71/262.77	   U14(x0, x1, mark(x2))
743.71/262.77	   U14(active(x0), x1, x2)
743.71/262.77	   U14(x0, active(x1), x2)
743.71/262.77	   U14(x0, x1, active(x2))
743.71/262.77	   U15(mark(x0), x1)
743.71/262.77	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.77	   U22(active(x0), x1)
743.71/262.77	   U22(x0, active(x1))
743.71/262.77	   U23(mark(x0))
743.71/262.77	   U23(active(x0))
743.71/262.77	   U31(mark(x0), x1, x2)
743.71/262.77	   U31(x0, mark(x1), x2)
743.71/262.77	   U31(x0, x1, mark(x2))
743.71/262.77	   U31(active(x0), x1, x2)
743.71/262.77	   U31(x0, active(x1), x2)
743.71/262.77	   U31(x0, x1, active(x2))
743.71/262.77	   U32(mark(x0), x1, x2)
743.71/262.77	   U32(x0, mark(x1), x2)
743.71/262.77	   U32(x0, x1, mark(x2))
743.71/262.77	   U32(active(x0), x1, x2)
743.71/262.77	   U32(x0, active(x1), x2)
743.71/262.77	   U32(x0, x1, active(x2))
743.71/262.77	   U33(mark(x0), x1, x2)
743.71/262.77	   U33(x0, mark(x1), x2)
743.71/262.77	   U33(x0, x1, mark(x2))
743.71/262.77	   U33(active(x0), x1, x2)
743.71/262.77	   U33(x0, active(x1), x2)
743.71/262.77	   U33(x0, x1, active(x2))
743.71/262.77	   U34(mark(x0), x1, x2)
743.71/262.77	   U34(x0, mark(x1), x2)
743.71/262.77	   U34(x0, x1, mark(x2))
743.71/262.77	   U34(active(x0), x1, x2)
743.71/262.77	   U34(x0, active(x1), x2)
743.71/262.77	   U34(x0, x1, active(x2))
743.71/262.77	   U35(mark(x0), x1)
743.71/262.77	   U35(x0, mark(x1))
743.71/262.77	   U35(active(x0), x1)
743.71/262.77	   U35(x0, active(x1))
743.71/262.77	   U36(mark(x0))
743.71/262.77	   U36(active(x0))
743.71/262.77	   U41(mark(x0), x1)
743.71/262.77	   U41(x0, mark(x1))
743.71/262.77	   U41(active(x0), x1)
743.71/262.77	   U41(x0, active(x1))
743.71/262.77	   U42(mark(x0))
743.71/262.77	   U42(active(x0))
743.71/262.77	   U51(mark(x0))
743.71/262.77	   U51(active(x0))
743.71/262.77	   U61(mark(x0), x1)
743.71/262.77	   U61(x0, mark(x1))
743.71/262.77	   U61(active(x0), x1)
743.71/262.77	   U61(x0, active(x1))
743.71/262.77	   U62(mark(x0))
743.71/262.77	   U62(active(x0))
743.71/262.77	   U71(mark(x0), x1)
743.71/262.77	   U71(x0, mark(x1))
743.71/262.77	   U71(active(x0), x1)
743.71/262.77	   U71(x0, active(x1))
743.71/262.77	   U72(mark(x0), x1)
743.71/262.77	   U72(x0, mark(x1))
743.71/262.77	   U72(active(x0), x1)
743.71/262.77	   U72(x0, active(x1))
743.71/262.77	   U81(mark(x0), x1, x2)
743.71/262.77	   U81(x0, mark(x1), x2)
743.71/262.77	   U81(x0, x1, mark(x2))
743.71/262.77	   U81(active(x0), x1, x2)
743.71/262.77	   U81(x0, active(x1), x2)
743.71/262.77	   U81(x0, x1, active(x2))
743.71/262.77	   U82(mark(x0), x1, x2)
743.71/262.77	   U82(x0, mark(x1), x2)
743.71/262.77	   U82(x0, x1, mark(x2))
743.71/262.77	   U82(active(x0), x1, x2)
743.71/262.77	   U82(x0, active(x1), x2)
743.71/262.77	   U82(x0, x1, active(x2))
743.71/262.77	   U83(mark(x0), x1, x2)
743.71/262.77	   U83(x0, mark(x1), x2)
743.71/262.77	   U83(x0, x1, mark(x2))
743.71/262.77	   U83(active(x0), x1, x2)
743.71/262.77	   U83(x0, active(x1), x2)
743.71/262.77	   U83(x0, x1, active(x2))
743.71/262.77	   U84(mark(x0), x1, x2)
743.71/262.77	   U84(x0, mark(x1), x2)
743.71/262.77	   U84(x0, x1, mark(x2))
743.71/262.77	   U84(active(x0), x1, x2)
743.71/262.77	   U84(x0, active(x1), x2)
743.71/262.77	   U84(x0, x1, active(x2))
743.71/262.77	   s(mark(x0))
743.71/262.77	   s(active(x0))
743.71/262.77	   U91(mark(x0), x1)
743.71/262.77	   U91(x0, mark(x1))
743.71/262.77	   U91(active(x0), x1)
743.71/262.77	   U91(x0, active(x1))
743.71/262.77	   U92(mark(x0))
743.71/262.77	   U92(active(x0))
743.71/262.77	
743.71/262.77	We have to consider all minimal (P,Q,R)-chains.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(34) UsableRulesProof (EQUIVALENT)
743.71/262.77	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.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(35)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U83^1(X1, mark(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(mark(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, mark(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(active(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, active(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, active(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	R is empty.
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	   U101(mark(x0), x1, x2)
743.71/262.77	   U101(x0, mark(x1), x2)
743.71/262.77	   U101(x0, x1, mark(x2))
743.71/262.77	   U101(active(x0), x1, x2)
743.71/262.77	   U101(x0, active(x1), x2)
743.71/262.77	   U101(x0, x1, active(x2))
743.71/262.77	   U102(mark(x0), x1, x2)
743.71/262.77	   U102(x0, mark(x1), x2)
743.71/262.77	   U102(x0, x1, mark(x2))
743.71/262.77	   U102(active(x0), x1, x2)
743.71/262.77	   U102(x0, active(x1), x2)
743.71/262.77	   U102(x0, x1, active(x2))
743.71/262.77	   isNatKind(mark(x0))
743.71/262.77	   isNatKind(active(x0))
743.71/262.77	   U103(mark(x0), x1, x2)
743.71/262.77	   U103(x0, mark(x1), x2)
743.71/262.77	   U103(x0, x1, mark(x2))
743.71/262.77	   U103(active(x0), x1, x2)
743.71/262.77	   U103(x0, active(x1), x2)
743.71/262.77	   U103(x0, x1, active(x2))
743.71/262.77	   isNat(mark(x0))
743.71/262.77	   isNat(active(x0))
743.71/262.77	   U104(mark(x0), x1, x2)
743.71/262.77	   U104(x0, mark(x1), x2)
743.71/262.77	   U104(x0, x1, mark(x2))
743.71/262.77	   U104(active(x0), x1, x2)
743.71/262.77	   U104(x0, active(x1), x2)
743.71/262.77	   U104(x0, x1, active(x2))
743.71/262.77	   plus(mark(x0), x1)
743.71/262.77	   plus(x0, mark(x1))
743.71/262.77	   plus(active(x0), x1)
743.71/262.77	   plus(x0, active(x1))
743.71/262.77	   x(mark(x0), x1)
743.71/262.77	   x(x0, mark(x1))
743.71/262.77	   x(active(x0), x1)
743.71/262.77	   x(x0, active(x1))
743.71/262.77	   U11(mark(x0), x1, x2)
743.71/262.77	   U11(x0, mark(x1), x2)
743.71/262.77	   U11(x0, x1, mark(x2))
743.71/262.77	   U11(active(x0), x1, x2)
743.71/262.77	   U11(x0, active(x1), x2)
743.71/262.77	   U11(x0, x1, active(x2))
743.71/262.77	   U12(mark(x0), x1, x2)
743.71/262.77	   U12(x0, mark(x1), x2)
743.71/262.77	   U12(x0, x1, mark(x2))
743.71/262.77	   U12(active(x0), x1, x2)
743.71/262.77	   U12(x0, active(x1), x2)
743.71/262.77	   U12(x0, x1, active(x2))
743.71/262.77	   U13(mark(x0), x1, x2)
743.71/262.77	   U13(x0, mark(x1), x2)
743.71/262.77	   U13(x0, x1, mark(x2))
743.71/262.77	   U13(active(x0), x1, x2)
743.71/262.77	   U13(x0, active(x1), x2)
743.71/262.77	   U13(x0, x1, active(x2))
743.71/262.77	   U14(mark(x0), x1, x2)
743.71/262.77	   U14(x0, mark(x1), x2)
743.71/262.77	   U14(x0, x1, mark(x2))
743.71/262.77	   U14(active(x0), x1, x2)
743.71/262.77	   U14(x0, active(x1), x2)
743.71/262.77	   U14(x0, x1, active(x2))
743.71/262.77	   U15(mark(x0), x1)
743.71/262.77	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.77	   U22(active(x0), x1)
743.71/262.77	   U22(x0, active(x1))
743.71/262.77	   U23(mark(x0))
743.71/262.77	   U23(active(x0))
743.71/262.77	   U31(mark(x0), x1, x2)
743.71/262.77	   U31(x0, mark(x1), x2)
743.71/262.77	   U31(x0, x1, mark(x2))
743.71/262.77	   U31(active(x0), x1, x2)
743.71/262.77	   U31(x0, active(x1), x2)
743.71/262.77	   U31(x0, x1, active(x2))
743.71/262.77	   U32(mark(x0), x1, x2)
743.71/262.77	   U32(x0, mark(x1), x2)
743.71/262.77	   U32(x0, x1, mark(x2))
743.71/262.77	   U32(active(x0), x1, x2)
743.71/262.77	   U32(x0, active(x1), x2)
743.71/262.77	   U32(x0, x1, active(x2))
743.71/262.77	   U33(mark(x0), x1, x2)
743.71/262.77	   U33(x0, mark(x1), x2)
743.71/262.77	   U33(x0, x1, mark(x2))
743.71/262.77	   U33(active(x0), x1, x2)
743.71/262.77	   U33(x0, active(x1), x2)
743.71/262.77	   U33(x0, x1, active(x2))
743.71/262.77	   U34(mark(x0), x1, x2)
743.71/262.77	   U34(x0, mark(x1), x2)
743.71/262.77	   U34(x0, x1, mark(x2))
743.71/262.77	   U34(active(x0), x1, x2)
743.71/262.77	   U34(x0, active(x1), x2)
743.71/262.77	   U34(x0, x1, active(x2))
743.71/262.77	   U35(mark(x0), x1)
743.71/262.77	   U35(x0, mark(x1))
743.71/262.77	   U35(active(x0), x1)
743.71/262.77	   U35(x0, active(x1))
743.71/262.77	   U36(mark(x0))
743.71/262.77	   U36(active(x0))
743.71/262.77	   U41(mark(x0), x1)
743.71/262.77	   U41(x0, mark(x1))
743.71/262.77	   U41(active(x0), x1)
743.71/262.77	   U41(x0, active(x1))
743.71/262.77	   U42(mark(x0))
743.71/262.77	   U42(active(x0))
743.71/262.77	   U51(mark(x0))
743.71/262.77	   U51(active(x0))
743.71/262.77	   U61(mark(x0), x1)
743.71/262.77	   U61(x0, mark(x1))
743.71/262.77	   U61(active(x0), x1)
743.71/262.77	   U61(x0, active(x1))
743.71/262.77	   U62(mark(x0))
743.71/262.77	   U62(active(x0))
743.71/262.77	   U71(mark(x0), x1)
743.71/262.77	   U71(x0, mark(x1))
743.71/262.77	   U71(active(x0), x1)
743.71/262.77	   U71(x0, active(x1))
743.71/262.77	   U72(mark(x0), x1)
743.71/262.77	   U72(x0, mark(x1))
743.71/262.77	   U72(active(x0), x1)
743.71/262.77	   U72(x0, active(x1))
743.71/262.77	   U81(mark(x0), x1, x2)
743.71/262.77	   U81(x0, mark(x1), x2)
743.71/262.77	   U81(x0, x1, mark(x2))
743.71/262.77	   U81(active(x0), x1, x2)
743.71/262.77	   U81(x0, active(x1), x2)
743.71/262.77	   U81(x0, x1, active(x2))
743.71/262.77	   U82(mark(x0), x1, x2)
743.71/262.77	   U82(x0, mark(x1), x2)
743.71/262.77	   U82(x0, x1, mark(x2))
743.71/262.77	   U82(active(x0), x1, x2)
743.71/262.77	   U82(x0, active(x1), x2)
743.71/262.77	   U82(x0, x1, active(x2))
743.71/262.77	   U83(mark(x0), x1, x2)
743.71/262.77	   U83(x0, mark(x1), x2)
743.71/262.77	   U83(x0, x1, mark(x2))
743.71/262.77	   U83(active(x0), x1, x2)
743.71/262.77	   U83(x0, active(x1), x2)
743.71/262.77	   U83(x0, x1, active(x2))
743.71/262.77	   U84(mark(x0), x1, x2)
743.71/262.77	   U84(x0, mark(x1), x2)
743.71/262.77	   U84(x0, x1, mark(x2))
743.71/262.77	   U84(active(x0), x1, x2)
743.71/262.77	   U84(x0, active(x1), x2)
743.71/262.77	   U84(x0, x1, active(x2))
743.71/262.77	   s(mark(x0))
743.71/262.77	   s(active(x0))
743.71/262.77	   U91(mark(x0), x1)
743.71/262.77	   U91(x0, mark(x1))
743.71/262.77	   U91(active(x0), x1)
743.71/262.77	   U91(x0, active(x1))
743.71/262.77	   U92(mark(x0))
743.71/262.77	   U92(active(x0))
743.71/262.77	
743.71/262.77	We have to consider all minimal (P,Q,R)-chains.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(36) QReductionProof (EQUIVALENT)
743.71/262.77	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.77	
743.71/262.77	   U101(mark(x0), x1, x2)
743.71/262.77	   U101(x0, mark(x1), x2)
743.71/262.77	   U101(x0, x1, mark(x2))
743.71/262.77	   U101(active(x0), x1, x2)
743.71/262.77	   U101(x0, active(x1), x2)
743.71/262.77	   U101(x0, x1, active(x2))
743.71/262.77	   U102(mark(x0), x1, x2)
743.71/262.77	   U102(x0, mark(x1), x2)
743.71/262.77	   U102(x0, x1, mark(x2))
743.71/262.77	   U102(active(x0), x1, x2)
743.71/262.77	   U102(x0, active(x1), x2)
743.71/262.77	   U102(x0, x1, active(x2))
743.71/262.77	   isNatKind(mark(x0))
743.71/262.77	   isNatKind(active(x0))
743.71/262.77	   U103(mark(x0), x1, x2)
743.71/262.77	   U103(x0, mark(x1), x2)
743.71/262.77	   U103(x0, x1, mark(x2))
743.71/262.77	   U103(active(x0), x1, x2)
743.71/262.77	   U103(x0, active(x1), x2)
743.71/262.77	   U103(x0, x1, active(x2))
743.71/262.77	   isNat(mark(x0))
743.71/262.77	   isNat(active(x0))
743.71/262.77	   U104(mark(x0), x1, x2)
743.71/262.77	   U104(x0, mark(x1), x2)
743.71/262.77	   U104(x0, x1, mark(x2))
743.71/262.77	   U104(active(x0), x1, x2)
743.71/262.77	   U104(x0, active(x1), x2)
743.71/262.77	   U104(x0, x1, active(x2))
743.71/262.77	   plus(mark(x0), x1)
743.71/262.77	   plus(x0, mark(x1))
743.71/262.77	   plus(active(x0), x1)
743.71/262.77	   plus(x0, active(x1))
743.71/262.77	   x(mark(x0), x1)
743.71/262.77	   x(x0, mark(x1))
743.71/262.77	   x(active(x0), x1)
743.71/262.77	   x(x0, active(x1))
743.71/262.77	   U11(mark(x0), x1, x2)
743.71/262.77	   U11(x0, mark(x1), x2)
743.71/262.77	   U11(x0, x1, mark(x2))
743.71/262.77	   U11(active(x0), x1, x2)
743.71/262.77	   U11(x0, active(x1), x2)
743.71/262.77	   U11(x0, x1, active(x2))
743.71/262.77	   U12(mark(x0), x1, x2)
743.71/262.77	   U12(x0, mark(x1), x2)
743.71/262.77	   U12(x0, x1, mark(x2))
743.71/262.77	   U12(active(x0), x1, x2)
743.71/262.77	   U12(x0, active(x1), x2)
743.71/262.77	   U12(x0, x1, active(x2))
743.71/262.77	   U13(mark(x0), x1, x2)
743.71/262.77	   U13(x0, mark(x1), x2)
743.71/262.77	   U13(x0, x1, mark(x2))
743.71/262.77	   U13(active(x0), x1, x2)
743.71/262.77	   U13(x0, active(x1), x2)
743.71/262.77	   U13(x0, x1, active(x2))
743.71/262.77	   U14(mark(x0), x1, x2)
743.71/262.77	   U14(x0, mark(x1), x2)
743.71/262.77	   U14(x0, x1, mark(x2))
743.71/262.77	   U14(active(x0), x1, x2)
743.71/262.77	   U14(x0, active(x1), x2)
743.71/262.77	   U14(x0, x1, active(x2))
743.71/262.77	   U15(mark(x0), x1)
743.71/262.77	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.77	   U22(active(x0), x1)
743.71/262.77	   U22(x0, active(x1))
743.71/262.77	   U23(mark(x0))
743.71/262.77	   U23(active(x0))
743.71/262.77	   U31(mark(x0), x1, x2)
743.71/262.77	   U31(x0, mark(x1), x2)
743.71/262.77	   U31(x0, x1, mark(x2))
743.71/262.77	   U31(active(x0), x1, x2)
743.71/262.77	   U31(x0, active(x1), x2)
743.71/262.77	   U31(x0, x1, active(x2))
743.71/262.77	   U32(mark(x0), x1, x2)
743.71/262.77	   U32(x0, mark(x1), x2)
743.71/262.77	   U32(x0, x1, mark(x2))
743.71/262.77	   U32(active(x0), x1, x2)
743.71/262.77	   U32(x0, active(x1), x2)
743.71/262.77	   U32(x0, x1, active(x2))
743.71/262.77	   U33(mark(x0), x1, x2)
743.71/262.77	   U33(x0, mark(x1), x2)
743.71/262.77	   U33(x0, x1, mark(x2))
743.71/262.77	   U33(active(x0), x1, x2)
743.71/262.77	   U33(x0, active(x1), x2)
743.71/262.77	   U33(x0, x1, active(x2))
743.71/262.77	   U34(mark(x0), x1, x2)
743.71/262.77	   U34(x0, mark(x1), x2)
743.71/262.77	   U34(x0, x1, mark(x2))
743.71/262.77	   U34(active(x0), x1, x2)
743.71/262.77	   U34(x0, active(x1), x2)
743.71/262.77	   U34(x0, x1, active(x2))
743.71/262.77	   U35(mark(x0), x1)
743.71/262.77	   U35(x0, mark(x1))
743.71/262.77	   U35(active(x0), x1)
743.71/262.77	   U35(x0, active(x1))
743.71/262.77	   U36(mark(x0))
743.71/262.77	   U36(active(x0))
743.71/262.77	   U41(mark(x0), x1)
743.71/262.77	   U41(x0, mark(x1))
743.71/262.77	   U41(active(x0), x1)
743.71/262.77	   U41(x0, active(x1))
743.71/262.77	   U42(mark(x0))
743.71/262.77	   U42(active(x0))
743.71/262.77	   U51(mark(x0))
743.71/262.77	   U51(active(x0))
743.71/262.77	   U61(mark(x0), x1)
743.71/262.77	   U61(x0, mark(x1))
743.71/262.77	   U61(active(x0), x1)
743.71/262.77	   U61(x0, active(x1))
743.71/262.77	   U62(mark(x0))
743.71/262.77	   U62(active(x0))
743.71/262.77	   U71(mark(x0), x1)
743.71/262.77	   U71(x0, mark(x1))
743.71/262.77	   U71(active(x0), x1)
743.71/262.77	   U71(x0, active(x1))
743.71/262.77	   U72(mark(x0), x1)
743.71/262.77	   U72(x0, mark(x1))
743.71/262.77	   U72(active(x0), x1)
743.71/262.77	   U72(x0, active(x1))
743.71/262.77	   U81(mark(x0), x1, x2)
743.71/262.77	   U81(x0, mark(x1), x2)
743.71/262.77	   U81(x0, x1, mark(x2))
743.71/262.77	   U81(active(x0), x1, x2)
743.71/262.77	   U81(x0, active(x1), x2)
743.71/262.77	   U81(x0, x1, active(x2))
743.71/262.77	   U82(mark(x0), x1, x2)
743.71/262.77	   U82(x0, mark(x1), x2)
743.71/262.77	   U82(x0, x1, mark(x2))
743.71/262.77	   U82(active(x0), x1, x2)
743.71/262.77	   U82(x0, active(x1), x2)
743.71/262.77	   U82(x0, x1, active(x2))
743.71/262.77	   U83(mark(x0), x1, x2)
743.71/262.77	   U83(x0, mark(x1), x2)
743.71/262.77	   U83(x0, x1, mark(x2))
743.71/262.77	   U83(active(x0), x1, x2)
743.71/262.77	   U83(x0, active(x1), x2)
743.71/262.77	   U83(x0, x1, active(x2))
743.71/262.77	   U84(mark(x0), x1, x2)
743.71/262.77	   U84(x0, mark(x1), x2)
743.71/262.77	   U84(x0, x1, mark(x2))
743.71/262.77	   U84(active(x0), x1, x2)
743.71/262.77	   U84(x0, active(x1), x2)
743.71/262.77	   U84(x0, x1, active(x2))
743.71/262.77	   s(mark(x0))
743.71/262.77	   s(active(x0))
743.71/262.77	   U91(mark(x0), x1)
743.71/262.77	   U91(x0, mark(x1))
743.71/262.77	   U91(active(x0), x1)
743.71/262.77	   U91(x0, active(x1))
743.71/262.77	   U92(mark(x0))
743.71/262.77	   U92(active(x0))
743.71/262.77	
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(37)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U83^1(X1, mark(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(mark(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, mark(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(active(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, active(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	   U83^1(X1, X2, active(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	R is empty.
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	
743.71/262.77	We have to consider all minimal (P,Q,R)-chains.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(38) QDPSizeChangeProof (EQUIVALENT)
743.71/262.77	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. 
743.71/262.77	
743.71/262.77	From the DPs we obtained the following set of size-change graphs:
743.71/262.77	*U83^1(X1, mark(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U83^1(mark(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U83^1(X1, X2, mark(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U83^1(active(X1), X2, X3) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U83^1(X1, active(X2), X3) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.77	
743.71/262.77	
743.71/262.77	*U83^1(X1, X2, active(X3)) -> U83^1(X1, X2, X3)
743.71/262.77	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.77	
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(39)
743.71/262.77	YES
743.71/262.77	
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(40)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U82^1(X1, mark(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(mark(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, X2, mark(X3)) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(active(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, active(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, X2, active(X3)) -> U82^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	The TRS R consists of the following rules:
743.71/262.77	
743.71/262.77	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.77	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.77	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.77	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.77	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.77	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.77	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.77	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.77	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.77	   active(U16(tt)) -> mark(tt)
743.71/262.77	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.77	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.77	   active(U23(tt)) -> mark(tt)
743.71/262.77	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.77	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.77	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.77	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.77	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.77	   active(U36(tt)) -> mark(tt)
743.71/262.77	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.77	   active(U42(tt)) -> mark(tt)
743.71/262.77	   active(U51(tt)) -> mark(tt)
743.71/262.77	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.77	   active(U62(tt)) -> mark(tt)
743.71/262.77	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.77	   active(U72(tt, N)) -> mark(N)
743.71/262.77	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.77	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.77	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.77	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.77	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.77	   active(U92(tt)) -> mark(0)
743.71/262.77	   active(isNat(0)) -> mark(tt)
743.71/262.77	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.77	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.77	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.77	   active(isNatKind(0)) -> mark(tt)
743.71/262.77	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.77	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.77	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.77	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.77	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.77	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.77	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.77	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.77	   mark(tt) -> active(tt)
743.71/262.77	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.77	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.77	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.77	   mark(isNat(X)) -> active(isNat(X))
743.71/262.77	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.77	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.77	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.77	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.77	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.77	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.77	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.77	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.77	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.77	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.77	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.77	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.77	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.77	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.77	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.77	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.77	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.77	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.77	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.77	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.77	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.77	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.77	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.77	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.77	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.77	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.77	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.77	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.77	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.77	   mark(s(X)) -> active(s(mark(X)))
743.71/262.77	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.77	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.77	   mark(0) -> active(0)
743.71/262.77	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.77	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.77	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.77	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.77	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.77	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.77	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.77	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.77	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.77	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.77	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.77	   isNat(mark(X)) -> isNat(X)
743.71/262.77	   isNat(active(X)) -> isNat(X)
743.71/262.77	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.77	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.77	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.77	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.77	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.77	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.77	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.77	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.77	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.77	   x(active(X1), X2) -> x(X1, X2)
743.71/262.77	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.77	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.77	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.77	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.77	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.77	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.77	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.77	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.77	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.77	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.77	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.77	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.77	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.77	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.77	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.77	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.77	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.77	   U16(mark(X)) -> U16(X)
743.71/262.77	   U16(active(X)) -> U16(X)
743.71/262.77	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.77	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.77	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.77	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.77	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.77	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.77	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.77	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.77	   U23(mark(X)) -> U23(X)
743.71/262.77	   U23(active(X)) -> U23(X)
743.71/262.77	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.77	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.77	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.77	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.77	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.77	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.77	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.77	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.77	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.77	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.77	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.77	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.77	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.77	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.77	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.77	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.77	   U36(mark(X)) -> U36(X)
743.71/262.77	   U36(active(X)) -> U36(X)
743.71/262.77	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.77	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.77	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.77	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.77	   U42(mark(X)) -> U42(X)
743.71/262.77	   U42(active(X)) -> U42(X)
743.71/262.77	   U51(mark(X)) -> U51(X)
743.71/262.77	   U51(active(X)) -> U51(X)
743.71/262.77	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.77	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.77	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.77	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.77	   U62(mark(X)) -> U62(X)
743.71/262.77	   U62(active(X)) -> U62(X)
743.71/262.77	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.77	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.77	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.77	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.77	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.77	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.77	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.77	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.77	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.77	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.77	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.77	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.77	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.77	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.77	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.77	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.77	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.77	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.77	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.77	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.77	   s(mark(X)) -> s(X)
743.71/262.77	   s(active(X)) -> s(X)
743.71/262.77	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.77	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.77	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.77	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.77	   U92(mark(X)) -> U92(X)
743.71/262.77	   U92(active(X)) -> U92(X)
743.71/262.77	
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	   U101(mark(x0), x1, x2)
743.71/262.77	   U101(x0, mark(x1), x2)
743.71/262.77	   U101(x0, x1, mark(x2))
743.71/262.77	   U101(active(x0), x1, x2)
743.71/262.77	   U101(x0, active(x1), x2)
743.71/262.77	   U101(x0, x1, active(x2))
743.71/262.77	   U102(mark(x0), x1, x2)
743.71/262.77	   U102(x0, mark(x1), x2)
743.71/262.77	   U102(x0, x1, mark(x2))
743.71/262.77	   U102(active(x0), x1, x2)
743.71/262.77	   U102(x0, active(x1), x2)
743.71/262.77	   U102(x0, x1, active(x2))
743.71/262.77	   isNatKind(mark(x0))
743.71/262.77	   isNatKind(active(x0))
743.71/262.77	   U103(mark(x0), x1, x2)
743.71/262.77	   U103(x0, mark(x1), x2)
743.71/262.77	   U103(x0, x1, mark(x2))
743.71/262.77	   U103(active(x0), x1, x2)
743.71/262.77	   U103(x0, active(x1), x2)
743.71/262.77	   U103(x0, x1, active(x2))
743.71/262.77	   isNat(mark(x0))
743.71/262.77	   isNat(active(x0))
743.71/262.77	   U104(mark(x0), x1, x2)
743.71/262.77	   U104(x0, mark(x1), x2)
743.71/262.77	   U104(x0, x1, mark(x2))
743.71/262.77	   U104(active(x0), x1, x2)
743.71/262.77	   U104(x0, active(x1), x2)
743.71/262.77	   U104(x0, x1, active(x2))
743.71/262.77	   plus(mark(x0), x1)
743.71/262.77	   plus(x0, mark(x1))
743.71/262.77	   plus(active(x0), x1)
743.71/262.77	   plus(x0, active(x1))
743.71/262.77	   x(mark(x0), x1)
743.71/262.77	   x(x0, mark(x1))
743.71/262.77	   x(active(x0), x1)
743.71/262.77	   x(x0, active(x1))
743.71/262.77	   U11(mark(x0), x1, x2)
743.71/262.77	   U11(x0, mark(x1), x2)
743.71/262.77	   U11(x0, x1, mark(x2))
743.71/262.77	   U11(active(x0), x1, x2)
743.71/262.77	   U11(x0, active(x1), x2)
743.71/262.77	   U11(x0, x1, active(x2))
743.71/262.77	   U12(mark(x0), x1, x2)
743.71/262.77	   U12(x0, mark(x1), x2)
743.71/262.77	   U12(x0, x1, mark(x2))
743.71/262.77	   U12(active(x0), x1, x2)
743.71/262.77	   U12(x0, active(x1), x2)
743.71/262.77	   U12(x0, x1, active(x2))
743.71/262.77	   U13(mark(x0), x1, x2)
743.71/262.77	   U13(x0, mark(x1), x2)
743.71/262.77	   U13(x0, x1, mark(x2))
743.71/262.77	   U13(active(x0), x1, x2)
743.71/262.77	   U13(x0, active(x1), x2)
743.71/262.77	   U13(x0, x1, active(x2))
743.71/262.77	   U14(mark(x0), x1, x2)
743.71/262.77	   U14(x0, mark(x1), x2)
743.71/262.77	   U14(x0, x1, mark(x2))
743.71/262.77	   U14(active(x0), x1, x2)
743.71/262.77	   U14(x0, active(x1), x2)
743.71/262.77	   U14(x0, x1, active(x2))
743.71/262.77	   U15(mark(x0), x1)
743.71/262.77	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.77	   U22(active(x0), x1)
743.71/262.77	   U22(x0, active(x1))
743.71/262.77	   U23(mark(x0))
743.71/262.77	   U23(active(x0))
743.71/262.77	   U31(mark(x0), x1, x2)
743.71/262.77	   U31(x0, mark(x1), x2)
743.71/262.77	   U31(x0, x1, mark(x2))
743.71/262.77	   U31(active(x0), x1, x2)
743.71/262.77	   U31(x0, active(x1), x2)
743.71/262.77	   U31(x0, x1, active(x2))
743.71/262.77	   U32(mark(x0), x1, x2)
743.71/262.77	   U32(x0, mark(x1), x2)
743.71/262.77	   U32(x0, x1, mark(x2))
743.71/262.77	   U32(active(x0), x1, x2)
743.71/262.77	   U32(x0, active(x1), x2)
743.71/262.77	   U32(x0, x1, active(x2))
743.71/262.77	   U33(mark(x0), x1, x2)
743.71/262.77	   U33(x0, mark(x1), x2)
743.71/262.77	   U33(x0, x1, mark(x2))
743.71/262.77	   U33(active(x0), x1, x2)
743.71/262.77	   U33(x0, active(x1), x2)
743.71/262.77	   U33(x0, x1, active(x2))
743.71/262.77	   U34(mark(x0), x1, x2)
743.71/262.77	   U34(x0, mark(x1), x2)
743.71/262.77	   U34(x0, x1, mark(x2))
743.71/262.77	   U34(active(x0), x1, x2)
743.71/262.77	   U34(x0, active(x1), x2)
743.71/262.77	   U34(x0, x1, active(x2))
743.71/262.77	   U35(mark(x0), x1)
743.71/262.77	   U35(x0, mark(x1))
743.71/262.77	   U35(active(x0), x1)
743.71/262.77	   U35(x0, active(x1))
743.71/262.77	   U36(mark(x0))
743.71/262.77	   U36(active(x0))
743.71/262.77	   U41(mark(x0), x1)
743.71/262.77	   U41(x0, mark(x1))
743.71/262.77	   U41(active(x0), x1)
743.71/262.77	   U41(x0, active(x1))
743.71/262.77	   U42(mark(x0))
743.71/262.77	   U42(active(x0))
743.71/262.77	   U51(mark(x0))
743.71/262.77	   U51(active(x0))
743.71/262.77	   U61(mark(x0), x1)
743.71/262.77	   U61(x0, mark(x1))
743.71/262.77	   U61(active(x0), x1)
743.71/262.77	   U61(x0, active(x1))
743.71/262.77	   U62(mark(x0))
743.71/262.77	   U62(active(x0))
743.71/262.77	   U71(mark(x0), x1)
743.71/262.77	   U71(x0, mark(x1))
743.71/262.77	   U71(active(x0), x1)
743.71/262.77	   U71(x0, active(x1))
743.71/262.77	   U72(mark(x0), x1)
743.71/262.77	   U72(x0, mark(x1))
743.71/262.77	   U72(active(x0), x1)
743.71/262.77	   U72(x0, active(x1))
743.71/262.77	   U81(mark(x0), x1, x2)
743.71/262.77	   U81(x0, mark(x1), x2)
743.71/262.77	   U81(x0, x1, mark(x2))
743.71/262.77	   U81(active(x0), x1, x2)
743.71/262.77	   U81(x0, active(x1), x2)
743.71/262.77	   U81(x0, x1, active(x2))
743.71/262.77	   U82(mark(x0), x1, x2)
743.71/262.77	   U82(x0, mark(x1), x2)
743.71/262.77	   U82(x0, x1, mark(x2))
743.71/262.77	   U82(active(x0), x1, x2)
743.71/262.77	   U82(x0, active(x1), x2)
743.71/262.77	   U82(x0, x1, active(x2))
743.71/262.77	   U83(mark(x0), x1, x2)
743.71/262.77	   U83(x0, mark(x1), x2)
743.71/262.77	   U83(x0, x1, mark(x2))
743.71/262.77	   U83(active(x0), x1, x2)
743.71/262.77	   U83(x0, active(x1), x2)
743.71/262.77	   U83(x0, x1, active(x2))
743.71/262.77	   U84(mark(x0), x1, x2)
743.71/262.77	   U84(x0, mark(x1), x2)
743.71/262.77	   U84(x0, x1, mark(x2))
743.71/262.77	   U84(active(x0), x1, x2)
743.71/262.77	   U84(x0, active(x1), x2)
743.71/262.77	   U84(x0, x1, active(x2))
743.71/262.77	   s(mark(x0))
743.71/262.77	   s(active(x0))
743.71/262.77	   U91(mark(x0), x1)
743.71/262.77	   U91(x0, mark(x1))
743.71/262.77	   U91(active(x0), x1)
743.71/262.77	   U91(x0, active(x1))
743.71/262.77	   U92(mark(x0))
743.71/262.77	   U92(active(x0))
743.71/262.77	
743.71/262.77	We have to consider all minimal (P,Q,R)-chains.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(41) UsableRulesProof (EQUIVALENT)
743.71/262.77	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.
743.71/262.77	----------------------------------------
743.71/262.77	
743.71/262.77	(42)
743.71/262.77	Obligation:
743.71/262.77	Q DP problem:
743.71/262.77	The TRS P consists of the following rules:
743.71/262.77	
743.71/262.77	   U82^1(X1, mark(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(mark(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, X2, mark(X3)) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(active(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, active(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.77	   U82^1(X1, X2, active(X3)) -> U82^1(X1, X2, X3)
743.71/262.77	
743.71/262.77	R is empty.
743.71/262.77	The set Q consists of the following terms:
743.71/262.77	
743.71/262.77	   active(U101(tt, x0, x1))
743.71/262.77	   active(U102(tt, x0, x1))
743.71/262.77	   active(U103(tt, x0, x1))
743.71/262.77	   active(U104(tt, x0, x1))
743.71/262.77	   active(U11(tt, x0, x1))
743.71/262.77	   active(U12(tt, x0, x1))
743.71/262.77	   active(U13(tt, x0, x1))
743.71/262.77	   active(U14(tt, x0, x1))
743.71/262.77	   active(U15(tt, x0))
743.71/262.77	   active(U16(tt))
743.71/262.77	   active(U21(tt, x0))
743.71/262.77	   active(U22(tt, x0))
743.71/262.77	   active(U23(tt))
743.71/262.77	   active(U31(tt, x0, x1))
743.71/262.77	   active(U32(tt, x0, x1))
743.71/262.77	   active(U33(tt, x0, x1))
743.71/262.77	   active(U34(tt, x0, x1))
743.71/262.77	   active(U35(tt, x0))
743.71/262.77	   active(U36(tt))
743.71/262.77	   active(U41(tt, x0))
743.71/262.77	   active(U42(tt))
743.71/262.77	   active(U51(tt))
743.71/262.77	   active(U61(tt, x0))
743.71/262.77	   active(U62(tt))
743.71/262.77	   active(U71(tt, x0))
743.71/262.77	   active(U72(tt, x0))
743.71/262.77	   active(U81(tt, x0, x1))
743.71/262.77	   active(U82(tt, x0, x1))
743.71/262.77	   active(U83(tt, x0, x1))
743.71/262.77	   active(U84(tt, x0, x1))
743.71/262.77	   active(U91(tt, x0))
743.71/262.77	   active(U92(tt))
743.71/262.77	   active(isNat(0))
743.71/262.77	   active(isNat(plus(x0, x1)))
743.71/262.77	   active(isNat(s(x0)))
743.71/262.77	   active(isNat(x(x0, x1)))
743.71/262.77	   active(isNatKind(0))
743.71/262.77	   active(isNatKind(plus(x0, x1)))
743.71/262.77	   active(isNatKind(s(x0)))
743.71/262.77	   active(isNatKind(x(x0, x1)))
743.71/262.77	   active(plus(x0, 0))
743.71/262.77	   active(plus(x0, s(x1)))
743.71/262.77	   active(x(x0, 0))
743.71/262.77	   active(x(x0, s(x1)))
743.71/262.77	   mark(U101(x0, x1, x2))
743.71/262.77	   mark(tt)
743.71/262.77	   mark(U102(x0, x1, x2))
743.71/262.77	   mark(isNatKind(x0))
743.71/262.77	   mark(U103(x0, x1, x2))
743.71/262.77	   mark(isNat(x0))
743.71/262.77	   mark(U104(x0, x1, x2))
743.71/262.77	   mark(plus(x0, x1))
743.71/262.77	   mark(x(x0, x1))
743.71/262.77	   mark(U11(x0, x1, x2))
743.71/262.77	   mark(U12(x0, x1, x2))
743.71/262.77	   mark(U13(x0, x1, x2))
743.71/262.77	   mark(U14(x0, x1, x2))
743.71/262.77	   mark(U15(x0, x1))
743.71/262.77	   mark(U16(x0))
743.71/262.77	   mark(U21(x0, x1))
743.71/262.77	   mark(U22(x0, x1))
743.71/262.77	   mark(U23(x0))
743.71/262.77	   mark(U31(x0, x1, x2))
743.71/262.77	   mark(U32(x0, x1, x2))
743.71/262.77	   mark(U33(x0, x1, x2))
743.71/262.77	   mark(U34(x0, x1, x2))
743.71/262.77	   mark(U35(x0, x1))
743.71/262.77	   mark(U36(x0))
743.71/262.77	   mark(U41(x0, x1))
743.71/262.77	   mark(U42(x0))
743.71/262.77	   mark(U51(x0))
743.71/262.77	   mark(U61(x0, x1))
743.71/262.77	   mark(U62(x0))
743.71/262.77	   mark(U71(x0, x1))
743.71/262.77	   mark(U72(x0, x1))
743.71/262.77	   mark(U81(x0, x1, x2))
743.71/262.77	   mark(U82(x0, x1, x2))
743.71/262.77	   mark(U83(x0, x1, x2))
743.71/262.77	   mark(U84(x0, x1, x2))
743.71/262.77	   mark(s(x0))
743.71/262.77	   mark(U91(x0, x1))
743.71/262.77	   mark(U92(x0))
743.71/262.77	   mark(0)
743.71/262.77	   U101(mark(x0), x1, x2)
743.71/262.77	   U101(x0, mark(x1), x2)
743.71/262.77	   U101(x0, x1, mark(x2))
743.71/262.77	   U101(active(x0), x1, x2)
743.71/262.77	   U101(x0, active(x1), x2)
743.71/262.77	   U101(x0, x1, active(x2))
743.71/262.77	   U102(mark(x0), x1, x2)
743.71/262.77	   U102(x0, mark(x1), x2)
743.71/262.77	   U102(x0, x1, mark(x2))
743.71/262.77	   U102(active(x0), x1, x2)
743.71/262.77	   U102(x0, active(x1), x2)
743.71/262.77	   U102(x0, x1, active(x2))
743.71/262.77	   isNatKind(mark(x0))
743.71/262.77	   isNatKind(active(x0))
743.71/262.77	   U103(mark(x0), x1, x2)
743.71/262.77	   U103(x0, mark(x1), x2)
743.71/262.77	   U103(x0, x1, mark(x2))
743.71/262.77	   U103(active(x0), x1, x2)
743.71/262.77	   U103(x0, active(x1), x2)
743.71/262.77	   U103(x0, x1, active(x2))
743.71/262.77	   isNat(mark(x0))
743.71/262.77	   isNat(active(x0))
743.71/262.77	   U104(mark(x0), x1, x2)
743.71/262.77	   U104(x0, mark(x1), x2)
743.71/262.77	   U104(x0, x1, mark(x2))
743.71/262.77	   U104(active(x0), x1, x2)
743.71/262.77	   U104(x0, active(x1), x2)
743.71/262.77	   U104(x0, x1, active(x2))
743.71/262.77	   plus(mark(x0), x1)
743.71/262.77	   plus(x0, mark(x1))
743.71/262.77	   plus(active(x0), x1)
743.71/262.77	   plus(x0, active(x1))
743.71/262.77	   x(mark(x0), x1)
743.71/262.77	   x(x0, mark(x1))
743.71/262.77	   x(active(x0), x1)
743.71/262.77	   x(x0, active(x1))
743.71/262.77	   U11(mark(x0), x1, x2)
743.71/262.77	   U11(x0, mark(x1), x2)
743.71/262.77	   U11(x0, x1, mark(x2))
743.71/262.77	   U11(active(x0), x1, x2)
743.71/262.77	   U11(x0, active(x1), x2)
743.71/262.77	   U11(x0, x1, active(x2))
743.71/262.77	   U12(mark(x0), x1, x2)
743.71/262.77	   U12(x0, mark(x1), x2)
743.71/262.77	   U12(x0, x1, mark(x2))
743.71/262.77	   U12(active(x0), x1, x2)
743.71/262.77	   U12(x0, active(x1), x2)
743.71/262.77	   U12(x0, x1, active(x2))
743.71/262.77	   U13(mark(x0), x1, x2)
743.71/262.77	   U13(x0, mark(x1), x2)
743.71/262.77	   U13(x0, x1, mark(x2))
743.71/262.77	   U13(active(x0), x1, x2)
743.71/262.77	   U13(x0, active(x1), x2)
743.71/262.77	   U13(x0, x1, active(x2))
743.71/262.77	   U14(mark(x0), x1, x2)
743.71/262.77	   U14(x0, mark(x1), x2)
743.71/262.77	   U14(x0, x1, mark(x2))
743.71/262.77	   U14(active(x0), x1, x2)
743.71/262.77	   U14(x0, active(x1), x2)
743.71/262.77	   U14(x0, x1, active(x2))
743.71/262.77	   U15(mark(x0), x1)
743.71/262.77	   U15(x0, mark(x1))
743.71/262.77	   U15(active(x0), x1)
743.71/262.77	   U15(x0, active(x1))
743.71/262.77	   U16(mark(x0))
743.71/262.77	   U16(active(x0))
743.71/262.77	   U21(mark(x0), x1)
743.71/262.77	   U21(x0, mark(x1))
743.71/262.77	   U21(active(x0), x1)
743.71/262.77	   U21(x0, active(x1))
743.71/262.77	   U22(mark(x0), x1)
743.71/262.77	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(43) QReductionProof (EQUIVALENT)
743.71/262.78	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.78	
743.71/262.78	   U101(mark(x0), x1, x2)
743.71/262.78	   U101(x0, mark(x1), x2)
743.71/262.78	   U101(x0, x1, mark(x2))
743.71/262.78	   U101(active(x0), x1, x2)
743.71/262.78	   U101(x0, active(x1), x2)
743.71/262.78	   U101(x0, x1, active(x2))
743.71/262.78	   U102(mark(x0), x1, x2)
743.71/262.78	   U102(x0, mark(x1), x2)
743.71/262.78	   U102(x0, x1, mark(x2))
743.71/262.78	   U102(active(x0), x1, x2)
743.71/262.78	   U102(x0, active(x1), x2)
743.71/262.78	   U102(x0, x1, active(x2))
743.71/262.78	   isNatKind(mark(x0))
743.71/262.78	   isNatKind(active(x0))
743.71/262.78	   U103(mark(x0), x1, x2)
743.71/262.78	   U103(x0, mark(x1), x2)
743.71/262.78	   U103(x0, x1, mark(x2))
743.71/262.78	   U103(active(x0), x1, x2)
743.71/262.78	   U103(x0, active(x1), x2)
743.71/262.78	   U103(x0, x1, active(x2))
743.71/262.78	   isNat(mark(x0))
743.71/262.78	   isNat(active(x0))
743.71/262.78	   U104(mark(x0), x1, x2)
743.71/262.78	   U104(x0, mark(x1), x2)
743.71/262.78	   U104(x0, x1, mark(x2))
743.71/262.78	   U104(active(x0), x1, x2)
743.71/262.78	   U104(x0, active(x1), x2)
743.71/262.78	   U104(x0, x1, active(x2))
743.71/262.78	   plus(mark(x0), x1)
743.71/262.78	   plus(x0, mark(x1))
743.71/262.78	   plus(active(x0), x1)
743.71/262.78	   plus(x0, active(x1))
743.71/262.78	   x(mark(x0), x1)
743.71/262.78	   x(x0, mark(x1))
743.71/262.78	   x(active(x0), x1)
743.71/262.78	   x(x0, active(x1))
743.71/262.78	   U11(mark(x0), x1, x2)
743.71/262.78	   U11(x0, mark(x1), x2)
743.71/262.78	   U11(x0, x1, mark(x2))
743.71/262.78	   U11(active(x0), x1, x2)
743.71/262.78	   U11(x0, active(x1), x2)
743.71/262.78	   U11(x0, x1, active(x2))
743.71/262.78	   U12(mark(x0), x1, x2)
743.71/262.78	   U12(x0, mark(x1), x2)
743.71/262.78	   U12(x0, x1, mark(x2))
743.71/262.78	   U12(active(x0), x1, x2)
743.71/262.78	   U12(x0, active(x1), x2)
743.71/262.78	   U12(x0, x1, active(x2))
743.71/262.78	   U13(mark(x0), x1, x2)
743.71/262.78	   U13(x0, mark(x1), x2)
743.71/262.78	   U13(x0, x1, mark(x2))
743.71/262.78	   U13(active(x0), x1, x2)
743.71/262.78	   U13(x0, active(x1), x2)
743.71/262.78	   U13(x0, x1, active(x2))
743.71/262.78	   U14(mark(x0), x1, x2)
743.71/262.78	   U14(x0, mark(x1), x2)
743.71/262.78	   U14(x0, x1, mark(x2))
743.71/262.78	   U14(active(x0), x1, x2)
743.71/262.78	   U14(x0, active(x1), x2)
743.71/262.78	   U14(x0, x1, active(x2))
743.71/262.78	   U15(mark(x0), x1)
743.71/262.78	   U15(x0, mark(x1))
743.71/262.78	   U15(active(x0), x1)
743.71/262.78	   U15(x0, active(x1))
743.71/262.78	   U16(mark(x0))
743.71/262.78	   U16(active(x0))
743.71/262.78	   U21(mark(x0), x1)
743.71/262.78	   U21(x0, mark(x1))
743.71/262.78	   U21(active(x0), x1)
743.71/262.78	   U21(x0, active(x1))
743.71/262.78	   U22(mark(x0), x1)
743.71/262.78	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(44)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U82^1(X1, mark(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.78	   U82^1(mark(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.78	   U82^1(X1, X2, mark(X3)) -> U82^1(X1, X2, X3)
743.71/262.78	   U82^1(active(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.78	   U82^1(X1, active(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.78	   U82^1(X1, X2, active(X3)) -> U82^1(X1, X2, X3)
743.71/262.78	
743.71/262.78	R is empty.
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.78	   active(U11(tt, x0, x1))
743.71/262.78	   active(U12(tt, x0, x1))
743.71/262.78	   active(U13(tt, x0, x1))
743.71/262.78	   active(U14(tt, x0, x1))
743.71/262.78	   active(U15(tt, x0))
743.71/262.78	   active(U16(tt))
743.71/262.78	   active(U21(tt, x0))
743.71/262.78	   active(U22(tt, x0))
743.71/262.78	   active(U23(tt))
743.71/262.78	   active(U31(tt, x0, x1))
743.71/262.78	   active(U32(tt, x0, x1))
743.71/262.78	   active(U33(tt, x0, x1))
743.71/262.78	   active(U34(tt, x0, x1))
743.71/262.78	   active(U35(tt, x0))
743.71/262.78	   active(U36(tt))
743.71/262.78	   active(U41(tt, x0))
743.71/262.78	   active(U42(tt))
743.71/262.78	   active(U51(tt))
743.71/262.78	   active(U61(tt, x0))
743.71/262.78	   active(U62(tt))
743.71/262.78	   active(U71(tt, x0))
743.71/262.78	   active(U72(tt, x0))
743.71/262.78	   active(U81(tt, x0, x1))
743.71/262.78	   active(U82(tt, x0, x1))
743.71/262.78	   active(U83(tt, x0, x1))
743.71/262.78	   active(U84(tt, x0, x1))
743.71/262.78	   active(U91(tt, x0))
743.71/262.78	   active(U92(tt))
743.71/262.78	   active(isNat(0))
743.71/262.78	   active(isNat(plus(x0, x1)))
743.71/262.78	   active(isNat(s(x0)))
743.71/262.78	   active(isNat(x(x0, x1)))
743.71/262.78	   active(isNatKind(0))
743.71/262.78	   active(isNatKind(plus(x0, x1)))
743.71/262.78	   active(isNatKind(s(x0)))
743.71/262.78	   active(isNatKind(x(x0, x1)))
743.71/262.78	   active(plus(x0, 0))
743.71/262.78	   active(plus(x0, s(x1)))
743.71/262.78	   active(x(x0, 0))
743.71/262.78	   active(x(x0, s(x1)))
743.71/262.78	   mark(U101(x0, x1, x2))
743.71/262.78	   mark(tt)
743.71/262.78	   mark(U102(x0, x1, x2))
743.71/262.78	   mark(isNatKind(x0))
743.71/262.78	   mark(U103(x0, x1, x2))
743.71/262.78	   mark(isNat(x0))
743.71/262.78	   mark(U104(x0, x1, x2))
743.71/262.78	   mark(plus(x0, x1))
743.71/262.78	   mark(x(x0, x1))
743.71/262.78	   mark(U11(x0, x1, x2))
743.71/262.78	   mark(U12(x0, x1, x2))
743.71/262.78	   mark(U13(x0, x1, x2))
743.71/262.78	   mark(U14(x0, x1, x2))
743.71/262.78	   mark(U15(x0, x1))
743.71/262.78	   mark(U16(x0))
743.71/262.78	   mark(U21(x0, x1))
743.71/262.78	   mark(U22(x0, x1))
743.71/262.78	   mark(U23(x0))
743.71/262.78	   mark(U31(x0, x1, x2))
743.71/262.78	   mark(U32(x0, x1, x2))
743.71/262.78	   mark(U33(x0, x1, x2))
743.71/262.78	   mark(U34(x0, x1, x2))
743.71/262.78	   mark(U35(x0, x1))
743.71/262.78	   mark(U36(x0))
743.71/262.78	   mark(U41(x0, x1))
743.71/262.78	   mark(U42(x0))
743.71/262.78	   mark(U51(x0))
743.71/262.78	   mark(U61(x0, x1))
743.71/262.78	   mark(U62(x0))
743.71/262.78	   mark(U71(x0, x1))
743.71/262.78	   mark(U72(x0, x1))
743.71/262.78	   mark(U81(x0, x1, x2))
743.71/262.78	   mark(U82(x0, x1, x2))
743.71/262.78	   mark(U83(x0, x1, x2))
743.71/262.78	   mark(U84(x0, x1, x2))
743.71/262.78	   mark(s(x0))
743.71/262.78	   mark(U91(x0, x1))
743.71/262.78	   mark(U92(x0))
743.71/262.78	   mark(0)
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(45) QDPSizeChangeProof (EQUIVALENT)
743.71/262.78	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. 
743.71/262.78	
743.71/262.78	From the DPs we obtained the following set of size-change graphs:
743.71/262.78	*U82^1(X1, mark(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U82^1(mark(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U82^1(X1, X2, mark(X3)) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U82^1(active(X1), X2, X3) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U82^1(X1, active(X2), X3) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U82^1(X1, X2, active(X3)) -> U82^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.78	
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(46)
743.71/262.78	YES
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(47)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U81^1(X1, mark(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(mark(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, mark(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(active(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, active(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, active(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	
743.71/262.78	The TRS R consists of the following rules:
743.71/262.78	
743.71/262.78	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.78	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.78	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.78	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.78	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.78	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.78	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.78	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.78	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.78	   active(U16(tt)) -> mark(tt)
743.71/262.78	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.78	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.78	   active(U23(tt)) -> mark(tt)
743.71/262.78	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.78	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.78	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.78	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.78	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.78	   active(U36(tt)) -> mark(tt)
743.71/262.78	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.78	   active(U42(tt)) -> mark(tt)
743.71/262.78	   active(U51(tt)) -> mark(tt)
743.71/262.78	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.78	   active(U62(tt)) -> mark(tt)
743.71/262.78	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.78	   active(U72(tt, N)) -> mark(N)
743.71/262.78	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.78	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.78	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.78	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.78	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.78	   active(U92(tt)) -> mark(0)
743.71/262.78	   active(isNat(0)) -> mark(tt)
743.71/262.78	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.78	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.78	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.78	   active(isNatKind(0)) -> mark(tt)
743.71/262.78	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.78	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.78	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.78	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.78	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.78	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.78	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.78	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.78	   mark(tt) -> active(tt)
743.71/262.78	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.78	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.78	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.78	   mark(isNat(X)) -> active(isNat(X))
743.71/262.78	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.78	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.78	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.78	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.78	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.78	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.78	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.78	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.78	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.78	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.78	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.78	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.78	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.78	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.78	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.78	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.78	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.78	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.78	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.78	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.78	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.78	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.78	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.78	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.78	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.78	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.78	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.78	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.78	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.78	   mark(s(X)) -> active(s(mark(X)))
743.71/262.78	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.78	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.78	   mark(0) -> active(0)
743.71/262.78	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.78	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.78	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.78	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.78	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.78	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.78	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.78	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.78	   isNat(mark(X)) -> isNat(X)
743.71/262.78	   isNat(active(X)) -> isNat(X)
743.71/262.78	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.78	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.78	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.78	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.78	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.78	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.78	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.78	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.78	   x(active(X1), X2) -> x(X1, X2)
743.71/262.78	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.78	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.78	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.78	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.78	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.78	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.78	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.78	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.78	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.78	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.78	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.78	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.78	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.78	   U16(mark(X)) -> U16(X)
743.71/262.78	   U16(active(X)) -> U16(X)
743.71/262.78	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.78	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.78	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.78	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.78	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.78	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.78	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.78	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.78	   U23(mark(X)) -> U23(X)
743.71/262.78	   U23(active(X)) -> U23(X)
743.71/262.78	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.78	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.78	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.78	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.78	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.78	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.78	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.78	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.78	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.78	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.78	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.78	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.78	   U36(mark(X)) -> U36(X)
743.71/262.78	   U36(active(X)) -> U36(X)
743.71/262.78	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.78	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.78	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.78	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.78	   U42(mark(X)) -> U42(X)
743.71/262.78	   U42(active(X)) -> U42(X)
743.71/262.78	   U51(mark(X)) -> U51(X)
743.71/262.78	   U51(active(X)) -> U51(X)
743.71/262.78	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.78	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.78	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.78	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.78	   U62(mark(X)) -> U62(X)
743.71/262.78	   U62(active(X)) -> U62(X)
743.71/262.78	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.78	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.78	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.78	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.78	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.78	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.78	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.78	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.78	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.78	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.78	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.78	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.78	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.78	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.78	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.78	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.78	   s(mark(X)) -> s(X)
743.71/262.78	   s(active(X)) -> s(X)
743.71/262.78	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.78	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.78	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.78	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.78	   U92(mark(X)) -> U92(X)
743.71/262.78	   U92(active(X)) -> U92(X)
743.71/262.78	
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.78	   active(U11(tt, x0, x1))
743.71/262.78	   active(U12(tt, x0, x1))
743.71/262.78	   active(U13(tt, x0, x1))
743.71/262.78	   active(U14(tt, x0, x1))
743.71/262.78	   active(U15(tt, x0))
743.71/262.78	   active(U16(tt))
743.71/262.78	   active(U21(tt, x0))
743.71/262.78	   active(U22(tt, x0))
743.71/262.78	   active(U23(tt))
743.71/262.78	   active(U31(tt, x0, x1))
743.71/262.78	   active(U32(tt, x0, x1))
743.71/262.78	   active(U33(tt, x0, x1))
743.71/262.78	   active(U34(tt, x0, x1))
743.71/262.78	   active(U35(tt, x0))
743.71/262.78	   active(U36(tt))
743.71/262.78	   active(U41(tt, x0))
743.71/262.78	   active(U42(tt))
743.71/262.78	   active(U51(tt))
743.71/262.78	   active(U61(tt, x0))
743.71/262.78	   active(U62(tt))
743.71/262.78	   active(U71(tt, x0))
743.71/262.78	   active(U72(tt, x0))
743.71/262.78	   active(U81(tt, x0, x1))
743.71/262.78	   active(U82(tt, x0, x1))
743.71/262.78	   active(U83(tt, x0, x1))
743.71/262.78	   active(U84(tt, x0, x1))
743.71/262.78	   active(U91(tt, x0))
743.71/262.78	   active(U92(tt))
743.71/262.78	   active(isNat(0))
743.71/262.78	   active(isNat(plus(x0, x1)))
743.71/262.78	   active(isNat(s(x0)))
743.71/262.78	   active(isNat(x(x0, x1)))
743.71/262.78	   active(isNatKind(0))
743.71/262.78	   active(isNatKind(plus(x0, x1)))
743.71/262.78	   active(isNatKind(s(x0)))
743.71/262.78	   active(isNatKind(x(x0, x1)))
743.71/262.78	   active(plus(x0, 0))
743.71/262.78	   active(plus(x0, s(x1)))
743.71/262.78	   active(x(x0, 0))
743.71/262.78	   active(x(x0, s(x1)))
743.71/262.78	   mark(U101(x0, x1, x2))
743.71/262.78	   mark(tt)
743.71/262.78	   mark(U102(x0, x1, x2))
743.71/262.78	   mark(isNatKind(x0))
743.71/262.78	   mark(U103(x0, x1, x2))
743.71/262.78	   mark(isNat(x0))
743.71/262.78	   mark(U104(x0, x1, x2))
743.71/262.78	   mark(plus(x0, x1))
743.71/262.78	   mark(x(x0, x1))
743.71/262.78	   mark(U11(x0, x1, x2))
743.71/262.78	   mark(U12(x0, x1, x2))
743.71/262.78	   mark(U13(x0, x1, x2))
743.71/262.78	   mark(U14(x0, x1, x2))
743.71/262.78	   mark(U15(x0, x1))
743.71/262.78	   mark(U16(x0))
743.71/262.78	   mark(U21(x0, x1))
743.71/262.78	   mark(U22(x0, x1))
743.71/262.78	   mark(U23(x0))
743.71/262.78	   mark(U31(x0, x1, x2))
743.71/262.78	   mark(U32(x0, x1, x2))
743.71/262.78	   mark(U33(x0, x1, x2))
743.71/262.78	   mark(U34(x0, x1, x2))
743.71/262.78	   mark(U35(x0, x1))
743.71/262.78	   mark(U36(x0))
743.71/262.78	   mark(U41(x0, x1))
743.71/262.78	   mark(U42(x0))
743.71/262.78	   mark(U51(x0))
743.71/262.78	   mark(U61(x0, x1))
743.71/262.78	   mark(U62(x0))
743.71/262.78	   mark(U71(x0, x1))
743.71/262.78	   mark(U72(x0, x1))
743.71/262.78	   mark(U81(x0, x1, x2))
743.71/262.78	   mark(U82(x0, x1, x2))
743.71/262.78	   mark(U83(x0, x1, x2))
743.71/262.78	   mark(U84(x0, x1, x2))
743.71/262.78	   mark(s(x0))
743.71/262.78	   mark(U91(x0, x1))
743.71/262.78	   mark(U92(x0))
743.71/262.78	   mark(0)
743.71/262.78	   U101(mark(x0), x1, x2)
743.71/262.78	   U101(x0, mark(x1), x2)
743.71/262.78	   U101(x0, x1, mark(x2))
743.71/262.78	   U101(active(x0), x1, x2)
743.71/262.78	   U101(x0, active(x1), x2)
743.71/262.78	   U101(x0, x1, active(x2))
743.71/262.78	   U102(mark(x0), x1, x2)
743.71/262.78	   U102(x0, mark(x1), x2)
743.71/262.78	   U102(x0, x1, mark(x2))
743.71/262.78	   U102(active(x0), x1, x2)
743.71/262.78	   U102(x0, active(x1), x2)
743.71/262.78	   U102(x0, x1, active(x2))
743.71/262.78	   isNatKind(mark(x0))
743.71/262.78	   isNatKind(active(x0))
743.71/262.78	   U103(mark(x0), x1, x2)
743.71/262.78	   U103(x0, mark(x1), x2)
743.71/262.78	   U103(x0, x1, mark(x2))
743.71/262.78	   U103(active(x0), x1, x2)
743.71/262.78	   U103(x0, active(x1), x2)
743.71/262.78	   U103(x0, x1, active(x2))
743.71/262.78	   isNat(mark(x0))
743.71/262.78	   isNat(active(x0))
743.71/262.78	   U104(mark(x0), x1, x2)
743.71/262.78	   U104(x0, mark(x1), x2)
743.71/262.78	   U104(x0, x1, mark(x2))
743.71/262.78	   U104(active(x0), x1, x2)
743.71/262.78	   U104(x0, active(x1), x2)
743.71/262.78	   U104(x0, x1, active(x2))
743.71/262.78	   plus(mark(x0), x1)
743.71/262.78	   plus(x0, mark(x1))
743.71/262.78	   plus(active(x0), x1)
743.71/262.78	   plus(x0, active(x1))
743.71/262.78	   x(mark(x0), x1)
743.71/262.78	   x(x0, mark(x1))
743.71/262.78	   x(active(x0), x1)
743.71/262.78	   x(x0, active(x1))
743.71/262.78	   U11(mark(x0), x1, x2)
743.71/262.78	   U11(x0, mark(x1), x2)
743.71/262.78	   U11(x0, x1, mark(x2))
743.71/262.78	   U11(active(x0), x1, x2)
743.71/262.78	   U11(x0, active(x1), x2)
743.71/262.78	   U11(x0, x1, active(x2))
743.71/262.78	   U12(mark(x0), x1, x2)
743.71/262.78	   U12(x0, mark(x1), x2)
743.71/262.78	   U12(x0, x1, mark(x2))
743.71/262.78	   U12(active(x0), x1, x2)
743.71/262.78	   U12(x0, active(x1), x2)
743.71/262.78	   U12(x0, x1, active(x2))
743.71/262.78	   U13(mark(x0), x1, x2)
743.71/262.78	   U13(x0, mark(x1), x2)
743.71/262.78	   U13(x0, x1, mark(x2))
743.71/262.78	   U13(active(x0), x1, x2)
743.71/262.78	   U13(x0, active(x1), x2)
743.71/262.78	   U13(x0, x1, active(x2))
743.71/262.78	   U14(mark(x0), x1, x2)
743.71/262.78	   U14(x0, mark(x1), x2)
743.71/262.78	   U14(x0, x1, mark(x2))
743.71/262.78	   U14(active(x0), x1, x2)
743.71/262.78	   U14(x0, active(x1), x2)
743.71/262.78	   U14(x0, x1, active(x2))
743.71/262.78	   U15(mark(x0), x1)
743.71/262.78	   U15(x0, mark(x1))
743.71/262.78	   U15(active(x0), x1)
743.71/262.78	   U15(x0, active(x1))
743.71/262.78	   U16(mark(x0))
743.71/262.78	   U16(active(x0))
743.71/262.78	   U21(mark(x0), x1)
743.71/262.78	   U21(x0, mark(x1))
743.71/262.78	   U21(active(x0), x1)
743.71/262.78	   U21(x0, active(x1))
743.71/262.78	   U22(mark(x0), x1)
743.71/262.78	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(48) UsableRulesProof (EQUIVALENT)
743.71/262.78	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.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(49)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U81^1(X1, mark(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(mark(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, mark(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(active(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, active(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, active(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	
743.71/262.78	R is empty.
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.78	   active(U11(tt, x0, x1))
743.71/262.78	   active(U12(tt, x0, x1))
743.71/262.78	   active(U13(tt, x0, x1))
743.71/262.78	   active(U14(tt, x0, x1))
743.71/262.78	   active(U15(tt, x0))
743.71/262.78	   active(U16(tt))
743.71/262.78	   active(U21(tt, x0))
743.71/262.78	   active(U22(tt, x0))
743.71/262.78	   active(U23(tt))
743.71/262.78	   active(U31(tt, x0, x1))
743.71/262.78	   active(U32(tt, x0, x1))
743.71/262.78	   active(U33(tt, x0, x1))
743.71/262.78	   active(U34(tt, x0, x1))
743.71/262.78	   active(U35(tt, x0))
743.71/262.78	   active(U36(tt))
743.71/262.78	   active(U41(tt, x0))
743.71/262.78	   active(U42(tt))
743.71/262.78	   active(U51(tt))
743.71/262.78	   active(U61(tt, x0))
743.71/262.78	   active(U62(tt))
743.71/262.78	   active(U71(tt, x0))
743.71/262.78	   active(U72(tt, x0))
743.71/262.78	   active(U81(tt, x0, x1))
743.71/262.78	   active(U82(tt, x0, x1))
743.71/262.78	   active(U83(tt, x0, x1))
743.71/262.78	   active(U84(tt, x0, x1))
743.71/262.78	   active(U91(tt, x0))
743.71/262.78	   active(U92(tt))
743.71/262.78	   active(isNat(0))
743.71/262.78	   active(isNat(plus(x0, x1)))
743.71/262.78	   active(isNat(s(x0)))
743.71/262.78	   active(isNat(x(x0, x1)))
743.71/262.78	   active(isNatKind(0))
743.71/262.78	   active(isNatKind(plus(x0, x1)))
743.71/262.78	   active(isNatKind(s(x0)))
743.71/262.78	   active(isNatKind(x(x0, x1)))
743.71/262.78	   active(plus(x0, 0))
743.71/262.78	   active(plus(x0, s(x1)))
743.71/262.78	   active(x(x0, 0))
743.71/262.78	   active(x(x0, s(x1)))
743.71/262.78	   mark(U101(x0, x1, x2))
743.71/262.78	   mark(tt)
743.71/262.78	   mark(U102(x0, x1, x2))
743.71/262.78	   mark(isNatKind(x0))
743.71/262.78	   mark(U103(x0, x1, x2))
743.71/262.78	   mark(isNat(x0))
743.71/262.78	   mark(U104(x0, x1, x2))
743.71/262.78	   mark(plus(x0, x1))
743.71/262.78	   mark(x(x0, x1))
743.71/262.78	   mark(U11(x0, x1, x2))
743.71/262.78	   mark(U12(x0, x1, x2))
743.71/262.78	   mark(U13(x0, x1, x2))
743.71/262.78	   mark(U14(x0, x1, x2))
743.71/262.78	   mark(U15(x0, x1))
743.71/262.78	   mark(U16(x0))
743.71/262.78	   mark(U21(x0, x1))
743.71/262.78	   mark(U22(x0, x1))
743.71/262.78	   mark(U23(x0))
743.71/262.78	   mark(U31(x0, x1, x2))
743.71/262.78	   mark(U32(x0, x1, x2))
743.71/262.78	   mark(U33(x0, x1, x2))
743.71/262.78	   mark(U34(x0, x1, x2))
743.71/262.78	   mark(U35(x0, x1))
743.71/262.78	   mark(U36(x0))
743.71/262.78	   mark(U41(x0, x1))
743.71/262.78	   mark(U42(x0))
743.71/262.78	   mark(U51(x0))
743.71/262.78	   mark(U61(x0, x1))
743.71/262.78	   mark(U62(x0))
743.71/262.78	   mark(U71(x0, x1))
743.71/262.78	   mark(U72(x0, x1))
743.71/262.78	   mark(U81(x0, x1, x2))
743.71/262.78	   mark(U82(x0, x1, x2))
743.71/262.78	   mark(U83(x0, x1, x2))
743.71/262.78	   mark(U84(x0, x1, x2))
743.71/262.78	   mark(s(x0))
743.71/262.78	   mark(U91(x0, x1))
743.71/262.78	   mark(U92(x0))
743.71/262.78	   mark(0)
743.71/262.78	   U101(mark(x0), x1, x2)
743.71/262.78	   U101(x0, mark(x1), x2)
743.71/262.78	   U101(x0, x1, mark(x2))
743.71/262.78	   U101(active(x0), x1, x2)
743.71/262.78	   U101(x0, active(x1), x2)
743.71/262.78	   U101(x0, x1, active(x2))
743.71/262.78	   U102(mark(x0), x1, x2)
743.71/262.78	   U102(x0, mark(x1), x2)
743.71/262.78	   U102(x0, x1, mark(x2))
743.71/262.78	   U102(active(x0), x1, x2)
743.71/262.78	   U102(x0, active(x1), x2)
743.71/262.78	   U102(x0, x1, active(x2))
743.71/262.78	   isNatKind(mark(x0))
743.71/262.78	   isNatKind(active(x0))
743.71/262.78	   U103(mark(x0), x1, x2)
743.71/262.78	   U103(x0, mark(x1), x2)
743.71/262.78	   U103(x0, x1, mark(x2))
743.71/262.78	   U103(active(x0), x1, x2)
743.71/262.78	   U103(x0, active(x1), x2)
743.71/262.78	   U103(x0, x1, active(x2))
743.71/262.78	   isNat(mark(x0))
743.71/262.78	   isNat(active(x0))
743.71/262.78	   U104(mark(x0), x1, x2)
743.71/262.78	   U104(x0, mark(x1), x2)
743.71/262.78	   U104(x0, x1, mark(x2))
743.71/262.78	   U104(active(x0), x1, x2)
743.71/262.78	   U104(x0, active(x1), x2)
743.71/262.78	   U104(x0, x1, active(x2))
743.71/262.78	   plus(mark(x0), x1)
743.71/262.78	   plus(x0, mark(x1))
743.71/262.78	   plus(active(x0), x1)
743.71/262.78	   plus(x0, active(x1))
743.71/262.78	   x(mark(x0), x1)
743.71/262.78	   x(x0, mark(x1))
743.71/262.78	   x(active(x0), x1)
743.71/262.78	   x(x0, active(x1))
743.71/262.78	   U11(mark(x0), x1, x2)
743.71/262.78	   U11(x0, mark(x1), x2)
743.71/262.78	   U11(x0, x1, mark(x2))
743.71/262.78	   U11(active(x0), x1, x2)
743.71/262.78	   U11(x0, active(x1), x2)
743.71/262.78	   U11(x0, x1, active(x2))
743.71/262.78	   U12(mark(x0), x1, x2)
743.71/262.78	   U12(x0, mark(x1), x2)
743.71/262.78	   U12(x0, x1, mark(x2))
743.71/262.78	   U12(active(x0), x1, x2)
743.71/262.78	   U12(x0, active(x1), x2)
743.71/262.78	   U12(x0, x1, active(x2))
743.71/262.78	   U13(mark(x0), x1, x2)
743.71/262.78	   U13(x0, mark(x1), x2)
743.71/262.78	   U13(x0, x1, mark(x2))
743.71/262.78	   U13(active(x0), x1, x2)
743.71/262.78	   U13(x0, active(x1), x2)
743.71/262.78	   U13(x0, x1, active(x2))
743.71/262.78	   U14(mark(x0), x1, x2)
743.71/262.78	   U14(x0, mark(x1), x2)
743.71/262.78	   U14(x0, x1, mark(x2))
743.71/262.78	   U14(active(x0), x1, x2)
743.71/262.78	   U14(x0, active(x1), x2)
743.71/262.78	   U14(x0, x1, active(x2))
743.71/262.78	   U15(mark(x0), x1)
743.71/262.78	   U15(x0, mark(x1))
743.71/262.78	   U15(active(x0), x1)
743.71/262.78	   U15(x0, active(x1))
743.71/262.78	   U16(mark(x0))
743.71/262.78	   U16(active(x0))
743.71/262.78	   U21(mark(x0), x1)
743.71/262.78	   U21(x0, mark(x1))
743.71/262.78	   U21(active(x0), x1)
743.71/262.78	   U21(x0, active(x1))
743.71/262.78	   U22(mark(x0), x1)
743.71/262.78	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(50) QReductionProof (EQUIVALENT)
743.71/262.78	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.78	
743.71/262.78	   U101(mark(x0), x1, x2)
743.71/262.78	   U101(x0, mark(x1), x2)
743.71/262.78	   U101(x0, x1, mark(x2))
743.71/262.78	   U101(active(x0), x1, x2)
743.71/262.78	   U101(x0, active(x1), x2)
743.71/262.78	   U101(x0, x1, active(x2))
743.71/262.78	   U102(mark(x0), x1, x2)
743.71/262.78	   U102(x0, mark(x1), x2)
743.71/262.78	   U102(x0, x1, mark(x2))
743.71/262.78	   U102(active(x0), x1, x2)
743.71/262.78	   U102(x0, active(x1), x2)
743.71/262.78	   U102(x0, x1, active(x2))
743.71/262.78	   isNatKind(mark(x0))
743.71/262.78	   isNatKind(active(x0))
743.71/262.78	   U103(mark(x0), x1, x2)
743.71/262.78	   U103(x0, mark(x1), x2)
743.71/262.78	   U103(x0, x1, mark(x2))
743.71/262.78	   U103(active(x0), x1, x2)
743.71/262.78	   U103(x0, active(x1), x2)
743.71/262.78	   U103(x0, x1, active(x2))
743.71/262.78	   isNat(mark(x0))
743.71/262.78	   isNat(active(x0))
743.71/262.78	   U104(mark(x0), x1, x2)
743.71/262.78	   U104(x0, mark(x1), x2)
743.71/262.78	   U104(x0, x1, mark(x2))
743.71/262.78	   U104(active(x0), x1, x2)
743.71/262.78	   U104(x0, active(x1), x2)
743.71/262.78	   U104(x0, x1, active(x2))
743.71/262.78	   plus(mark(x0), x1)
743.71/262.78	   plus(x0, mark(x1))
743.71/262.78	   plus(active(x0), x1)
743.71/262.78	   plus(x0, active(x1))
743.71/262.78	   x(mark(x0), x1)
743.71/262.78	   x(x0, mark(x1))
743.71/262.78	   x(active(x0), x1)
743.71/262.78	   x(x0, active(x1))
743.71/262.78	   U11(mark(x0), x1, x2)
743.71/262.78	   U11(x0, mark(x1), x2)
743.71/262.78	   U11(x0, x1, mark(x2))
743.71/262.78	   U11(active(x0), x1, x2)
743.71/262.78	   U11(x0, active(x1), x2)
743.71/262.78	   U11(x0, x1, active(x2))
743.71/262.78	   U12(mark(x0), x1, x2)
743.71/262.78	   U12(x0, mark(x1), x2)
743.71/262.78	   U12(x0, x1, mark(x2))
743.71/262.78	   U12(active(x0), x1, x2)
743.71/262.78	   U12(x0, active(x1), x2)
743.71/262.78	   U12(x0, x1, active(x2))
743.71/262.78	   U13(mark(x0), x1, x2)
743.71/262.78	   U13(x0, mark(x1), x2)
743.71/262.78	   U13(x0, x1, mark(x2))
743.71/262.78	   U13(active(x0), x1, x2)
743.71/262.78	   U13(x0, active(x1), x2)
743.71/262.78	   U13(x0, x1, active(x2))
743.71/262.78	   U14(mark(x0), x1, x2)
743.71/262.78	   U14(x0, mark(x1), x2)
743.71/262.78	   U14(x0, x1, mark(x2))
743.71/262.78	   U14(active(x0), x1, x2)
743.71/262.78	   U14(x0, active(x1), x2)
743.71/262.78	   U14(x0, x1, active(x2))
743.71/262.78	   U15(mark(x0), x1)
743.71/262.78	   U15(x0, mark(x1))
743.71/262.78	   U15(active(x0), x1)
743.71/262.78	   U15(x0, active(x1))
743.71/262.78	   U16(mark(x0))
743.71/262.78	   U16(active(x0))
743.71/262.78	   U21(mark(x0), x1)
743.71/262.78	   U21(x0, mark(x1))
743.71/262.78	   U21(active(x0), x1)
743.71/262.78	   U21(x0, active(x1))
743.71/262.78	   U22(mark(x0), x1)
743.71/262.78	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(51)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U81^1(X1, mark(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(mark(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, mark(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(active(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, active(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	   U81^1(X1, X2, active(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	
743.71/262.78	R is empty.
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.78	   active(U11(tt, x0, x1))
743.71/262.78	   active(U12(tt, x0, x1))
743.71/262.78	   active(U13(tt, x0, x1))
743.71/262.78	   active(U14(tt, x0, x1))
743.71/262.78	   active(U15(tt, x0))
743.71/262.78	   active(U16(tt))
743.71/262.78	   active(U21(tt, x0))
743.71/262.78	   active(U22(tt, x0))
743.71/262.78	   active(U23(tt))
743.71/262.78	   active(U31(tt, x0, x1))
743.71/262.78	   active(U32(tt, x0, x1))
743.71/262.78	   active(U33(tt, x0, x1))
743.71/262.78	   active(U34(tt, x0, x1))
743.71/262.78	   active(U35(tt, x0))
743.71/262.78	   active(U36(tt))
743.71/262.78	   active(U41(tt, x0))
743.71/262.78	   active(U42(tt))
743.71/262.78	   active(U51(tt))
743.71/262.78	   active(U61(tt, x0))
743.71/262.78	   active(U62(tt))
743.71/262.78	   active(U71(tt, x0))
743.71/262.78	   active(U72(tt, x0))
743.71/262.78	   active(U81(tt, x0, x1))
743.71/262.78	   active(U82(tt, x0, x1))
743.71/262.78	   active(U83(tt, x0, x1))
743.71/262.78	   active(U84(tt, x0, x1))
743.71/262.78	   active(U91(tt, x0))
743.71/262.78	   active(U92(tt))
743.71/262.78	   active(isNat(0))
743.71/262.78	   active(isNat(plus(x0, x1)))
743.71/262.78	   active(isNat(s(x0)))
743.71/262.78	   active(isNat(x(x0, x1)))
743.71/262.78	   active(isNatKind(0))
743.71/262.78	   active(isNatKind(plus(x0, x1)))
743.71/262.78	   active(isNatKind(s(x0)))
743.71/262.78	   active(isNatKind(x(x0, x1)))
743.71/262.78	   active(plus(x0, 0))
743.71/262.78	   active(plus(x0, s(x1)))
743.71/262.78	   active(x(x0, 0))
743.71/262.78	   active(x(x0, s(x1)))
743.71/262.78	   mark(U101(x0, x1, x2))
743.71/262.78	   mark(tt)
743.71/262.78	   mark(U102(x0, x1, x2))
743.71/262.78	   mark(isNatKind(x0))
743.71/262.78	   mark(U103(x0, x1, x2))
743.71/262.78	   mark(isNat(x0))
743.71/262.78	   mark(U104(x0, x1, x2))
743.71/262.78	   mark(plus(x0, x1))
743.71/262.78	   mark(x(x0, x1))
743.71/262.78	   mark(U11(x0, x1, x2))
743.71/262.78	   mark(U12(x0, x1, x2))
743.71/262.78	   mark(U13(x0, x1, x2))
743.71/262.78	   mark(U14(x0, x1, x2))
743.71/262.78	   mark(U15(x0, x1))
743.71/262.78	   mark(U16(x0))
743.71/262.78	   mark(U21(x0, x1))
743.71/262.78	   mark(U22(x0, x1))
743.71/262.78	   mark(U23(x0))
743.71/262.78	   mark(U31(x0, x1, x2))
743.71/262.78	   mark(U32(x0, x1, x2))
743.71/262.78	   mark(U33(x0, x1, x2))
743.71/262.78	   mark(U34(x0, x1, x2))
743.71/262.78	   mark(U35(x0, x1))
743.71/262.78	   mark(U36(x0))
743.71/262.78	   mark(U41(x0, x1))
743.71/262.78	   mark(U42(x0))
743.71/262.78	   mark(U51(x0))
743.71/262.78	   mark(U61(x0, x1))
743.71/262.78	   mark(U62(x0))
743.71/262.78	   mark(U71(x0, x1))
743.71/262.78	   mark(U72(x0, x1))
743.71/262.78	   mark(U81(x0, x1, x2))
743.71/262.78	   mark(U82(x0, x1, x2))
743.71/262.78	   mark(U83(x0, x1, x2))
743.71/262.78	   mark(U84(x0, x1, x2))
743.71/262.78	   mark(s(x0))
743.71/262.78	   mark(U91(x0, x1))
743.71/262.78	   mark(U92(x0))
743.71/262.78	   mark(0)
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(52) QDPSizeChangeProof (EQUIVALENT)
743.71/262.78	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. 
743.71/262.78	
743.71/262.78	From the DPs we obtained the following set of size-change graphs:
743.71/262.78	*U81^1(X1, mark(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U81^1(mark(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U81^1(X1, X2, mark(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U81^1(active(X1), X2, X3) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U81^1(X1, active(X2), X3) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
743.71/262.78	
743.71/262.78	
743.71/262.78	*U81^1(X1, X2, active(X3)) -> U81^1(X1, X2, X3)
743.71/262.78	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
743.71/262.78	
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(53)
743.71/262.78	YES
743.71/262.78	
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(54)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U72^1(X1, mark(X2)) -> U72^1(X1, X2)
743.71/262.78	   U72^1(mark(X1), X2) -> U72^1(X1, X2)
743.71/262.78	   U72^1(active(X1), X2) -> U72^1(X1, X2)
743.71/262.78	   U72^1(X1, active(X2)) -> U72^1(X1, X2)
743.71/262.78	
743.71/262.78	The TRS R consists of the following rules:
743.71/262.78	
743.71/262.78	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.78	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.78	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.78	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.78	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.78	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.78	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.78	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.78	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.78	   active(U16(tt)) -> mark(tt)
743.71/262.78	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.78	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.78	   active(U23(tt)) -> mark(tt)
743.71/262.78	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.78	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.78	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.78	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.78	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.78	   active(U36(tt)) -> mark(tt)
743.71/262.78	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.78	   active(U42(tt)) -> mark(tt)
743.71/262.78	   active(U51(tt)) -> mark(tt)
743.71/262.78	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.78	   active(U62(tt)) -> mark(tt)
743.71/262.78	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.78	   active(U72(tt, N)) -> mark(N)
743.71/262.78	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.78	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.78	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.78	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.78	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.78	   active(U92(tt)) -> mark(0)
743.71/262.78	   active(isNat(0)) -> mark(tt)
743.71/262.78	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.78	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.78	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.78	   active(isNatKind(0)) -> mark(tt)
743.71/262.78	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.78	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.78	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.78	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.78	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.78	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.78	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.78	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.78	   mark(tt) -> active(tt)
743.71/262.78	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.78	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.78	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.78	   mark(isNat(X)) -> active(isNat(X))
743.71/262.78	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.78	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.78	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.78	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.78	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.78	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.78	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.78	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.78	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.78	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.78	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.78	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.78	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.78	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.78	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.78	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.78	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.78	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.78	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.78	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.78	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.78	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.78	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.78	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.78	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.78	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.78	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.78	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.78	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.78	   mark(s(X)) -> active(s(mark(X)))
743.71/262.78	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.78	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.78	   mark(0) -> active(0)
743.71/262.78	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.78	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.78	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.78	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.78	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.78	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.78	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.78	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.78	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.78	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.78	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.78	   isNat(mark(X)) -> isNat(X)
743.71/262.78	   isNat(active(X)) -> isNat(X)
743.71/262.78	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.78	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.78	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.78	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.78	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.78	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.78	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.78	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.78	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.78	   x(active(X1), X2) -> x(X1, X2)
743.71/262.78	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.78	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.78	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.78	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.78	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.78	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.78	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.78	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.78	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.78	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.78	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.78	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.78	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.78	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.78	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.78	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.78	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.78	   U16(mark(X)) -> U16(X)
743.71/262.78	   U16(active(X)) -> U16(X)
743.71/262.78	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.78	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.78	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.78	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.78	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.78	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.78	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.78	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.78	   U23(mark(X)) -> U23(X)
743.71/262.78	   U23(active(X)) -> U23(X)
743.71/262.78	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.78	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.78	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.78	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.78	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.78	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.78	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.78	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.78	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.78	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.78	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.78	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.78	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.78	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.78	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.78	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.78	   U36(mark(X)) -> U36(X)
743.71/262.78	   U36(active(X)) -> U36(X)
743.71/262.78	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.78	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.78	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.78	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.78	   U42(mark(X)) -> U42(X)
743.71/262.78	   U42(active(X)) -> U42(X)
743.71/262.78	   U51(mark(X)) -> U51(X)
743.71/262.78	   U51(active(X)) -> U51(X)
743.71/262.78	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.78	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.78	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.78	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.78	   U62(mark(X)) -> U62(X)
743.71/262.78	   U62(active(X)) -> U62(X)
743.71/262.78	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.78	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.78	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.78	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.78	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.78	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.78	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.78	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.78	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.78	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.78	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.78	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.78	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.78	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.78	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.78	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.78	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.78	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.78	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.78	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.78	   s(mark(X)) -> s(X)
743.71/262.78	   s(active(X)) -> s(X)
743.71/262.78	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.78	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.78	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.78	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.78	   U92(mark(X)) -> U92(X)
743.71/262.78	   U92(active(X)) -> U92(X)
743.71/262.78	
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.78	   active(U11(tt, x0, x1))
743.71/262.78	   active(U12(tt, x0, x1))
743.71/262.78	   active(U13(tt, x0, x1))
743.71/262.78	   active(U14(tt, x0, x1))
743.71/262.78	   active(U15(tt, x0))
743.71/262.78	   active(U16(tt))
743.71/262.78	   active(U21(tt, x0))
743.71/262.78	   active(U22(tt, x0))
743.71/262.78	   active(U23(tt))
743.71/262.78	   active(U31(tt, x0, x1))
743.71/262.78	   active(U32(tt, x0, x1))
743.71/262.78	   active(U33(tt, x0, x1))
743.71/262.78	   active(U34(tt, x0, x1))
743.71/262.78	   active(U35(tt, x0))
743.71/262.78	   active(U36(tt))
743.71/262.78	   active(U41(tt, x0))
743.71/262.78	   active(U42(tt))
743.71/262.78	   active(U51(tt))
743.71/262.78	   active(U61(tt, x0))
743.71/262.78	   active(U62(tt))
743.71/262.78	   active(U71(tt, x0))
743.71/262.78	   active(U72(tt, x0))
743.71/262.78	   active(U81(tt, x0, x1))
743.71/262.78	   active(U82(tt, x0, x1))
743.71/262.78	   active(U83(tt, x0, x1))
743.71/262.78	   active(U84(tt, x0, x1))
743.71/262.78	   active(U91(tt, x0))
743.71/262.78	   active(U92(tt))
743.71/262.78	   active(isNat(0))
743.71/262.78	   active(isNat(plus(x0, x1)))
743.71/262.78	   active(isNat(s(x0)))
743.71/262.78	   active(isNat(x(x0, x1)))
743.71/262.78	   active(isNatKind(0))
743.71/262.78	   active(isNatKind(plus(x0, x1)))
743.71/262.78	   active(isNatKind(s(x0)))
743.71/262.78	   active(isNatKind(x(x0, x1)))
743.71/262.78	   active(plus(x0, 0))
743.71/262.78	   active(plus(x0, s(x1)))
743.71/262.78	   active(x(x0, 0))
743.71/262.78	   active(x(x0, s(x1)))
743.71/262.78	   mark(U101(x0, x1, x2))
743.71/262.78	   mark(tt)
743.71/262.78	   mark(U102(x0, x1, x2))
743.71/262.78	   mark(isNatKind(x0))
743.71/262.78	   mark(U103(x0, x1, x2))
743.71/262.78	   mark(isNat(x0))
743.71/262.78	   mark(U104(x0, x1, x2))
743.71/262.78	   mark(plus(x0, x1))
743.71/262.78	   mark(x(x0, x1))
743.71/262.78	   mark(U11(x0, x1, x2))
743.71/262.78	   mark(U12(x0, x1, x2))
743.71/262.78	   mark(U13(x0, x1, x2))
743.71/262.78	   mark(U14(x0, x1, x2))
743.71/262.78	   mark(U15(x0, x1))
743.71/262.78	   mark(U16(x0))
743.71/262.78	   mark(U21(x0, x1))
743.71/262.78	   mark(U22(x0, x1))
743.71/262.78	   mark(U23(x0))
743.71/262.78	   mark(U31(x0, x1, x2))
743.71/262.78	   mark(U32(x0, x1, x2))
743.71/262.78	   mark(U33(x0, x1, x2))
743.71/262.78	   mark(U34(x0, x1, x2))
743.71/262.78	   mark(U35(x0, x1))
743.71/262.78	   mark(U36(x0))
743.71/262.78	   mark(U41(x0, x1))
743.71/262.78	   mark(U42(x0))
743.71/262.78	   mark(U51(x0))
743.71/262.78	   mark(U61(x0, x1))
743.71/262.78	   mark(U62(x0))
743.71/262.78	   mark(U71(x0, x1))
743.71/262.78	   mark(U72(x0, x1))
743.71/262.78	   mark(U81(x0, x1, x2))
743.71/262.78	   mark(U82(x0, x1, x2))
743.71/262.78	   mark(U83(x0, x1, x2))
743.71/262.78	   mark(U84(x0, x1, x2))
743.71/262.78	   mark(s(x0))
743.71/262.78	   mark(U91(x0, x1))
743.71/262.78	   mark(U92(x0))
743.71/262.78	   mark(0)
743.71/262.78	   U101(mark(x0), x1, x2)
743.71/262.78	   U101(x0, mark(x1), x2)
743.71/262.78	   U101(x0, x1, mark(x2))
743.71/262.78	   U101(active(x0), x1, x2)
743.71/262.78	   U101(x0, active(x1), x2)
743.71/262.78	   U101(x0, x1, active(x2))
743.71/262.78	   U102(mark(x0), x1, x2)
743.71/262.78	   U102(x0, mark(x1), x2)
743.71/262.78	   U102(x0, x1, mark(x2))
743.71/262.78	   U102(active(x0), x1, x2)
743.71/262.78	   U102(x0, active(x1), x2)
743.71/262.78	   U102(x0, x1, active(x2))
743.71/262.78	   isNatKind(mark(x0))
743.71/262.78	   isNatKind(active(x0))
743.71/262.78	   U103(mark(x0), x1, x2)
743.71/262.78	   U103(x0, mark(x1), x2)
743.71/262.78	   U103(x0, x1, mark(x2))
743.71/262.78	   U103(active(x0), x1, x2)
743.71/262.78	   U103(x0, active(x1), x2)
743.71/262.78	   U103(x0, x1, active(x2))
743.71/262.78	   isNat(mark(x0))
743.71/262.78	   isNat(active(x0))
743.71/262.78	   U104(mark(x0), x1, x2)
743.71/262.78	   U104(x0, mark(x1), x2)
743.71/262.78	   U104(x0, x1, mark(x2))
743.71/262.78	   U104(active(x0), x1, x2)
743.71/262.78	   U104(x0, active(x1), x2)
743.71/262.78	   U104(x0, x1, active(x2))
743.71/262.78	   plus(mark(x0), x1)
743.71/262.78	   plus(x0, mark(x1))
743.71/262.78	   plus(active(x0), x1)
743.71/262.78	   plus(x0, active(x1))
743.71/262.78	   x(mark(x0), x1)
743.71/262.78	   x(x0, mark(x1))
743.71/262.78	   x(active(x0), x1)
743.71/262.78	   x(x0, active(x1))
743.71/262.78	   U11(mark(x0), x1, x2)
743.71/262.78	   U11(x0, mark(x1), x2)
743.71/262.78	   U11(x0, x1, mark(x2))
743.71/262.78	   U11(active(x0), x1, x2)
743.71/262.78	   U11(x0, active(x1), x2)
743.71/262.78	   U11(x0, x1, active(x2))
743.71/262.78	   U12(mark(x0), x1, x2)
743.71/262.78	   U12(x0, mark(x1), x2)
743.71/262.78	   U12(x0, x1, mark(x2))
743.71/262.78	   U12(active(x0), x1, x2)
743.71/262.78	   U12(x0, active(x1), x2)
743.71/262.78	   U12(x0, x1, active(x2))
743.71/262.78	   U13(mark(x0), x1, x2)
743.71/262.78	   U13(x0, mark(x1), x2)
743.71/262.78	   U13(x0, x1, mark(x2))
743.71/262.78	   U13(active(x0), x1, x2)
743.71/262.78	   U13(x0, active(x1), x2)
743.71/262.78	   U13(x0, x1, active(x2))
743.71/262.78	   U14(mark(x0), x1, x2)
743.71/262.78	   U14(x0, mark(x1), x2)
743.71/262.78	   U14(x0, x1, mark(x2))
743.71/262.78	   U14(active(x0), x1, x2)
743.71/262.78	   U14(x0, active(x1), x2)
743.71/262.78	   U14(x0, x1, active(x2))
743.71/262.78	   U15(mark(x0), x1)
743.71/262.78	   U15(x0, mark(x1))
743.71/262.78	   U15(active(x0), x1)
743.71/262.78	   U15(x0, active(x1))
743.71/262.78	   U16(mark(x0))
743.71/262.78	   U16(active(x0))
743.71/262.78	   U21(mark(x0), x1)
743.71/262.78	   U21(x0, mark(x1))
743.71/262.78	   U21(active(x0), x1)
743.71/262.78	   U21(x0, active(x1))
743.71/262.78	   U22(mark(x0), x1)
743.71/262.78	   U22(x0, mark(x1))
743.71/262.78	   U22(active(x0), x1)
743.71/262.78	   U22(x0, active(x1))
743.71/262.78	   U23(mark(x0))
743.71/262.78	   U23(active(x0))
743.71/262.78	   U31(mark(x0), x1, x2)
743.71/262.78	   U31(x0, mark(x1), x2)
743.71/262.78	   U31(x0, x1, mark(x2))
743.71/262.78	   U31(active(x0), x1, x2)
743.71/262.78	   U31(x0, active(x1), x2)
743.71/262.78	   U31(x0, x1, active(x2))
743.71/262.78	   U32(mark(x0), x1, x2)
743.71/262.78	   U32(x0, mark(x1), x2)
743.71/262.78	   U32(x0, x1, mark(x2))
743.71/262.78	   U32(active(x0), x1, x2)
743.71/262.78	   U32(x0, active(x1), x2)
743.71/262.78	   U32(x0, x1, active(x2))
743.71/262.78	   U33(mark(x0), x1, x2)
743.71/262.78	   U33(x0, mark(x1), x2)
743.71/262.78	   U33(x0, x1, mark(x2))
743.71/262.78	   U33(active(x0), x1, x2)
743.71/262.78	   U33(x0, active(x1), x2)
743.71/262.78	   U33(x0, x1, active(x2))
743.71/262.78	   U34(mark(x0), x1, x2)
743.71/262.78	   U34(x0, mark(x1), x2)
743.71/262.78	   U34(x0, x1, mark(x2))
743.71/262.78	   U34(active(x0), x1, x2)
743.71/262.78	   U34(x0, active(x1), x2)
743.71/262.78	   U34(x0, x1, active(x2))
743.71/262.78	   U35(mark(x0), x1)
743.71/262.78	   U35(x0, mark(x1))
743.71/262.78	   U35(active(x0), x1)
743.71/262.78	   U35(x0, active(x1))
743.71/262.78	   U36(mark(x0))
743.71/262.78	   U36(active(x0))
743.71/262.78	   U41(mark(x0), x1)
743.71/262.78	   U41(x0, mark(x1))
743.71/262.78	   U41(active(x0), x1)
743.71/262.78	   U41(x0, active(x1))
743.71/262.78	   U42(mark(x0))
743.71/262.78	   U42(active(x0))
743.71/262.78	   U51(mark(x0))
743.71/262.78	   U51(active(x0))
743.71/262.78	   U61(mark(x0), x1)
743.71/262.78	   U61(x0, mark(x1))
743.71/262.78	   U61(active(x0), x1)
743.71/262.78	   U61(x0, active(x1))
743.71/262.78	   U62(mark(x0))
743.71/262.78	   U62(active(x0))
743.71/262.78	   U71(mark(x0), x1)
743.71/262.78	   U71(x0, mark(x1))
743.71/262.78	   U71(active(x0), x1)
743.71/262.78	   U71(x0, active(x1))
743.71/262.78	   U72(mark(x0), x1)
743.71/262.78	   U72(x0, mark(x1))
743.71/262.78	   U72(active(x0), x1)
743.71/262.78	   U72(x0, active(x1))
743.71/262.78	   U81(mark(x0), x1, x2)
743.71/262.78	   U81(x0, mark(x1), x2)
743.71/262.78	   U81(x0, x1, mark(x2))
743.71/262.78	   U81(active(x0), x1, x2)
743.71/262.78	   U81(x0, active(x1), x2)
743.71/262.78	   U81(x0, x1, active(x2))
743.71/262.78	   U82(mark(x0), x1, x2)
743.71/262.78	   U82(x0, mark(x1), x2)
743.71/262.78	   U82(x0, x1, mark(x2))
743.71/262.78	   U82(active(x0), x1, x2)
743.71/262.78	   U82(x0, active(x1), x2)
743.71/262.78	   U82(x0, x1, active(x2))
743.71/262.78	   U83(mark(x0), x1, x2)
743.71/262.78	   U83(x0, mark(x1), x2)
743.71/262.78	   U83(x0, x1, mark(x2))
743.71/262.78	   U83(active(x0), x1, x2)
743.71/262.78	   U83(x0, active(x1), x2)
743.71/262.78	   U83(x0, x1, active(x2))
743.71/262.78	   U84(mark(x0), x1, x2)
743.71/262.78	   U84(x0, mark(x1), x2)
743.71/262.78	   U84(x0, x1, mark(x2))
743.71/262.78	   U84(active(x0), x1, x2)
743.71/262.78	   U84(x0, active(x1), x2)
743.71/262.78	   U84(x0, x1, active(x2))
743.71/262.78	   s(mark(x0))
743.71/262.78	   s(active(x0))
743.71/262.78	   U91(mark(x0), x1)
743.71/262.78	   U91(x0, mark(x1))
743.71/262.78	   U91(active(x0), x1)
743.71/262.78	   U91(x0, active(x1))
743.71/262.78	   U92(mark(x0))
743.71/262.78	   U92(active(x0))
743.71/262.78	
743.71/262.78	We have to consider all minimal (P,Q,R)-chains.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(55) UsableRulesProof (EQUIVALENT)
743.71/262.78	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.
743.71/262.78	----------------------------------------
743.71/262.78	
743.71/262.78	(56)
743.71/262.78	Obligation:
743.71/262.78	Q DP problem:
743.71/262.78	The TRS P consists of the following rules:
743.71/262.78	
743.71/262.78	   U72^1(X1, mark(X2)) -> U72^1(X1, X2)
743.71/262.78	   U72^1(mark(X1), X2) -> U72^1(X1, X2)
743.71/262.78	   U72^1(active(X1), X2) -> U72^1(X1, X2)
743.71/262.78	   U72^1(X1, active(X2)) -> U72^1(X1, X2)
743.71/262.78	
743.71/262.78	R is empty.
743.71/262.78	The set Q consists of the following terms:
743.71/262.78	
743.71/262.78	   active(U101(tt, x0, x1))
743.71/262.78	   active(U102(tt, x0, x1))
743.71/262.78	   active(U103(tt, x0, x1))
743.71/262.78	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.71/262.79	   U12(active(x0), x1, x2)
743.71/262.79	   U12(x0, active(x1), x2)
743.71/262.79	   U12(x0, x1, active(x2))
743.71/262.79	   U13(mark(x0), x1, x2)
743.71/262.79	   U13(x0, mark(x1), x2)
743.71/262.79	   U13(x0, x1, mark(x2))
743.71/262.79	   U13(active(x0), x1, x2)
743.71/262.79	   U13(x0, active(x1), x2)
743.71/262.79	   U13(x0, x1, active(x2))
743.71/262.79	   U14(mark(x0), x1, x2)
743.71/262.79	   U14(x0, mark(x1), x2)
743.71/262.79	   U14(x0, x1, mark(x2))
743.71/262.79	   U14(active(x0), x1, x2)
743.71/262.79	   U14(x0, active(x1), x2)
743.71/262.79	   U14(x0, x1, active(x2))
743.71/262.79	   U15(mark(x0), x1)
743.71/262.79	   U15(x0, mark(x1))
743.71/262.79	   U15(active(x0), x1)
743.71/262.79	   U15(x0, active(x1))
743.71/262.79	   U16(mark(x0))
743.71/262.79	   U16(active(x0))
743.71/262.79	   U21(mark(x0), x1)
743.71/262.79	   U21(x0, mark(x1))
743.71/262.79	   U21(active(x0), x1)
743.71/262.79	   U21(x0, active(x1))
743.71/262.79	   U22(mark(x0), x1)
743.71/262.79	   U22(x0, mark(x1))
743.71/262.79	   U22(active(x0), x1)
743.71/262.79	   U22(x0, active(x1))
743.71/262.79	   U23(mark(x0))
743.71/262.79	   U23(active(x0))
743.71/262.79	   U31(mark(x0), x1, x2)
743.71/262.79	   U31(x0, mark(x1), x2)
743.71/262.79	   U31(x0, x1, mark(x2))
743.71/262.79	   U31(active(x0), x1, x2)
743.71/262.79	   U31(x0, active(x1), x2)
743.71/262.79	   U31(x0, x1, active(x2))
743.71/262.79	   U32(mark(x0), x1, x2)
743.71/262.79	   U32(x0, mark(x1), x2)
743.71/262.79	   U32(x0, x1, mark(x2))
743.71/262.79	   U32(active(x0), x1, x2)
743.71/262.79	   U32(x0, active(x1), x2)
743.71/262.79	   U32(x0, x1, active(x2))
743.71/262.79	   U33(mark(x0), x1, x2)
743.71/262.79	   U33(x0, mark(x1), x2)
743.71/262.79	   U33(x0, x1, mark(x2))
743.71/262.79	   U33(active(x0), x1, x2)
743.71/262.79	   U33(x0, active(x1), x2)
743.71/262.79	   U33(x0, x1, active(x2))
743.71/262.79	   U34(mark(x0), x1, x2)
743.71/262.79	   U34(x0, mark(x1), x2)
743.71/262.79	   U34(x0, x1, mark(x2))
743.71/262.79	   U34(active(x0), x1, x2)
743.71/262.79	   U34(x0, active(x1), x2)
743.71/262.79	   U34(x0, x1, active(x2))
743.71/262.79	   U35(mark(x0), x1)
743.71/262.79	   U35(x0, mark(x1))
743.71/262.79	   U35(active(x0), x1)
743.71/262.79	   U35(x0, active(x1))
743.71/262.79	   U36(mark(x0))
743.71/262.79	   U36(active(x0))
743.71/262.79	   U41(mark(x0), x1)
743.71/262.79	   U41(x0, mark(x1))
743.71/262.79	   U41(active(x0), x1)
743.71/262.79	   U41(x0, active(x1))
743.71/262.79	   U42(mark(x0))
743.71/262.79	   U42(active(x0))
743.71/262.79	   U51(mark(x0))
743.71/262.79	   U51(active(x0))
743.71/262.79	   U61(mark(x0), x1)
743.71/262.79	   U61(x0, mark(x1))
743.71/262.79	   U61(active(x0), x1)
743.71/262.79	   U61(x0, active(x1))
743.71/262.79	   U62(mark(x0))
743.71/262.79	   U62(active(x0))
743.71/262.79	   U71(mark(x0), x1)
743.71/262.79	   U71(x0, mark(x1))
743.71/262.79	   U71(active(x0), x1)
743.71/262.79	   U71(x0, active(x1))
743.71/262.79	   U72(mark(x0), x1)
743.71/262.79	   U72(x0, mark(x1))
743.71/262.79	   U72(active(x0), x1)
743.71/262.79	   U72(x0, active(x1))
743.71/262.79	   U81(mark(x0), x1, x2)
743.71/262.79	   U81(x0, mark(x1), x2)
743.71/262.79	   U81(x0, x1, mark(x2))
743.71/262.79	   U81(active(x0), x1, x2)
743.71/262.79	   U81(x0, active(x1), x2)
743.71/262.79	   U81(x0, x1, active(x2))
743.71/262.79	   U82(mark(x0), x1, x2)
743.71/262.79	   U82(x0, mark(x1), x2)
743.71/262.79	   U82(x0, x1, mark(x2))
743.71/262.79	   U82(active(x0), x1, x2)
743.71/262.79	   U82(x0, active(x1), x2)
743.71/262.79	   U82(x0, x1, active(x2))
743.71/262.79	   U83(mark(x0), x1, x2)
743.71/262.79	   U83(x0, mark(x1), x2)
743.71/262.79	   U83(x0, x1, mark(x2))
743.71/262.79	   U83(active(x0), x1, x2)
743.71/262.79	   U83(x0, active(x1), x2)
743.71/262.79	   U83(x0, x1, active(x2))
743.71/262.79	   U84(mark(x0), x1, x2)
743.71/262.79	   U84(x0, mark(x1), x2)
743.71/262.79	   U84(x0, x1, mark(x2))
743.71/262.79	   U84(active(x0), x1, x2)
743.71/262.79	   U84(x0, active(x1), x2)
743.71/262.79	   U84(x0, x1, active(x2))
743.71/262.79	   s(mark(x0))
743.71/262.79	   s(active(x0))
743.71/262.79	   U91(mark(x0), x1)
743.71/262.79	   U91(x0, mark(x1))
743.71/262.79	   U91(active(x0), x1)
743.71/262.79	   U91(x0, active(x1))
743.71/262.79	   U92(mark(x0))
743.71/262.79	   U92(active(x0))
743.71/262.79	
743.71/262.79	We have to consider all minimal (P,Q,R)-chains.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(57) QReductionProof (EQUIVALENT)
743.71/262.79	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.79	
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.71/262.79	   U12(active(x0), x1, x2)
743.71/262.79	   U12(x0, active(x1), x2)
743.71/262.79	   U12(x0, x1, active(x2))
743.71/262.79	   U13(mark(x0), x1, x2)
743.71/262.79	   U13(x0, mark(x1), x2)
743.71/262.79	   U13(x0, x1, mark(x2))
743.71/262.79	   U13(active(x0), x1, x2)
743.71/262.79	   U13(x0, active(x1), x2)
743.71/262.79	   U13(x0, x1, active(x2))
743.71/262.79	   U14(mark(x0), x1, x2)
743.71/262.79	   U14(x0, mark(x1), x2)
743.71/262.79	   U14(x0, x1, mark(x2))
743.71/262.79	   U14(active(x0), x1, x2)
743.71/262.79	   U14(x0, active(x1), x2)
743.71/262.79	   U14(x0, x1, active(x2))
743.71/262.79	   U15(mark(x0), x1)
743.71/262.79	   U15(x0, mark(x1))
743.71/262.79	   U15(active(x0), x1)
743.71/262.79	   U15(x0, active(x1))
743.71/262.79	   U16(mark(x0))
743.71/262.79	   U16(active(x0))
743.71/262.79	   U21(mark(x0), x1)
743.71/262.79	   U21(x0, mark(x1))
743.71/262.79	   U21(active(x0), x1)
743.71/262.79	   U21(x0, active(x1))
743.71/262.79	   U22(mark(x0), x1)
743.71/262.79	   U22(x0, mark(x1))
743.71/262.79	   U22(active(x0), x1)
743.71/262.79	   U22(x0, active(x1))
743.71/262.79	   U23(mark(x0))
743.71/262.79	   U23(active(x0))
743.71/262.79	   U31(mark(x0), x1, x2)
743.71/262.79	   U31(x0, mark(x1), x2)
743.71/262.79	   U31(x0, x1, mark(x2))
743.71/262.79	   U31(active(x0), x1, x2)
743.71/262.79	   U31(x0, active(x1), x2)
743.71/262.79	   U31(x0, x1, active(x2))
743.71/262.79	   U32(mark(x0), x1, x2)
743.71/262.79	   U32(x0, mark(x1), x2)
743.71/262.79	   U32(x0, x1, mark(x2))
743.71/262.79	   U32(active(x0), x1, x2)
743.71/262.79	   U32(x0, active(x1), x2)
743.71/262.79	   U32(x0, x1, active(x2))
743.71/262.79	   U33(mark(x0), x1, x2)
743.71/262.79	   U33(x0, mark(x1), x2)
743.71/262.79	   U33(x0, x1, mark(x2))
743.71/262.79	   U33(active(x0), x1, x2)
743.71/262.79	   U33(x0, active(x1), x2)
743.71/262.79	   U33(x0, x1, active(x2))
743.71/262.79	   U34(mark(x0), x1, x2)
743.71/262.79	   U34(x0, mark(x1), x2)
743.71/262.79	   U34(x0, x1, mark(x2))
743.71/262.79	   U34(active(x0), x1, x2)
743.71/262.79	   U34(x0, active(x1), x2)
743.71/262.79	   U34(x0, x1, active(x2))
743.71/262.79	   U35(mark(x0), x1)
743.71/262.79	   U35(x0, mark(x1))
743.71/262.79	   U35(active(x0), x1)
743.71/262.79	   U35(x0, active(x1))
743.71/262.79	   U36(mark(x0))
743.71/262.79	   U36(active(x0))
743.71/262.79	   U41(mark(x0), x1)
743.71/262.79	   U41(x0, mark(x1))
743.71/262.79	   U41(active(x0), x1)
743.71/262.79	   U41(x0, active(x1))
743.71/262.79	   U42(mark(x0))
743.71/262.79	   U42(active(x0))
743.71/262.79	   U51(mark(x0))
743.71/262.79	   U51(active(x0))
743.71/262.79	   U61(mark(x0), x1)
743.71/262.79	   U61(x0, mark(x1))
743.71/262.79	   U61(active(x0), x1)
743.71/262.79	   U61(x0, active(x1))
743.71/262.79	   U62(mark(x0))
743.71/262.79	   U62(active(x0))
743.71/262.79	   U71(mark(x0), x1)
743.71/262.79	   U71(x0, mark(x1))
743.71/262.79	   U71(active(x0), x1)
743.71/262.79	   U71(x0, active(x1))
743.71/262.79	   U72(mark(x0), x1)
743.71/262.79	   U72(x0, mark(x1))
743.71/262.79	   U72(active(x0), x1)
743.71/262.79	   U72(x0, active(x1))
743.71/262.79	   U81(mark(x0), x1, x2)
743.71/262.79	   U81(x0, mark(x1), x2)
743.71/262.79	   U81(x0, x1, mark(x2))
743.71/262.79	   U81(active(x0), x1, x2)
743.71/262.79	   U81(x0, active(x1), x2)
743.71/262.79	   U81(x0, x1, active(x2))
743.71/262.79	   U82(mark(x0), x1, x2)
743.71/262.79	   U82(x0, mark(x1), x2)
743.71/262.79	   U82(x0, x1, mark(x2))
743.71/262.79	   U82(active(x0), x1, x2)
743.71/262.79	   U82(x0, active(x1), x2)
743.71/262.79	   U82(x0, x1, active(x2))
743.71/262.79	   U83(mark(x0), x1, x2)
743.71/262.79	   U83(x0, mark(x1), x2)
743.71/262.79	   U83(x0, x1, mark(x2))
743.71/262.79	   U83(active(x0), x1, x2)
743.71/262.79	   U83(x0, active(x1), x2)
743.71/262.79	   U83(x0, x1, active(x2))
743.71/262.79	   U84(mark(x0), x1, x2)
743.71/262.79	   U84(x0, mark(x1), x2)
743.71/262.79	   U84(x0, x1, mark(x2))
743.71/262.79	   U84(active(x0), x1, x2)
743.71/262.79	   U84(x0, active(x1), x2)
743.71/262.79	   U84(x0, x1, active(x2))
743.71/262.79	   s(mark(x0))
743.71/262.79	   s(active(x0))
743.71/262.79	   U91(mark(x0), x1)
743.71/262.79	   U91(x0, mark(x1))
743.71/262.79	   U91(active(x0), x1)
743.71/262.79	   U91(x0, active(x1))
743.71/262.79	   U92(mark(x0))
743.71/262.79	   U92(active(x0))
743.71/262.79	
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(58)
743.71/262.79	Obligation:
743.71/262.79	Q DP problem:
743.71/262.79	The TRS P consists of the following rules:
743.71/262.79	
743.71/262.79	   U72^1(X1, mark(X2)) -> U72^1(X1, X2)
743.71/262.79	   U72^1(mark(X1), X2) -> U72^1(X1, X2)
743.71/262.79	   U72^1(active(X1), X2) -> U72^1(X1, X2)
743.71/262.79	   U72^1(X1, active(X2)) -> U72^1(X1, X2)
743.71/262.79	
743.71/262.79	R is empty.
743.71/262.79	The set Q consists of the following terms:
743.71/262.79	
743.71/262.79	   active(U101(tt, x0, x1))
743.71/262.79	   active(U102(tt, x0, x1))
743.71/262.79	   active(U103(tt, x0, x1))
743.71/262.79	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	
743.71/262.79	We have to consider all minimal (P,Q,R)-chains.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(59) QDPSizeChangeProof (EQUIVALENT)
743.71/262.79	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. 
743.71/262.79	
743.71/262.79	From the DPs we obtained the following set of size-change graphs:
743.71/262.79	*U72^1(X1, mark(X2)) -> U72^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 >= 1, 2 > 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U72^1(mark(X1), X2) -> U72^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 > 1, 2 >= 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U72^1(active(X1), X2) -> U72^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 > 1, 2 >= 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U72^1(X1, active(X2)) -> U72^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 >= 1, 2 > 2
743.71/262.79	
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(60)
743.71/262.79	YES
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(61)
743.71/262.79	Obligation:
743.71/262.79	Q DP problem:
743.71/262.79	The TRS P consists of the following rules:
743.71/262.79	
743.71/262.79	   U71^1(X1, mark(X2)) -> U71^1(X1, X2)
743.71/262.79	   U71^1(mark(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(active(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(X1, active(X2)) -> U71^1(X1, X2)
743.71/262.79	
743.71/262.79	The TRS R consists of the following rules:
743.71/262.79	
743.71/262.79	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.79	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.79	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.79	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.79	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.79	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.79	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.79	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.79	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.79	   active(U16(tt)) -> mark(tt)
743.71/262.79	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.79	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.79	   active(U23(tt)) -> mark(tt)
743.71/262.79	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.79	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.79	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.79	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.79	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.79	   active(U36(tt)) -> mark(tt)
743.71/262.79	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.79	   active(U42(tt)) -> mark(tt)
743.71/262.79	   active(U51(tt)) -> mark(tt)
743.71/262.79	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.79	   active(U62(tt)) -> mark(tt)
743.71/262.79	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.79	   active(U72(tt, N)) -> mark(N)
743.71/262.79	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.79	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.79	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.79	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.79	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.79	   active(U92(tt)) -> mark(0)
743.71/262.79	   active(isNat(0)) -> mark(tt)
743.71/262.79	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.79	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.79	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.79	   active(isNatKind(0)) -> mark(tt)
743.71/262.79	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.79	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.79	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.79	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.79	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.79	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.79	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.79	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.79	   mark(tt) -> active(tt)
743.71/262.79	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.79	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.79	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.79	   mark(isNat(X)) -> active(isNat(X))
743.71/262.79	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.79	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.79	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.79	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.79	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.79	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.79	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.79	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.79	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.79	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.79	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.79	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.79	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.79	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.79	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.79	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.79	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.79	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.79	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.79	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.79	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.79	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.79	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.79	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.79	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.79	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.79	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.79	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.79	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.79	   mark(s(X)) -> active(s(mark(X)))
743.71/262.79	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.79	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.79	   mark(0) -> active(0)
743.71/262.79	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.79	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.79	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.79	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.79	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.79	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.79	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.79	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.79	   isNat(mark(X)) -> isNat(X)
743.71/262.79	   isNat(active(X)) -> isNat(X)
743.71/262.79	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.79	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.79	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.79	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.79	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.79	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.79	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.79	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.79	   x(active(X1), X2) -> x(X1, X2)
743.71/262.79	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.79	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.79	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.79	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.79	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.79	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.79	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.79	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.79	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.79	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.79	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.79	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.79	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.79	   U16(mark(X)) -> U16(X)
743.71/262.79	   U16(active(X)) -> U16(X)
743.71/262.79	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.79	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.79	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.79	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.79	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.79	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.79	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.79	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.79	   U23(mark(X)) -> U23(X)
743.71/262.79	   U23(active(X)) -> U23(X)
743.71/262.79	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.79	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.79	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.79	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.79	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.79	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.79	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.79	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.79	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.79	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.79	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.79	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.79	   U36(mark(X)) -> U36(X)
743.71/262.79	   U36(active(X)) -> U36(X)
743.71/262.79	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.79	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.79	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.79	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.79	   U42(mark(X)) -> U42(X)
743.71/262.79	   U42(active(X)) -> U42(X)
743.71/262.79	   U51(mark(X)) -> U51(X)
743.71/262.79	   U51(active(X)) -> U51(X)
743.71/262.79	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.79	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.79	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.79	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.79	   U62(mark(X)) -> U62(X)
743.71/262.79	   U62(active(X)) -> U62(X)
743.71/262.79	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.79	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.79	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.79	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.79	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.79	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.79	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.79	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.79	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.79	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.79	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.79	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.79	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.79	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.79	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.79	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.79	   s(mark(X)) -> s(X)
743.71/262.79	   s(active(X)) -> s(X)
743.71/262.79	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.79	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.79	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.79	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.79	   U92(mark(X)) -> U92(X)
743.71/262.79	   U92(active(X)) -> U92(X)
743.71/262.79	
743.71/262.79	The set Q consists of the following terms:
743.71/262.79	
743.71/262.79	   active(U101(tt, x0, x1))
743.71/262.79	   active(U102(tt, x0, x1))
743.71/262.79	   active(U103(tt, x0, x1))
743.71/262.79	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.71/262.79	   U12(active(x0), x1, x2)
743.71/262.79	   U12(x0, active(x1), x2)
743.71/262.79	   U12(x0, x1, active(x2))
743.71/262.79	   U13(mark(x0), x1, x2)
743.71/262.79	   U13(x0, mark(x1), x2)
743.71/262.79	   U13(x0, x1, mark(x2))
743.71/262.79	   U13(active(x0), x1, x2)
743.71/262.79	   U13(x0, active(x1), x2)
743.71/262.79	   U13(x0, x1, active(x2))
743.71/262.79	   U14(mark(x0), x1, x2)
743.71/262.79	   U14(x0, mark(x1), x2)
743.71/262.79	   U14(x0, x1, mark(x2))
743.71/262.79	   U14(active(x0), x1, x2)
743.71/262.79	   U14(x0, active(x1), x2)
743.71/262.79	   U14(x0, x1, active(x2))
743.71/262.79	   U15(mark(x0), x1)
743.71/262.79	   U15(x0, mark(x1))
743.71/262.79	   U15(active(x0), x1)
743.71/262.79	   U15(x0, active(x1))
743.71/262.79	   U16(mark(x0))
743.71/262.79	   U16(active(x0))
743.71/262.79	   U21(mark(x0), x1)
743.71/262.79	   U21(x0, mark(x1))
743.71/262.79	   U21(active(x0), x1)
743.71/262.79	   U21(x0, active(x1))
743.71/262.79	   U22(mark(x0), x1)
743.71/262.79	   U22(x0, mark(x1))
743.71/262.79	   U22(active(x0), x1)
743.71/262.79	   U22(x0, active(x1))
743.71/262.79	   U23(mark(x0))
743.71/262.79	   U23(active(x0))
743.71/262.79	   U31(mark(x0), x1, x2)
743.71/262.79	   U31(x0, mark(x1), x2)
743.71/262.79	   U31(x0, x1, mark(x2))
743.71/262.79	   U31(active(x0), x1, x2)
743.71/262.79	   U31(x0, active(x1), x2)
743.71/262.79	   U31(x0, x1, active(x2))
743.71/262.79	   U32(mark(x0), x1, x2)
743.71/262.79	   U32(x0, mark(x1), x2)
743.71/262.79	   U32(x0, x1, mark(x2))
743.71/262.79	   U32(active(x0), x1, x2)
743.71/262.79	   U32(x0, active(x1), x2)
743.71/262.79	   U32(x0, x1, active(x2))
743.71/262.79	   U33(mark(x0), x1, x2)
743.71/262.79	   U33(x0, mark(x1), x2)
743.71/262.79	   U33(x0, x1, mark(x2))
743.71/262.79	   U33(active(x0), x1, x2)
743.71/262.79	   U33(x0, active(x1), x2)
743.71/262.79	   U33(x0, x1, active(x2))
743.71/262.79	   U34(mark(x0), x1, x2)
743.71/262.79	   U34(x0, mark(x1), x2)
743.71/262.79	   U34(x0, x1, mark(x2))
743.71/262.79	   U34(active(x0), x1, x2)
743.71/262.79	   U34(x0, active(x1), x2)
743.71/262.79	   U34(x0, x1, active(x2))
743.71/262.79	   U35(mark(x0), x1)
743.71/262.79	   U35(x0, mark(x1))
743.71/262.79	   U35(active(x0), x1)
743.71/262.79	   U35(x0, active(x1))
743.71/262.79	   U36(mark(x0))
743.71/262.79	   U36(active(x0))
743.71/262.79	   U41(mark(x0), x1)
743.71/262.79	   U41(x0, mark(x1))
743.71/262.79	   U41(active(x0), x1)
743.71/262.79	   U41(x0, active(x1))
743.71/262.79	   U42(mark(x0))
743.71/262.79	   U42(active(x0))
743.71/262.79	   U51(mark(x0))
743.71/262.79	   U51(active(x0))
743.71/262.79	   U61(mark(x0), x1)
743.71/262.79	   U61(x0, mark(x1))
743.71/262.79	   U61(active(x0), x1)
743.71/262.79	   U61(x0, active(x1))
743.71/262.79	   U62(mark(x0))
743.71/262.79	   U62(active(x0))
743.71/262.79	   U71(mark(x0), x1)
743.71/262.79	   U71(x0, mark(x1))
743.71/262.79	   U71(active(x0), x1)
743.71/262.79	   U71(x0, active(x1))
743.71/262.79	   U72(mark(x0), x1)
743.71/262.79	   U72(x0, mark(x1))
743.71/262.79	   U72(active(x0), x1)
743.71/262.79	   U72(x0, active(x1))
743.71/262.79	   U81(mark(x0), x1, x2)
743.71/262.79	   U81(x0, mark(x1), x2)
743.71/262.79	   U81(x0, x1, mark(x2))
743.71/262.79	   U81(active(x0), x1, x2)
743.71/262.79	   U81(x0, active(x1), x2)
743.71/262.79	   U81(x0, x1, active(x2))
743.71/262.79	   U82(mark(x0), x1, x2)
743.71/262.79	   U82(x0, mark(x1), x2)
743.71/262.79	   U82(x0, x1, mark(x2))
743.71/262.79	   U82(active(x0), x1, x2)
743.71/262.79	   U82(x0, active(x1), x2)
743.71/262.79	   U82(x0, x1, active(x2))
743.71/262.79	   U83(mark(x0), x1, x2)
743.71/262.79	   U83(x0, mark(x1), x2)
743.71/262.79	   U83(x0, x1, mark(x2))
743.71/262.79	   U83(active(x0), x1, x2)
743.71/262.79	   U83(x0, active(x1), x2)
743.71/262.79	   U83(x0, x1, active(x2))
743.71/262.79	   U84(mark(x0), x1, x2)
743.71/262.79	   U84(x0, mark(x1), x2)
743.71/262.79	   U84(x0, x1, mark(x2))
743.71/262.79	   U84(active(x0), x1, x2)
743.71/262.79	   U84(x0, active(x1), x2)
743.71/262.79	   U84(x0, x1, active(x2))
743.71/262.79	   s(mark(x0))
743.71/262.79	   s(active(x0))
743.71/262.79	   U91(mark(x0), x1)
743.71/262.79	   U91(x0, mark(x1))
743.71/262.79	   U91(active(x0), x1)
743.71/262.79	   U91(x0, active(x1))
743.71/262.79	   U92(mark(x0))
743.71/262.79	   U92(active(x0))
743.71/262.79	
743.71/262.79	We have to consider all minimal (P,Q,R)-chains.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(62) UsableRulesProof (EQUIVALENT)
743.71/262.79	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.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(63)
743.71/262.79	Obligation:
743.71/262.79	Q DP problem:
743.71/262.79	The TRS P consists of the following rules:
743.71/262.79	
743.71/262.79	   U71^1(X1, mark(X2)) -> U71^1(X1, X2)
743.71/262.79	   U71^1(mark(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(active(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(X1, active(X2)) -> U71^1(X1, X2)
743.71/262.79	
743.71/262.79	R is empty.
743.71/262.79	The set Q consists of the following terms:
743.71/262.79	
743.71/262.79	   active(U101(tt, x0, x1))
743.71/262.79	   active(U102(tt, x0, x1))
743.71/262.79	   active(U103(tt, x0, x1))
743.71/262.79	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.71/262.79	   U12(active(x0), x1, x2)
743.71/262.79	   U12(x0, active(x1), x2)
743.71/262.79	   U12(x0, x1, active(x2))
743.71/262.79	   U13(mark(x0), x1, x2)
743.71/262.79	   U13(x0, mark(x1), x2)
743.71/262.79	   U13(x0, x1, mark(x2))
743.71/262.79	   U13(active(x0), x1, x2)
743.71/262.79	   U13(x0, active(x1), x2)
743.71/262.79	   U13(x0, x1, active(x2))
743.71/262.79	   U14(mark(x0), x1, x2)
743.71/262.79	   U14(x0, mark(x1), x2)
743.71/262.79	   U14(x0, x1, mark(x2))
743.71/262.79	   U14(active(x0), x1, x2)
743.71/262.79	   U14(x0, active(x1), x2)
743.71/262.79	   U14(x0, x1, active(x2))
743.71/262.79	   U15(mark(x0), x1)
743.71/262.79	   U15(x0, mark(x1))
743.71/262.79	   U15(active(x0), x1)
743.71/262.79	   U15(x0, active(x1))
743.71/262.79	   U16(mark(x0))
743.71/262.79	   U16(active(x0))
743.71/262.79	   U21(mark(x0), x1)
743.71/262.79	   U21(x0, mark(x1))
743.71/262.79	   U21(active(x0), x1)
743.71/262.79	   U21(x0, active(x1))
743.71/262.79	   U22(mark(x0), x1)
743.71/262.79	   U22(x0, mark(x1))
743.71/262.79	   U22(active(x0), x1)
743.71/262.79	   U22(x0, active(x1))
743.71/262.79	   U23(mark(x0))
743.71/262.79	   U23(active(x0))
743.71/262.79	   U31(mark(x0), x1, x2)
743.71/262.79	   U31(x0, mark(x1), x2)
743.71/262.79	   U31(x0, x1, mark(x2))
743.71/262.79	   U31(active(x0), x1, x2)
743.71/262.79	   U31(x0, active(x1), x2)
743.71/262.79	   U31(x0, x1, active(x2))
743.71/262.79	   U32(mark(x0), x1, x2)
743.71/262.79	   U32(x0, mark(x1), x2)
743.71/262.79	   U32(x0, x1, mark(x2))
743.71/262.79	   U32(active(x0), x1, x2)
743.71/262.79	   U32(x0, active(x1), x2)
743.71/262.79	   U32(x0, x1, active(x2))
743.71/262.79	   U33(mark(x0), x1, x2)
743.71/262.79	   U33(x0, mark(x1), x2)
743.71/262.79	   U33(x0, x1, mark(x2))
743.71/262.79	   U33(active(x0), x1, x2)
743.71/262.79	   U33(x0, active(x1), x2)
743.71/262.79	   U33(x0, x1, active(x2))
743.71/262.79	   U34(mark(x0), x1, x2)
743.71/262.79	   U34(x0, mark(x1), x2)
743.71/262.79	   U34(x0, x1, mark(x2))
743.71/262.79	   U34(active(x0), x1, x2)
743.71/262.79	   U34(x0, active(x1), x2)
743.71/262.79	   U34(x0, x1, active(x2))
743.71/262.79	   U35(mark(x0), x1)
743.71/262.79	   U35(x0, mark(x1))
743.71/262.79	   U35(active(x0), x1)
743.71/262.79	   U35(x0, active(x1))
743.71/262.79	   U36(mark(x0))
743.71/262.79	   U36(active(x0))
743.71/262.79	   U41(mark(x0), x1)
743.71/262.79	   U41(x0, mark(x1))
743.71/262.79	   U41(active(x0), x1)
743.71/262.79	   U41(x0, active(x1))
743.71/262.79	   U42(mark(x0))
743.71/262.79	   U42(active(x0))
743.71/262.79	   U51(mark(x0))
743.71/262.79	   U51(active(x0))
743.71/262.79	   U61(mark(x0), x1)
743.71/262.79	   U61(x0, mark(x1))
743.71/262.79	   U61(active(x0), x1)
743.71/262.79	   U61(x0, active(x1))
743.71/262.79	   U62(mark(x0))
743.71/262.79	   U62(active(x0))
743.71/262.79	   U71(mark(x0), x1)
743.71/262.79	   U71(x0, mark(x1))
743.71/262.79	   U71(active(x0), x1)
743.71/262.79	   U71(x0, active(x1))
743.71/262.79	   U72(mark(x0), x1)
743.71/262.79	   U72(x0, mark(x1))
743.71/262.79	   U72(active(x0), x1)
743.71/262.79	   U72(x0, active(x1))
743.71/262.79	   U81(mark(x0), x1, x2)
743.71/262.79	   U81(x0, mark(x1), x2)
743.71/262.79	   U81(x0, x1, mark(x2))
743.71/262.79	   U81(active(x0), x1, x2)
743.71/262.79	   U81(x0, active(x1), x2)
743.71/262.79	   U81(x0, x1, active(x2))
743.71/262.79	   U82(mark(x0), x1, x2)
743.71/262.79	   U82(x0, mark(x1), x2)
743.71/262.79	   U82(x0, x1, mark(x2))
743.71/262.79	   U82(active(x0), x1, x2)
743.71/262.79	   U82(x0, active(x1), x2)
743.71/262.79	   U82(x0, x1, active(x2))
743.71/262.79	   U83(mark(x0), x1, x2)
743.71/262.79	   U83(x0, mark(x1), x2)
743.71/262.79	   U83(x0, x1, mark(x2))
743.71/262.79	   U83(active(x0), x1, x2)
743.71/262.79	   U83(x0, active(x1), x2)
743.71/262.79	   U83(x0, x1, active(x2))
743.71/262.79	   U84(mark(x0), x1, x2)
743.71/262.79	   U84(x0, mark(x1), x2)
743.71/262.79	   U84(x0, x1, mark(x2))
743.71/262.79	   U84(active(x0), x1, x2)
743.71/262.79	   U84(x0, active(x1), x2)
743.71/262.79	   U84(x0, x1, active(x2))
743.71/262.79	   s(mark(x0))
743.71/262.79	   s(active(x0))
743.71/262.79	   U91(mark(x0), x1)
743.71/262.79	   U91(x0, mark(x1))
743.71/262.79	   U91(active(x0), x1)
743.71/262.79	   U91(x0, active(x1))
743.71/262.79	   U92(mark(x0))
743.71/262.79	   U92(active(x0))
743.71/262.79	
743.71/262.79	We have to consider all minimal (P,Q,R)-chains.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(64) QReductionProof (EQUIVALENT)
743.71/262.79	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.71/262.79	
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.71/262.79	   U12(active(x0), x1, x2)
743.71/262.79	   U12(x0, active(x1), x2)
743.71/262.79	   U12(x0, x1, active(x2))
743.71/262.79	   U13(mark(x0), x1, x2)
743.71/262.79	   U13(x0, mark(x1), x2)
743.71/262.79	   U13(x0, x1, mark(x2))
743.71/262.79	   U13(active(x0), x1, x2)
743.71/262.79	   U13(x0, active(x1), x2)
743.71/262.79	   U13(x0, x1, active(x2))
743.71/262.79	   U14(mark(x0), x1, x2)
743.71/262.79	   U14(x0, mark(x1), x2)
743.71/262.79	   U14(x0, x1, mark(x2))
743.71/262.79	   U14(active(x0), x1, x2)
743.71/262.79	   U14(x0, active(x1), x2)
743.71/262.79	   U14(x0, x1, active(x2))
743.71/262.79	   U15(mark(x0), x1)
743.71/262.79	   U15(x0, mark(x1))
743.71/262.79	   U15(active(x0), x1)
743.71/262.79	   U15(x0, active(x1))
743.71/262.79	   U16(mark(x0))
743.71/262.79	   U16(active(x0))
743.71/262.79	   U21(mark(x0), x1)
743.71/262.79	   U21(x0, mark(x1))
743.71/262.79	   U21(active(x0), x1)
743.71/262.79	   U21(x0, active(x1))
743.71/262.79	   U22(mark(x0), x1)
743.71/262.79	   U22(x0, mark(x1))
743.71/262.79	   U22(active(x0), x1)
743.71/262.79	   U22(x0, active(x1))
743.71/262.79	   U23(mark(x0))
743.71/262.79	   U23(active(x0))
743.71/262.79	   U31(mark(x0), x1, x2)
743.71/262.79	   U31(x0, mark(x1), x2)
743.71/262.79	   U31(x0, x1, mark(x2))
743.71/262.79	   U31(active(x0), x1, x2)
743.71/262.79	   U31(x0, active(x1), x2)
743.71/262.79	   U31(x0, x1, active(x2))
743.71/262.79	   U32(mark(x0), x1, x2)
743.71/262.79	   U32(x0, mark(x1), x2)
743.71/262.79	   U32(x0, x1, mark(x2))
743.71/262.79	   U32(active(x0), x1, x2)
743.71/262.79	   U32(x0, active(x1), x2)
743.71/262.79	   U32(x0, x1, active(x2))
743.71/262.79	   U33(mark(x0), x1, x2)
743.71/262.79	   U33(x0, mark(x1), x2)
743.71/262.79	   U33(x0, x1, mark(x2))
743.71/262.79	   U33(active(x0), x1, x2)
743.71/262.79	   U33(x0, active(x1), x2)
743.71/262.79	   U33(x0, x1, active(x2))
743.71/262.79	   U34(mark(x0), x1, x2)
743.71/262.79	   U34(x0, mark(x1), x2)
743.71/262.79	   U34(x0, x1, mark(x2))
743.71/262.79	   U34(active(x0), x1, x2)
743.71/262.79	   U34(x0, active(x1), x2)
743.71/262.79	   U34(x0, x1, active(x2))
743.71/262.79	   U35(mark(x0), x1)
743.71/262.79	   U35(x0, mark(x1))
743.71/262.79	   U35(active(x0), x1)
743.71/262.79	   U35(x0, active(x1))
743.71/262.79	   U36(mark(x0))
743.71/262.79	   U36(active(x0))
743.71/262.79	   U41(mark(x0), x1)
743.71/262.79	   U41(x0, mark(x1))
743.71/262.79	   U41(active(x0), x1)
743.71/262.79	   U41(x0, active(x1))
743.71/262.79	   U42(mark(x0))
743.71/262.79	   U42(active(x0))
743.71/262.79	   U51(mark(x0))
743.71/262.79	   U51(active(x0))
743.71/262.79	   U61(mark(x0), x1)
743.71/262.79	   U61(x0, mark(x1))
743.71/262.79	   U61(active(x0), x1)
743.71/262.79	   U61(x0, active(x1))
743.71/262.79	   U62(mark(x0))
743.71/262.79	   U62(active(x0))
743.71/262.79	   U71(mark(x0), x1)
743.71/262.79	   U71(x0, mark(x1))
743.71/262.79	   U71(active(x0), x1)
743.71/262.79	   U71(x0, active(x1))
743.71/262.79	   U72(mark(x0), x1)
743.71/262.79	   U72(x0, mark(x1))
743.71/262.79	   U72(active(x0), x1)
743.71/262.79	   U72(x0, active(x1))
743.71/262.79	   U81(mark(x0), x1, x2)
743.71/262.79	   U81(x0, mark(x1), x2)
743.71/262.79	   U81(x0, x1, mark(x2))
743.71/262.79	   U81(active(x0), x1, x2)
743.71/262.79	   U81(x0, active(x1), x2)
743.71/262.79	   U81(x0, x1, active(x2))
743.71/262.79	   U82(mark(x0), x1, x2)
743.71/262.79	   U82(x0, mark(x1), x2)
743.71/262.79	   U82(x0, x1, mark(x2))
743.71/262.79	   U82(active(x0), x1, x2)
743.71/262.79	   U82(x0, active(x1), x2)
743.71/262.79	   U82(x0, x1, active(x2))
743.71/262.79	   U83(mark(x0), x1, x2)
743.71/262.79	   U83(x0, mark(x1), x2)
743.71/262.79	   U83(x0, x1, mark(x2))
743.71/262.79	   U83(active(x0), x1, x2)
743.71/262.79	   U83(x0, active(x1), x2)
743.71/262.79	   U83(x0, x1, active(x2))
743.71/262.79	   U84(mark(x0), x1, x2)
743.71/262.79	   U84(x0, mark(x1), x2)
743.71/262.79	   U84(x0, x1, mark(x2))
743.71/262.79	   U84(active(x0), x1, x2)
743.71/262.79	   U84(x0, active(x1), x2)
743.71/262.79	   U84(x0, x1, active(x2))
743.71/262.79	   s(mark(x0))
743.71/262.79	   s(active(x0))
743.71/262.79	   U91(mark(x0), x1)
743.71/262.79	   U91(x0, mark(x1))
743.71/262.79	   U91(active(x0), x1)
743.71/262.79	   U91(x0, active(x1))
743.71/262.79	   U92(mark(x0))
743.71/262.79	   U92(active(x0))
743.71/262.79	
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(65)
743.71/262.79	Obligation:
743.71/262.79	Q DP problem:
743.71/262.79	The TRS P consists of the following rules:
743.71/262.79	
743.71/262.79	   U71^1(X1, mark(X2)) -> U71^1(X1, X2)
743.71/262.79	   U71^1(mark(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(active(X1), X2) -> U71^1(X1, X2)
743.71/262.79	   U71^1(X1, active(X2)) -> U71^1(X1, X2)
743.71/262.79	
743.71/262.79	R is empty.
743.71/262.79	The set Q consists of the following terms:
743.71/262.79	
743.71/262.79	   active(U101(tt, x0, x1))
743.71/262.79	   active(U102(tt, x0, x1))
743.71/262.79	   active(U103(tt, x0, x1))
743.71/262.79	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	
743.71/262.79	We have to consider all minimal (P,Q,R)-chains.
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(66) QDPSizeChangeProof (EQUIVALENT)
743.71/262.79	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. 
743.71/262.79	
743.71/262.79	From the DPs we obtained the following set of size-change graphs:
743.71/262.79	*U71^1(X1, mark(X2)) -> U71^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 >= 1, 2 > 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U71^1(mark(X1), X2) -> U71^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 > 1, 2 >= 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U71^1(active(X1), X2) -> U71^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 > 1, 2 >= 2
743.71/262.79	
743.71/262.79	
743.71/262.79	*U71^1(X1, active(X2)) -> U71^1(X1, X2)
743.71/262.79	The graph contains the following edges 1 >= 1, 2 > 2
743.71/262.79	
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(67)
743.71/262.79	YES
743.71/262.79	
743.71/262.79	----------------------------------------
743.71/262.79	
743.71/262.79	(68)
743.71/262.79	Obligation:
743.71/262.79	Q DP problem:
743.71/262.79	The TRS P consists of the following rules:
743.71/262.79	
743.71/262.79	   U62^1(active(X)) -> U62^1(X)
743.71/262.79	   U62^1(mark(X)) -> U62^1(X)
743.71/262.79	
743.71/262.79	The TRS R consists of the following rules:
743.71/262.79	
743.71/262.79	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.71/262.79	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.71/262.79	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.71/262.79	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.71/262.79	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.71/262.79	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.71/262.79	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.71/262.79	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.71/262.79	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.71/262.79	   active(U16(tt)) -> mark(tt)
743.71/262.79	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.71/262.79	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.71/262.79	   active(U23(tt)) -> mark(tt)
743.71/262.79	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.71/262.79	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.71/262.79	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.71/262.79	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.71/262.79	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.71/262.79	   active(U36(tt)) -> mark(tt)
743.71/262.79	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.71/262.79	   active(U42(tt)) -> mark(tt)
743.71/262.79	   active(U51(tt)) -> mark(tt)
743.71/262.79	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.71/262.79	   active(U62(tt)) -> mark(tt)
743.71/262.79	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.71/262.79	   active(U72(tt, N)) -> mark(N)
743.71/262.79	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.71/262.79	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.71/262.79	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.71/262.79	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.71/262.79	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.71/262.79	   active(U92(tt)) -> mark(0)
743.71/262.79	   active(isNat(0)) -> mark(tt)
743.71/262.79	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.71/262.79	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.71/262.79	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.71/262.79	   active(isNatKind(0)) -> mark(tt)
743.71/262.79	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.71/262.79	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.71/262.79	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.71/262.79	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.71/262.79	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.71/262.79	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.71/262.79	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.71/262.79	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.71/262.79	   mark(tt) -> active(tt)
743.71/262.79	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.71/262.79	   mark(isNatKind(X)) -> active(isNatKind(X))
743.71/262.79	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.71/262.79	   mark(isNat(X)) -> active(isNat(X))
743.71/262.79	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.71/262.79	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.71/262.79	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.71/262.79	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.71/262.79	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.71/262.79	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.71/262.79	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.71/262.79	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.71/262.79	   mark(U16(X)) -> active(U16(mark(X)))
743.71/262.79	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.71/262.79	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.71/262.79	   mark(U23(X)) -> active(U23(mark(X)))
743.71/262.79	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.71/262.79	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.71/262.79	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.71/262.79	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.71/262.79	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.71/262.79	   mark(U36(X)) -> active(U36(mark(X)))
743.71/262.79	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.71/262.79	   mark(U42(X)) -> active(U42(mark(X)))
743.71/262.79	   mark(U51(X)) -> active(U51(mark(X)))
743.71/262.79	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.71/262.79	   mark(U62(X)) -> active(U62(mark(X)))
743.71/262.79	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.71/262.79	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.71/262.79	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.71/262.79	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.71/262.79	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.71/262.79	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.71/262.79	   mark(s(X)) -> active(s(mark(X)))
743.71/262.79	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.71/262.79	   mark(U92(X)) -> active(U92(mark(X)))
743.71/262.79	   mark(0) -> active(0)
743.71/262.79	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.71/262.79	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.71/262.79	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.71/262.79	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.71/262.79	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.71/262.79	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.71/262.79	   isNatKind(mark(X)) -> isNatKind(X)
743.71/262.79	   isNatKind(active(X)) -> isNatKind(X)
743.71/262.79	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.71/262.79	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.71/262.79	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.71/262.79	   isNat(mark(X)) -> isNat(X)
743.71/262.79	   isNat(active(X)) -> isNat(X)
743.71/262.79	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.71/262.79	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.71/262.79	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.71/262.79	   plus(mark(X1), X2) -> plus(X1, X2)
743.71/262.79	   plus(X1, mark(X2)) -> plus(X1, X2)
743.71/262.79	   plus(active(X1), X2) -> plus(X1, X2)
743.71/262.79	   plus(X1, active(X2)) -> plus(X1, X2)
743.71/262.79	   x(mark(X1), X2) -> x(X1, X2)
743.71/262.79	   x(X1, mark(X2)) -> x(X1, X2)
743.71/262.79	   x(active(X1), X2) -> x(X1, X2)
743.71/262.79	   x(X1, active(X2)) -> x(X1, X2)
743.71/262.79	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.71/262.79	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.71/262.79	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.71/262.79	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.71/262.79	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.71/262.79	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.71/262.79	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.71/262.79	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.71/262.79	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.71/262.79	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.71/262.79	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.71/262.79	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.71/262.79	   U15(mark(X1), X2) -> U15(X1, X2)
743.71/262.79	   U15(X1, mark(X2)) -> U15(X1, X2)
743.71/262.79	   U15(active(X1), X2) -> U15(X1, X2)
743.71/262.79	   U15(X1, active(X2)) -> U15(X1, X2)
743.71/262.79	   U16(mark(X)) -> U16(X)
743.71/262.79	   U16(active(X)) -> U16(X)
743.71/262.79	   U21(mark(X1), X2) -> U21(X1, X2)
743.71/262.79	   U21(X1, mark(X2)) -> U21(X1, X2)
743.71/262.79	   U21(active(X1), X2) -> U21(X1, X2)
743.71/262.79	   U21(X1, active(X2)) -> U21(X1, X2)
743.71/262.79	   U22(mark(X1), X2) -> U22(X1, X2)
743.71/262.79	   U22(X1, mark(X2)) -> U22(X1, X2)
743.71/262.79	   U22(active(X1), X2) -> U22(X1, X2)
743.71/262.79	   U22(X1, active(X2)) -> U22(X1, X2)
743.71/262.79	   U23(mark(X)) -> U23(X)
743.71/262.79	   U23(active(X)) -> U23(X)
743.71/262.79	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.71/262.79	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.71/262.79	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.71/262.79	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.71/262.79	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.71/262.79	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.71/262.79	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.71/262.79	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.71/262.79	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.71/262.79	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.71/262.79	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.71/262.79	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.71/262.79	   U35(mark(X1), X2) -> U35(X1, X2)
743.71/262.79	   U35(X1, mark(X2)) -> U35(X1, X2)
743.71/262.79	   U35(active(X1), X2) -> U35(X1, X2)
743.71/262.79	   U35(X1, active(X2)) -> U35(X1, X2)
743.71/262.79	   U36(mark(X)) -> U36(X)
743.71/262.79	   U36(active(X)) -> U36(X)
743.71/262.79	   U41(mark(X1), X2) -> U41(X1, X2)
743.71/262.79	   U41(X1, mark(X2)) -> U41(X1, X2)
743.71/262.79	   U41(active(X1), X2) -> U41(X1, X2)
743.71/262.79	   U41(X1, active(X2)) -> U41(X1, X2)
743.71/262.79	   U42(mark(X)) -> U42(X)
743.71/262.79	   U42(active(X)) -> U42(X)
743.71/262.79	   U51(mark(X)) -> U51(X)
743.71/262.79	   U51(active(X)) -> U51(X)
743.71/262.79	   U61(mark(X1), X2) -> U61(X1, X2)
743.71/262.79	   U61(X1, mark(X2)) -> U61(X1, X2)
743.71/262.79	   U61(active(X1), X2) -> U61(X1, X2)
743.71/262.79	   U61(X1, active(X2)) -> U61(X1, X2)
743.71/262.79	   U62(mark(X)) -> U62(X)
743.71/262.79	   U62(active(X)) -> U62(X)
743.71/262.79	   U71(mark(X1), X2) -> U71(X1, X2)
743.71/262.79	   U71(X1, mark(X2)) -> U71(X1, X2)
743.71/262.79	   U71(active(X1), X2) -> U71(X1, X2)
743.71/262.79	   U71(X1, active(X2)) -> U71(X1, X2)
743.71/262.79	   U72(mark(X1), X2) -> U72(X1, X2)
743.71/262.79	   U72(X1, mark(X2)) -> U72(X1, X2)
743.71/262.79	   U72(active(X1), X2) -> U72(X1, X2)
743.71/262.79	   U72(X1, active(X2)) -> U72(X1, X2)
743.71/262.79	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.71/262.79	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.71/262.79	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.71/262.79	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.71/262.79	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.71/262.79	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.71/262.79	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.71/262.79	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.71/262.79	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.71/262.79	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.71/262.79	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.71/262.79	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.71/262.79	   s(mark(X)) -> s(X)
743.71/262.79	   s(active(X)) -> s(X)
743.71/262.79	   U91(mark(X1), X2) -> U91(X1, X2)
743.71/262.79	   U91(X1, mark(X2)) -> U91(X1, X2)
743.71/262.79	   U91(active(X1), X2) -> U91(X1, X2)
743.71/262.79	   U91(X1, active(X2)) -> U91(X1, X2)
743.71/262.79	   U92(mark(X)) -> U92(X)
743.71/262.79	   U92(active(X)) -> U92(X)
743.71/262.79	
743.71/262.79	The set Q consists of the following terms:
743.71/262.79	
743.71/262.79	   active(U101(tt, x0, x1))
743.71/262.79	   active(U102(tt, x0, x1))
743.71/262.79	   active(U103(tt, x0, x1))
743.71/262.79	   active(U104(tt, x0, x1))
743.71/262.79	   active(U11(tt, x0, x1))
743.71/262.79	   active(U12(tt, x0, x1))
743.71/262.79	   active(U13(tt, x0, x1))
743.71/262.79	   active(U14(tt, x0, x1))
743.71/262.79	   active(U15(tt, x0))
743.71/262.79	   active(U16(tt))
743.71/262.79	   active(U21(tt, x0))
743.71/262.79	   active(U22(tt, x0))
743.71/262.79	   active(U23(tt))
743.71/262.79	   active(U31(tt, x0, x1))
743.71/262.79	   active(U32(tt, x0, x1))
743.71/262.79	   active(U33(tt, x0, x1))
743.71/262.79	   active(U34(tt, x0, x1))
743.71/262.79	   active(U35(tt, x0))
743.71/262.79	   active(U36(tt))
743.71/262.79	   active(U41(tt, x0))
743.71/262.79	   active(U42(tt))
743.71/262.79	   active(U51(tt))
743.71/262.79	   active(U61(tt, x0))
743.71/262.79	   active(U62(tt))
743.71/262.79	   active(U71(tt, x0))
743.71/262.79	   active(U72(tt, x0))
743.71/262.79	   active(U81(tt, x0, x1))
743.71/262.79	   active(U82(tt, x0, x1))
743.71/262.79	   active(U83(tt, x0, x1))
743.71/262.79	   active(U84(tt, x0, x1))
743.71/262.79	   active(U91(tt, x0))
743.71/262.79	   active(U92(tt))
743.71/262.79	   active(isNat(0))
743.71/262.79	   active(isNat(plus(x0, x1)))
743.71/262.79	   active(isNat(s(x0)))
743.71/262.79	   active(isNat(x(x0, x1)))
743.71/262.79	   active(isNatKind(0))
743.71/262.79	   active(isNatKind(plus(x0, x1)))
743.71/262.79	   active(isNatKind(s(x0)))
743.71/262.79	   active(isNatKind(x(x0, x1)))
743.71/262.79	   active(plus(x0, 0))
743.71/262.79	   active(plus(x0, s(x1)))
743.71/262.79	   active(x(x0, 0))
743.71/262.79	   active(x(x0, s(x1)))
743.71/262.79	   mark(U101(x0, x1, x2))
743.71/262.79	   mark(tt)
743.71/262.79	   mark(U102(x0, x1, x2))
743.71/262.79	   mark(isNatKind(x0))
743.71/262.79	   mark(U103(x0, x1, x2))
743.71/262.79	   mark(isNat(x0))
743.71/262.79	   mark(U104(x0, x1, x2))
743.71/262.79	   mark(plus(x0, x1))
743.71/262.79	   mark(x(x0, x1))
743.71/262.79	   mark(U11(x0, x1, x2))
743.71/262.79	   mark(U12(x0, x1, x2))
743.71/262.79	   mark(U13(x0, x1, x2))
743.71/262.79	   mark(U14(x0, x1, x2))
743.71/262.79	   mark(U15(x0, x1))
743.71/262.79	   mark(U16(x0))
743.71/262.79	   mark(U21(x0, x1))
743.71/262.79	   mark(U22(x0, x1))
743.71/262.79	   mark(U23(x0))
743.71/262.79	   mark(U31(x0, x1, x2))
743.71/262.79	   mark(U32(x0, x1, x2))
743.71/262.79	   mark(U33(x0, x1, x2))
743.71/262.79	   mark(U34(x0, x1, x2))
743.71/262.79	   mark(U35(x0, x1))
743.71/262.79	   mark(U36(x0))
743.71/262.79	   mark(U41(x0, x1))
743.71/262.79	   mark(U42(x0))
743.71/262.79	   mark(U51(x0))
743.71/262.79	   mark(U61(x0, x1))
743.71/262.79	   mark(U62(x0))
743.71/262.79	   mark(U71(x0, x1))
743.71/262.79	   mark(U72(x0, x1))
743.71/262.79	   mark(U81(x0, x1, x2))
743.71/262.79	   mark(U82(x0, x1, x2))
743.71/262.79	   mark(U83(x0, x1, x2))
743.71/262.79	   mark(U84(x0, x1, x2))
743.71/262.79	   mark(s(x0))
743.71/262.79	   mark(U91(x0, x1))
743.71/262.79	   mark(U92(x0))
743.71/262.79	   mark(0)
743.71/262.79	   U101(mark(x0), x1, x2)
743.71/262.79	   U101(x0, mark(x1), x2)
743.71/262.79	   U101(x0, x1, mark(x2))
743.71/262.79	   U101(active(x0), x1, x2)
743.71/262.79	   U101(x0, active(x1), x2)
743.71/262.79	   U101(x0, x1, active(x2))
743.71/262.79	   U102(mark(x0), x1, x2)
743.71/262.79	   U102(x0, mark(x1), x2)
743.71/262.79	   U102(x0, x1, mark(x2))
743.71/262.79	   U102(active(x0), x1, x2)
743.71/262.79	   U102(x0, active(x1), x2)
743.71/262.79	   U102(x0, x1, active(x2))
743.71/262.79	   isNatKind(mark(x0))
743.71/262.79	   isNatKind(active(x0))
743.71/262.79	   U103(mark(x0), x1, x2)
743.71/262.79	   U103(x0, mark(x1), x2)
743.71/262.79	   U103(x0, x1, mark(x2))
743.71/262.79	   U103(active(x0), x1, x2)
743.71/262.79	   U103(x0, active(x1), x2)
743.71/262.79	   U103(x0, x1, active(x2))
743.71/262.79	   isNat(mark(x0))
743.71/262.79	   isNat(active(x0))
743.71/262.79	   U104(mark(x0), x1, x2)
743.71/262.79	   U104(x0, mark(x1), x2)
743.71/262.79	   U104(x0, x1, mark(x2))
743.71/262.79	   U104(active(x0), x1, x2)
743.71/262.79	   U104(x0, active(x1), x2)
743.71/262.79	   U104(x0, x1, active(x2))
743.71/262.79	   plus(mark(x0), x1)
743.71/262.79	   plus(x0, mark(x1))
743.71/262.79	   plus(active(x0), x1)
743.71/262.79	   plus(x0, active(x1))
743.71/262.79	   x(mark(x0), x1)
743.71/262.79	   x(x0, mark(x1))
743.71/262.79	   x(active(x0), x1)
743.71/262.79	   x(x0, active(x1))
743.71/262.79	   U11(mark(x0), x1, x2)
743.71/262.79	   U11(x0, mark(x1), x2)
743.71/262.79	   U11(x0, x1, mark(x2))
743.71/262.79	   U11(active(x0), x1, x2)
743.71/262.79	   U11(x0, active(x1), x2)
743.71/262.79	   U11(x0, x1, active(x2))
743.71/262.79	   U12(mark(x0), x1, x2)
743.71/262.79	   U12(x0, mark(x1), x2)
743.71/262.79	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(69) UsableRulesProof (EQUIVALENT)
743.81/262.80	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.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(70)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U62^1(active(X)) -> U62^1(X)
743.81/262.80	   U62^1(mark(X)) -> U62^1(X)
743.81/262.80	
743.81/262.80	R is empty.
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.80	   active(U103(tt, x0, x1))
743.81/262.80	   active(U104(tt, x0, x1))
743.81/262.80	   active(U11(tt, x0, x1))
743.81/262.80	   active(U12(tt, x0, x1))
743.81/262.80	   active(U13(tt, x0, x1))
743.81/262.80	   active(U14(tt, x0, x1))
743.81/262.80	   active(U15(tt, x0))
743.81/262.80	   active(U16(tt))
743.81/262.80	   active(U21(tt, x0))
743.81/262.80	   active(U22(tt, x0))
743.81/262.80	   active(U23(tt))
743.81/262.80	   active(U31(tt, x0, x1))
743.81/262.80	   active(U32(tt, x0, x1))
743.81/262.80	   active(U33(tt, x0, x1))
743.81/262.80	   active(U34(tt, x0, x1))
743.81/262.80	   active(U35(tt, x0))
743.81/262.80	   active(U36(tt))
743.81/262.80	   active(U41(tt, x0))
743.81/262.80	   active(U42(tt))
743.81/262.80	   active(U51(tt))
743.81/262.80	   active(U61(tt, x0))
743.81/262.80	   active(U62(tt))
743.81/262.80	   active(U71(tt, x0))
743.81/262.80	   active(U72(tt, x0))
743.81/262.80	   active(U81(tt, x0, x1))
743.81/262.80	   active(U82(tt, x0, x1))
743.81/262.80	   active(U83(tt, x0, x1))
743.81/262.80	   active(U84(tt, x0, x1))
743.81/262.80	   active(U91(tt, x0))
743.81/262.80	   active(U92(tt))
743.81/262.80	   active(isNat(0))
743.81/262.80	   active(isNat(plus(x0, x1)))
743.81/262.80	   active(isNat(s(x0)))
743.81/262.80	   active(isNat(x(x0, x1)))
743.81/262.80	   active(isNatKind(0))
743.81/262.80	   active(isNatKind(plus(x0, x1)))
743.81/262.80	   active(isNatKind(s(x0)))
743.81/262.80	   active(isNatKind(x(x0, x1)))
743.81/262.80	   active(plus(x0, 0))
743.81/262.80	   active(plus(x0, s(x1)))
743.81/262.80	   active(x(x0, 0))
743.81/262.80	   active(x(x0, s(x1)))
743.81/262.80	   mark(U101(x0, x1, x2))
743.81/262.80	   mark(tt)
743.81/262.80	   mark(U102(x0, x1, x2))
743.81/262.80	   mark(isNatKind(x0))
743.81/262.80	   mark(U103(x0, x1, x2))
743.81/262.80	   mark(isNat(x0))
743.81/262.80	   mark(U104(x0, x1, x2))
743.81/262.80	   mark(plus(x0, x1))
743.81/262.80	   mark(x(x0, x1))
743.81/262.80	   mark(U11(x0, x1, x2))
743.81/262.80	   mark(U12(x0, x1, x2))
743.81/262.80	   mark(U13(x0, x1, x2))
743.81/262.80	   mark(U14(x0, x1, x2))
743.81/262.80	   mark(U15(x0, x1))
743.81/262.80	   mark(U16(x0))
743.81/262.80	   mark(U21(x0, x1))
743.81/262.80	   mark(U22(x0, x1))
743.81/262.80	   mark(U23(x0))
743.81/262.80	   mark(U31(x0, x1, x2))
743.81/262.80	   mark(U32(x0, x1, x2))
743.81/262.80	   mark(U33(x0, x1, x2))
743.81/262.80	   mark(U34(x0, x1, x2))
743.81/262.80	   mark(U35(x0, x1))
743.81/262.80	   mark(U36(x0))
743.81/262.80	   mark(U41(x0, x1))
743.81/262.80	   mark(U42(x0))
743.81/262.80	   mark(U51(x0))
743.81/262.80	   mark(U61(x0, x1))
743.81/262.80	   mark(U62(x0))
743.81/262.80	   mark(U71(x0, x1))
743.81/262.80	   mark(U72(x0, x1))
743.81/262.80	   mark(U81(x0, x1, x2))
743.81/262.80	   mark(U82(x0, x1, x2))
743.81/262.80	   mark(U83(x0, x1, x2))
743.81/262.80	   mark(U84(x0, x1, x2))
743.81/262.80	   mark(s(x0))
743.81/262.80	   mark(U91(x0, x1))
743.81/262.80	   mark(U92(x0))
743.81/262.80	   mark(0)
743.81/262.80	   U101(mark(x0), x1, x2)
743.81/262.80	   U101(x0, mark(x1), x2)
743.81/262.80	   U101(x0, x1, mark(x2))
743.81/262.80	   U101(active(x0), x1, x2)
743.81/262.80	   U101(x0, active(x1), x2)
743.81/262.80	   U101(x0, x1, active(x2))
743.81/262.80	   U102(mark(x0), x1, x2)
743.81/262.80	   U102(x0, mark(x1), x2)
743.81/262.80	   U102(x0, x1, mark(x2))
743.81/262.80	   U102(active(x0), x1, x2)
743.81/262.80	   U102(x0, active(x1), x2)
743.81/262.80	   U102(x0, x1, active(x2))
743.81/262.80	   isNatKind(mark(x0))
743.81/262.80	   isNatKind(active(x0))
743.81/262.80	   U103(mark(x0), x1, x2)
743.81/262.80	   U103(x0, mark(x1), x2)
743.81/262.80	   U103(x0, x1, mark(x2))
743.81/262.80	   U103(active(x0), x1, x2)
743.81/262.80	   U103(x0, active(x1), x2)
743.81/262.80	   U103(x0, x1, active(x2))
743.81/262.80	   isNat(mark(x0))
743.81/262.80	   isNat(active(x0))
743.81/262.80	   U104(mark(x0), x1, x2)
743.81/262.80	   U104(x0, mark(x1), x2)
743.81/262.80	   U104(x0, x1, mark(x2))
743.81/262.80	   U104(active(x0), x1, x2)
743.81/262.80	   U104(x0, active(x1), x2)
743.81/262.80	   U104(x0, x1, active(x2))
743.81/262.80	   plus(mark(x0), x1)
743.81/262.80	   plus(x0, mark(x1))
743.81/262.80	   plus(active(x0), x1)
743.81/262.80	   plus(x0, active(x1))
743.81/262.80	   x(mark(x0), x1)
743.81/262.80	   x(x0, mark(x1))
743.81/262.80	   x(active(x0), x1)
743.81/262.80	   x(x0, active(x1))
743.81/262.80	   U11(mark(x0), x1, x2)
743.81/262.80	   U11(x0, mark(x1), x2)
743.81/262.80	   U11(x0, x1, mark(x2))
743.81/262.80	   U11(active(x0), x1, x2)
743.81/262.80	   U11(x0, active(x1), x2)
743.81/262.80	   U11(x0, x1, active(x2))
743.81/262.80	   U12(mark(x0), x1, x2)
743.81/262.80	   U12(x0, mark(x1), x2)
743.81/262.80	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(71) QReductionProof (EQUIVALENT)
743.81/262.80	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.81/262.80	
743.81/262.80	   U101(mark(x0), x1, x2)
743.81/262.80	   U101(x0, mark(x1), x2)
743.81/262.80	   U101(x0, x1, mark(x2))
743.81/262.80	   U101(active(x0), x1, x2)
743.81/262.80	   U101(x0, active(x1), x2)
743.81/262.80	   U101(x0, x1, active(x2))
743.81/262.80	   U102(mark(x0), x1, x2)
743.81/262.80	   U102(x0, mark(x1), x2)
743.81/262.80	   U102(x0, x1, mark(x2))
743.81/262.80	   U102(active(x0), x1, x2)
743.81/262.80	   U102(x0, active(x1), x2)
743.81/262.80	   U102(x0, x1, active(x2))
743.81/262.80	   isNatKind(mark(x0))
743.81/262.80	   isNatKind(active(x0))
743.81/262.80	   U103(mark(x0), x1, x2)
743.81/262.80	   U103(x0, mark(x1), x2)
743.81/262.80	   U103(x0, x1, mark(x2))
743.81/262.80	   U103(active(x0), x1, x2)
743.81/262.80	   U103(x0, active(x1), x2)
743.81/262.80	   U103(x0, x1, active(x2))
743.81/262.80	   isNat(mark(x0))
743.81/262.80	   isNat(active(x0))
743.81/262.80	   U104(mark(x0), x1, x2)
743.81/262.80	   U104(x0, mark(x1), x2)
743.81/262.80	   U104(x0, x1, mark(x2))
743.81/262.80	   U104(active(x0), x1, x2)
743.81/262.80	   U104(x0, active(x1), x2)
743.81/262.80	   U104(x0, x1, active(x2))
743.81/262.80	   plus(mark(x0), x1)
743.81/262.80	   plus(x0, mark(x1))
743.81/262.80	   plus(active(x0), x1)
743.81/262.80	   plus(x0, active(x1))
743.81/262.80	   x(mark(x0), x1)
743.81/262.80	   x(x0, mark(x1))
743.81/262.80	   x(active(x0), x1)
743.81/262.80	   x(x0, active(x1))
743.81/262.80	   U11(mark(x0), x1, x2)
743.81/262.80	   U11(x0, mark(x1), x2)
743.81/262.80	   U11(x0, x1, mark(x2))
743.81/262.80	   U11(active(x0), x1, x2)
743.81/262.80	   U11(x0, active(x1), x2)
743.81/262.80	   U11(x0, x1, active(x2))
743.81/262.80	   U12(mark(x0), x1, x2)
743.81/262.80	   U12(x0, mark(x1), x2)
743.81/262.80	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(72)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U62^1(active(X)) -> U62^1(X)
743.81/262.80	   U62^1(mark(X)) -> U62^1(X)
743.81/262.80	
743.81/262.80	R is empty.
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.80	   active(U103(tt, x0, x1))
743.81/262.80	   active(U104(tt, x0, x1))
743.81/262.80	   active(U11(tt, x0, x1))
743.81/262.80	   active(U12(tt, x0, x1))
743.81/262.80	   active(U13(tt, x0, x1))
743.81/262.80	   active(U14(tt, x0, x1))
743.81/262.80	   active(U15(tt, x0))
743.81/262.80	   active(U16(tt))
743.81/262.80	   active(U21(tt, x0))
743.81/262.80	   active(U22(tt, x0))
743.81/262.80	   active(U23(tt))
743.81/262.80	   active(U31(tt, x0, x1))
743.81/262.80	   active(U32(tt, x0, x1))
743.81/262.80	   active(U33(tt, x0, x1))
743.81/262.80	   active(U34(tt, x0, x1))
743.81/262.80	   active(U35(tt, x0))
743.81/262.80	   active(U36(tt))
743.81/262.80	   active(U41(tt, x0))
743.81/262.80	   active(U42(tt))
743.81/262.80	   active(U51(tt))
743.81/262.80	   active(U61(tt, x0))
743.81/262.80	   active(U62(tt))
743.81/262.80	   active(U71(tt, x0))
743.81/262.80	   active(U72(tt, x0))
743.81/262.80	   active(U81(tt, x0, x1))
743.81/262.80	   active(U82(tt, x0, x1))
743.81/262.80	   active(U83(tt, x0, x1))
743.81/262.80	   active(U84(tt, x0, x1))
743.81/262.80	   active(U91(tt, x0))
743.81/262.80	   active(U92(tt))
743.81/262.80	   active(isNat(0))
743.81/262.80	   active(isNat(plus(x0, x1)))
743.81/262.80	   active(isNat(s(x0)))
743.81/262.80	   active(isNat(x(x0, x1)))
743.81/262.80	   active(isNatKind(0))
743.81/262.80	   active(isNatKind(plus(x0, x1)))
743.81/262.80	   active(isNatKind(s(x0)))
743.81/262.80	   active(isNatKind(x(x0, x1)))
743.81/262.80	   active(plus(x0, 0))
743.81/262.80	   active(plus(x0, s(x1)))
743.81/262.80	   active(x(x0, 0))
743.81/262.80	   active(x(x0, s(x1)))
743.81/262.80	   mark(U101(x0, x1, x2))
743.81/262.80	   mark(tt)
743.81/262.80	   mark(U102(x0, x1, x2))
743.81/262.80	   mark(isNatKind(x0))
743.81/262.80	   mark(U103(x0, x1, x2))
743.81/262.80	   mark(isNat(x0))
743.81/262.80	   mark(U104(x0, x1, x2))
743.81/262.80	   mark(plus(x0, x1))
743.81/262.80	   mark(x(x0, x1))
743.81/262.80	   mark(U11(x0, x1, x2))
743.81/262.80	   mark(U12(x0, x1, x2))
743.81/262.80	   mark(U13(x0, x1, x2))
743.81/262.80	   mark(U14(x0, x1, x2))
743.81/262.80	   mark(U15(x0, x1))
743.81/262.80	   mark(U16(x0))
743.81/262.80	   mark(U21(x0, x1))
743.81/262.80	   mark(U22(x0, x1))
743.81/262.80	   mark(U23(x0))
743.81/262.80	   mark(U31(x0, x1, x2))
743.81/262.80	   mark(U32(x0, x1, x2))
743.81/262.80	   mark(U33(x0, x1, x2))
743.81/262.80	   mark(U34(x0, x1, x2))
743.81/262.80	   mark(U35(x0, x1))
743.81/262.80	   mark(U36(x0))
743.81/262.80	   mark(U41(x0, x1))
743.81/262.80	   mark(U42(x0))
743.81/262.80	   mark(U51(x0))
743.81/262.80	   mark(U61(x0, x1))
743.81/262.80	   mark(U62(x0))
743.81/262.80	   mark(U71(x0, x1))
743.81/262.80	   mark(U72(x0, x1))
743.81/262.80	   mark(U81(x0, x1, x2))
743.81/262.80	   mark(U82(x0, x1, x2))
743.81/262.80	   mark(U83(x0, x1, x2))
743.81/262.80	   mark(U84(x0, x1, x2))
743.81/262.80	   mark(s(x0))
743.81/262.80	   mark(U91(x0, x1))
743.81/262.80	   mark(U92(x0))
743.81/262.80	   mark(0)
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(73) QDPSizeChangeProof (EQUIVALENT)
743.81/262.80	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. 
743.81/262.80	
743.81/262.80	From the DPs we obtained the following set of size-change graphs:
743.81/262.80	*U62^1(active(X)) -> U62^1(X)
743.81/262.80	The graph contains the following edges 1 > 1
743.81/262.80	
743.81/262.80	
743.81/262.80	*U62^1(mark(X)) -> U62^1(X)
743.81/262.80	The graph contains the following edges 1 > 1
743.81/262.80	
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(74)
743.81/262.80	YES
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(75)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U61^1(X1, mark(X2)) -> U61^1(X1, X2)
743.81/262.80	   U61^1(mark(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(active(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(X1, active(X2)) -> U61^1(X1, X2)
743.81/262.80	
743.81/262.80	The TRS R consists of the following rules:
743.81/262.80	
743.81/262.80	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.81/262.80	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.81/262.80	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.81/262.80	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.81/262.80	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.81/262.80	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.81/262.80	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.81/262.80	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.81/262.80	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.81/262.80	   active(U16(tt)) -> mark(tt)
743.81/262.80	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.81/262.80	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.81/262.80	   active(U23(tt)) -> mark(tt)
743.81/262.80	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.81/262.80	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.81/262.80	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.81/262.80	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.81/262.80	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.81/262.80	   active(U36(tt)) -> mark(tt)
743.81/262.80	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.81/262.80	   active(U42(tt)) -> mark(tt)
743.81/262.80	   active(U51(tt)) -> mark(tt)
743.81/262.80	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.81/262.80	   active(U62(tt)) -> mark(tt)
743.81/262.80	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.81/262.80	   active(U72(tt, N)) -> mark(N)
743.81/262.80	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.81/262.80	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.81/262.80	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.81/262.80	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.81/262.80	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.81/262.80	   active(U92(tt)) -> mark(0)
743.81/262.80	   active(isNat(0)) -> mark(tt)
743.81/262.80	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.81/262.80	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.81/262.80	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.81/262.80	   active(isNatKind(0)) -> mark(tt)
743.81/262.80	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.81/262.80	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.81/262.80	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.81/262.80	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.81/262.80	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.81/262.80	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.81/262.80	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.81/262.80	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.81/262.80	   mark(tt) -> active(tt)
743.81/262.80	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.81/262.80	   mark(isNatKind(X)) -> active(isNatKind(X))
743.81/262.80	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.81/262.80	   mark(isNat(X)) -> active(isNat(X))
743.81/262.80	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.81/262.80	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.81/262.80	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.81/262.80	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.81/262.80	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.81/262.80	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.81/262.80	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.81/262.80	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.81/262.80	   mark(U16(X)) -> active(U16(mark(X)))
743.81/262.80	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.81/262.80	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.81/262.80	   mark(U23(X)) -> active(U23(mark(X)))
743.81/262.80	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.81/262.80	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.81/262.80	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.81/262.80	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.81/262.80	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.81/262.80	   mark(U36(X)) -> active(U36(mark(X)))
743.81/262.80	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.81/262.80	   mark(U42(X)) -> active(U42(mark(X)))
743.81/262.80	   mark(U51(X)) -> active(U51(mark(X)))
743.81/262.80	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.81/262.80	   mark(U62(X)) -> active(U62(mark(X)))
743.81/262.80	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.81/262.80	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.81/262.80	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.81/262.80	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.81/262.80	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.81/262.80	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.81/262.80	   mark(s(X)) -> active(s(mark(X)))
743.81/262.80	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.81/262.80	   mark(U92(X)) -> active(U92(mark(X)))
743.81/262.80	   mark(0) -> active(0)
743.81/262.80	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.81/262.80	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.81/262.80	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.81/262.80	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.81/262.80	   isNatKind(mark(X)) -> isNatKind(X)
743.81/262.80	   isNatKind(active(X)) -> isNatKind(X)
743.81/262.80	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.81/262.80	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.81/262.80	   isNat(mark(X)) -> isNat(X)
743.81/262.80	   isNat(active(X)) -> isNat(X)
743.81/262.80	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.81/262.80	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.81/262.80	   plus(mark(X1), X2) -> plus(X1, X2)
743.81/262.80	   plus(X1, mark(X2)) -> plus(X1, X2)
743.81/262.80	   plus(active(X1), X2) -> plus(X1, X2)
743.81/262.80	   plus(X1, active(X2)) -> plus(X1, X2)
743.81/262.80	   x(mark(X1), X2) -> x(X1, X2)
743.81/262.80	   x(X1, mark(X2)) -> x(X1, X2)
743.81/262.80	   x(active(X1), X2) -> x(X1, X2)
743.81/262.80	   x(X1, active(X2)) -> x(X1, X2)
743.81/262.80	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.81/262.80	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.81/262.80	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.81/262.80	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.81/262.80	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.81/262.80	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.81/262.80	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.81/262.80	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.81/262.80	   U15(mark(X1), X2) -> U15(X1, X2)
743.81/262.80	   U15(X1, mark(X2)) -> U15(X1, X2)
743.81/262.80	   U15(active(X1), X2) -> U15(X1, X2)
743.81/262.80	   U15(X1, active(X2)) -> U15(X1, X2)
743.81/262.80	   U16(mark(X)) -> U16(X)
743.81/262.80	   U16(active(X)) -> U16(X)
743.81/262.80	   U21(mark(X1), X2) -> U21(X1, X2)
743.81/262.80	   U21(X1, mark(X2)) -> U21(X1, X2)
743.81/262.80	   U21(active(X1), X2) -> U21(X1, X2)
743.81/262.80	   U21(X1, active(X2)) -> U21(X1, X2)
743.81/262.80	   U22(mark(X1), X2) -> U22(X1, X2)
743.81/262.80	   U22(X1, mark(X2)) -> U22(X1, X2)
743.81/262.80	   U22(active(X1), X2) -> U22(X1, X2)
743.81/262.80	   U22(X1, active(X2)) -> U22(X1, X2)
743.81/262.80	   U23(mark(X)) -> U23(X)
743.81/262.80	   U23(active(X)) -> U23(X)
743.81/262.80	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.81/262.80	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.81/262.80	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.81/262.80	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.81/262.80	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.81/262.80	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.81/262.80	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.81/262.80	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.81/262.80	   U35(mark(X1), X2) -> U35(X1, X2)
743.81/262.80	   U35(X1, mark(X2)) -> U35(X1, X2)
743.81/262.80	   U35(active(X1), X2) -> U35(X1, X2)
743.81/262.80	   U35(X1, active(X2)) -> U35(X1, X2)
743.81/262.80	   U36(mark(X)) -> U36(X)
743.81/262.80	   U36(active(X)) -> U36(X)
743.81/262.80	   U41(mark(X1), X2) -> U41(X1, X2)
743.81/262.80	   U41(X1, mark(X2)) -> U41(X1, X2)
743.81/262.80	   U41(active(X1), X2) -> U41(X1, X2)
743.81/262.80	   U41(X1, active(X2)) -> U41(X1, X2)
743.81/262.80	   U42(mark(X)) -> U42(X)
743.81/262.80	   U42(active(X)) -> U42(X)
743.81/262.80	   U51(mark(X)) -> U51(X)
743.81/262.80	   U51(active(X)) -> U51(X)
743.81/262.80	   U61(mark(X1), X2) -> U61(X1, X2)
743.81/262.80	   U61(X1, mark(X2)) -> U61(X1, X2)
743.81/262.80	   U61(active(X1), X2) -> U61(X1, X2)
743.81/262.80	   U61(X1, active(X2)) -> U61(X1, X2)
743.81/262.80	   U62(mark(X)) -> U62(X)
743.81/262.80	   U62(active(X)) -> U62(X)
743.81/262.80	   U71(mark(X1), X2) -> U71(X1, X2)
743.81/262.80	   U71(X1, mark(X2)) -> U71(X1, X2)
743.81/262.80	   U71(active(X1), X2) -> U71(X1, X2)
743.81/262.80	   U71(X1, active(X2)) -> U71(X1, X2)
743.81/262.80	   U72(mark(X1), X2) -> U72(X1, X2)
743.81/262.80	   U72(X1, mark(X2)) -> U72(X1, X2)
743.81/262.80	   U72(active(X1), X2) -> U72(X1, X2)
743.81/262.80	   U72(X1, active(X2)) -> U72(X1, X2)
743.81/262.80	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.81/262.80	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.81/262.80	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.81/262.80	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.81/262.80	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.81/262.80	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.81/262.80	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.81/262.80	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.81/262.80	   s(mark(X)) -> s(X)
743.81/262.80	   s(active(X)) -> s(X)
743.81/262.80	   U91(mark(X1), X2) -> U91(X1, X2)
743.81/262.80	   U91(X1, mark(X2)) -> U91(X1, X2)
743.81/262.80	   U91(active(X1), X2) -> U91(X1, X2)
743.81/262.80	   U91(X1, active(X2)) -> U91(X1, X2)
743.81/262.80	   U92(mark(X)) -> U92(X)
743.81/262.80	   U92(active(X)) -> U92(X)
743.81/262.80	
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.80	   active(U103(tt, x0, x1))
743.81/262.80	   active(U104(tt, x0, x1))
743.81/262.80	   active(U11(tt, x0, x1))
743.81/262.80	   active(U12(tt, x0, x1))
743.81/262.80	   active(U13(tt, x0, x1))
743.81/262.80	   active(U14(tt, x0, x1))
743.81/262.80	   active(U15(tt, x0))
743.81/262.80	   active(U16(tt))
743.81/262.80	   active(U21(tt, x0))
743.81/262.80	   active(U22(tt, x0))
743.81/262.80	   active(U23(tt))
743.81/262.80	   active(U31(tt, x0, x1))
743.81/262.80	   active(U32(tt, x0, x1))
743.81/262.80	   active(U33(tt, x0, x1))
743.81/262.80	   active(U34(tt, x0, x1))
743.81/262.80	   active(U35(tt, x0))
743.81/262.80	   active(U36(tt))
743.81/262.80	   active(U41(tt, x0))
743.81/262.80	   active(U42(tt))
743.81/262.80	   active(U51(tt))
743.81/262.80	   active(U61(tt, x0))
743.81/262.80	   active(U62(tt))
743.81/262.80	   active(U71(tt, x0))
743.81/262.80	   active(U72(tt, x0))
743.81/262.80	   active(U81(tt, x0, x1))
743.81/262.80	   active(U82(tt, x0, x1))
743.81/262.80	   active(U83(tt, x0, x1))
743.81/262.80	   active(U84(tt, x0, x1))
743.81/262.80	   active(U91(tt, x0))
743.81/262.80	   active(U92(tt))
743.81/262.80	   active(isNat(0))
743.81/262.80	   active(isNat(plus(x0, x1)))
743.81/262.80	   active(isNat(s(x0)))
743.81/262.80	   active(isNat(x(x0, x1)))
743.81/262.80	   active(isNatKind(0))
743.81/262.80	   active(isNatKind(plus(x0, x1)))
743.81/262.80	   active(isNatKind(s(x0)))
743.81/262.80	   active(isNatKind(x(x0, x1)))
743.81/262.80	   active(plus(x0, 0))
743.81/262.80	   active(plus(x0, s(x1)))
743.81/262.80	   active(x(x0, 0))
743.81/262.80	   active(x(x0, s(x1)))
743.81/262.80	   mark(U101(x0, x1, x2))
743.81/262.80	   mark(tt)
743.81/262.80	   mark(U102(x0, x1, x2))
743.81/262.80	   mark(isNatKind(x0))
743.81/262.80	   mark(U103(x0, x1, x2))
743.81/262.80	   mark(isNat(x0))
743.81/262.80	   mark(U104(x0, x1, x2))
743.81/262.80	   mark(plus(x0, x1))
743.81/262.80	   mark(x(x0, x1))
743.81/262.80	   mark(U11(x0, x1, x2))
743.81/262.80	   mark(U12(x0, x1, x2))
743.81/262.80	   mark(U13(x0, x1, x2))
743.81/262.80	   mark(U14(x0, x1, x2))
743.81/262.80	   mark(U15(x0, x1))
743.81/262.80	   mark(U16(x0))
743.81/262.80	   mark(U21(x0, x1))
743.81/262.80	   mark(U22(x0, x1))
743.81/262.80	   mark(U23(x0))
743.81/262.80	   mark(U31(x0, x1, x2))
743.81/262.80	   mark(U32(x0, x1, x2))
743.81/262.80	   mark(U33(x0, x1, x2))
743.81/262.80	   mark(U34(x0, x1, x2))
743.81/262.80	   mark(U35(x0, x1))
743.81/262.80	   mark(U36(x0))
743.81/262.80	   mark(U41(x0, x1))
743.81/262.80	   mark(U42(x0))
743.81/262.80	   mark(U51(x0))
743.81/262.80	   mark(U61(x0, x1))
743.81/262.80	   mark(U62(x0))
743.81/262.80	   mark(U71(x0, x1))
743.81/262.80	   mark(U72(x0, x1))
743.81/262.80	   mark(U81(x0, x1, x2))
743.81/262.80	   mark(U82(x0, x1, x2))
743.81/262.80	   mark(U83(x0, x1, x2))
743.81/262.80	   mark(U84(x0, x1, x2))
743.81/262.80	   mark(s(x0))
743.81/262.80	   mark(U91(x0, x1))
743.81/262.80	   mark(U92(x0))
743.81/262.80	   mark(0)
743.81/262.80	   U101(mark(x0), x1, x2)
743.81/262.80	   U101(x0, mark(x1), x2)
743.81/262.80	   U101(x0, x1, mark(x2))
743.81/262.80	   U101(active(x0), x1, x2)
743.81/262.80	   U101(x0, active(x1), x2)
743.81/262.80	   U101(x0, x1, active(x2))
743.81/262.80	   U102(mark(x0), x1, x2)
743.81/262.80	   U102(x0, mark(x1), x2)
743.81/262.80	   U102(x0, x1, mark(x2))
743.81/262.80	   U102(active(x0), x1, x2)
743.81/262.80	   U102(x0, active(x1), x2)
743.81/262.80	   U102(x0, x1, active(x2))
743.81/262.80	   isNatKind(mark(x0))
743.81/262.80	   isNatKind(active(x0))
743.81/262.80	   U103(mark(x0), x1, x2)
743.81/262.80	   U103(x0, mark(x1), x2)
743.81/262.80	   U103(x0, x1, mark(x2))
743.81/262.80	   U103(active(x0), x1, x2)
743.81/262.80	   U103(x0, active(x1), x2)
743.81/262.80	   U103(x0, x1, active(x2))
743.81/262.80	   isNat(mark(x0))
743.81/262.80	   isNat(active(x0))
743.81/262.80	   U104(mark(x0), x1, x2)
743.81/262.80	   U104(x0, mark(x1), x2)
743.81/262.80	   U104(x0, x1, mark(x2))
743.81/262.80	   U104(active(x0), x1, x2)
743.81/262.80	   U104(x0, active(x1), x2)
743.81/262.80	   U104(x0, x1, active(x2))
743.81/262.80	   plus(mark(x0), x1)
743.81/262.80	   plus(x0, mark(x1))
743.81/262.80	   plus(active(x0), x1)
743.81/262.80	   plus(x0, active(x1))
743.81/262.80	   x(mark(x0), x1)
743.81/262.80	   x(x0, mark(x1))
743.81/262.80	   x(active(x0), x1)
743.81/262.80	   x(x0, active(x1))
743.81/262.80	   U11(mark(x0), x1, x2)
743.81/262.80	   U11(x0, mark(x1), x2)
743.81/262.80	   U11(x0, x1, mark(x2))
743.81/262.80	   U11(active(x0), x1, x2)
743.81/262.80	   U11(x0, active(x1), x2)
743.81/262.80	   U11(x0, x1, active(x2))
743.81/262.80	   U12(mark(x0), x1, x2)
743.81/262.80	   U12(x0, mark(x1), x2)
743.81/262.80	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(76) UsableRulesProof (EQUIVALENT)
743.81/262.80	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.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(77)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U61^1(X1, mark(X2)) -> U61^1(X1, X2)
743.81/262.80	   U61^1(mark(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(active(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(X1, active(X2)) -> U61^1(X1, X2)
743.81/262.80	
743.81/262.80	R is empty.
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.80	   active(U103(tt, x0, x1))
743.81/262.80	   active(U104(tt, x0, x1))
743.81/262.80	   active(U11(tt, x0, x1))
743.81/262.80	   active(U12(tt, x0, x1))
743.81/262.80	   active(U13(tt, x0, x1))
743.81/262.80	   active(U14(tt, x0, x1))
743.81/262.80	   active(U15(tt, x0))
743.81/262.80	   active(U16(tt))
743.81/262.80	   active(U21(tt, x0))
743.81/262.80	   active(U22(tt, x0))
743.81/262.80	   active(U23(tt))
743.81/262.80	   active(U31(tt, x0, x1))
743.81/262.80	   active(U32(tt, x0, x1))
743.81/262.80	   active(U33(tt, x0, x1))
743.81/262.80	   active(U34(tt, x0, x1))
743.81/262.80	   active(U35(tt, x0))
743.81/262.80	   active(U36(tt))
743.81/262.80	   active(U41(tt, x0))
743.81/262.80	   active(U42(tt))
743.81/262.80	   active(U51(tt))
743.81/262.80	   active(U61(tt, x0))
743.81/262.80	   active(U62(tt))
743.81/262.80	   active(U71(tt, x0))
743.81/262.80	   active(U72(tt, x0))
743.81/262.80	   active(U81(tt, x0, x1))
743.81/262.80	   active(U82(tt, x0, x1))
743.81/262.80	   active(U83(tt, x0, x1))
743.81/262.80	   active(U84(tt, x0, x1))
743.81/262.80	   active(U91(tt, x0))
743.81/262.80	   active(U92(tt))
743.81/262.80	   active(isNat(0))
743.81/262.80	   active(isNat(plus(x0, x1)))
743.81/262.80	   active(isNat(s(x0)))
743.81/262.80	   active(isNat(x(x0, x1)))
743.81/262.80	   active(isNatKind(0))
743.81/262.80	   active(isNatKind(plus(x0, x1)))
743.81/262.80	   active(isNatKind(s(x0)))
743.81/262.80	   active(isNatKind(x(x0, x1)))
743.81/262.80	   active(plus(x0, 0))
743.81/262.80	   active(plus(x0, s(x1)))
743.81/262.80	   active(x(x0, 0))
743.81/262.80	   active(x(x0, s(x1)))
743.81/262.80	   mark(U101(x0, x1, x2))
743.81/262.80	   mark(tt)
743.81/262.80	   mark(U102(x0, x1, x2))
743.81/262.80	   mark(isNatKind(x0))
743.81/262.80	   mark(U103(x0, x1, x2))
743.81/262.80	   mark(isNat(x0))
743.81/262.80	   mark(U104(x0, x1, x2))
743.81/262.80	   mark(plus(x0, x1))
743.81/262.80	   mark(x(x0, x1))
743.81/262.80	   mark(U11(x0, x1, x2))
743.81/262.80	   mark(U12(x0, x1, x2))
743.81/262.80	   mark(U13(x0, x1, x2))
743.81/262.80	   mark(U14(x0, x1, x2))
743.81/262.80	   mark(U15(x0, x1))
743.81/262.80	   mark(U16(x0))
743.81/262.80	   mark(U21(x0, x1))
743.81/262.80	   mark(U22(x0, x1))
743.81/262.80	   mark(U23(x0))
743.81/262.80	   mark(U31(x0, x1, x2))
743.81/262.80	   mark(U32(x0, x1, x2))
743.81/262.80	   mark(U33(x0, x1, x2))
743.81/262.80	   mark(U34(x0, x1, x2))
743.81/262.80	   mark(U35(x0, x1))
743.81/262.80	   mark(U36(x0))
743.81/262.80	   mark(U41(x0, x1))
743.81/262.80	   mark(U42(x0))
743.81/262.80	   mark(U51(x0))
743.81/262.80	   mark(U61(x0, x1))
743.81/262.80	   mark(U62(x0))
743.81/262.80	   mark(U71(x0, x1))
743.81/262.80	   mark(U72(x0, x1))
743.81/262.80	   mark(U81(x0, x1, x2))
743.81/262.80	   mark(U82(x0, x1, x2))
743.81/262.80	   mark(U83(x0, x1, x2))
743.81/262.80	   mark(U84(x0, x1, x2))
743.81/262.80	   mark(s(x0))
743.81/262.80	   mark(U91(x0, x1))
743.81/262.80	   mark(U92(x0))
743.81/262.80	   mark(0)
743.81/262.80	   U101(mark(x0), x1, x2)
743.81/262.80	   U101(x0, mark(x1), x2)
743.81/262.80	   U101(x0, x1, mark(x2))
743.81/262.80	   U101(active(x0), x1, x2)
743.81/262.80	   U101(x0, active(x1), x2)
743.81/262.80	   U101(x0, x1, active(x2))
743.81/262.80	   U102(mark(x0), x1, x2)
743.81/262.80	   U102(x0, mark(x1), x2)
743.81/262.80	   U102(x0, x1, mark(x2))
743.81/262.80	   U102(active(x0), x1, x2)
743.81/262.80	   U102(x0, active(x1), x2)
743.81/262.80	   U102(x0, x1, active(x2))
743.81/262.80	   isNatKind(mark(x0))
743.81/262.80	   isNatKind(active(x0))
743.81/262.80	   U103(mark(x0), x1, x2)
743.81/262.80	   U103(x0, mark(x1), x2)
743.81/262.80	   U103(x0, x1, mark(x2))
743.81/262.80	   U103(active(x0), x1, x2)
743.81/262.80	   U103(x0, active(x1), x2)
743.81/262.80	   U103(x0, x1, active(x2))
743.81/262.80	   isNat(mark(x0))
743.81/262.80	   isNat(active(x0))
743.81/262.80	   U104(mark(x0), x1, x2)
743.81/262.80	   U104(x0, mark(x1), x2)
743.81/262.80	   U104(x0, x1, mark(x2))
743.81/262.80	   U104(active(x0), x1, x2)
743.81/262.80	   U104(x0, active(x1), x2)
743.81/262.80	   U104(x0, x1, active(x2))
743.81/262.80	   plus(mark(x0), x1)
743.81/262.80	   plus(x0, mark(x1))
743.81/262.80	   plus(active(x0), x1)
743.81/262.80	   plus(x0, active(x1))
743.81/262.80	   x(mark(x0), x1)
743.81/262.80	   x(x0, mark(x1))
743.81/262.80	   x(active(x0), x1)
743.81/262.80	   x(x0, active(x1))
743.81/262.80	   U11(mark(x0), x1, x2)
743.81/262.80	   U11(x0, mark(x1), x2)
743.81/262.80	   U11(x0, x1, mark(x2))
743.81/262.80	   U11(active(x0), x1, x2)
743.81/262.80	   U11(x0, active(x1), x2)
743.81/262.80	   U11(x0, x1, active(x2))
743.81/262.80	   U12(mark(x0), x1, x2)
743.81/262.80	   U12(x0, mark(x1), x2)
743.81/262.80	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(78) QReductionProof (EQUIVALENT)
743.81/262.80	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.81/262.80	
743.81/262.80	   U101(mark(x0), x1, x2)
743.81/262.80	   U101(x0, mark(x1), x2)
743.81/262.80	   U101(x0, x1, mark(x2))
743.81/262.80	   U101(active(x0), x1, x2)
743.81/262.80	   U101(x0, active(x1), x2)
743.81/262.80	   U101(x0, x1, active(x2))
743.81/262.80	   U102(mark(x0), x1, x2)
743.81/262.80	   U102(x0, mark(x1), x2)
743.81/262.80	   U102(x0, x1, mark(x2))
743.81/262.80	   U102(active(x0), x1, x2)
743.81/262.80	   U102(x0, active(x1), x2)
743.81/262.80	   U102(x0, x1, active(x2))
743.81/262.80	   isNatKind(mark(x0))
743.81/262.80	   isNatKind(active(x0))
743.81/262.80	   U103(mark(x0), x1, x2)
743.81/262.80	   U103(x0, mark(x1), x2)
743.81/262.80	   U103(x0, x1, mark(x2))
743.81/262.80	   U103(active(x0), x1, x2)
743.81/262.80	   U103(x0, active(x1), x2)
743.81/262.80	   U103(x0, x1, active(x2))
743.81/262.80	   isNat(mark(x0))
743.81/262.80	   isNat(active(x0))
743.81/262.80	   U104(mark(x0), x1, x2)
743.81/262.80	   U104(x0, mark(x1), x2)
743.81/262.80	   U104(x0, x1, mark(x2))
743.81/262.80	   U104(active(x0), x1, x2)
743.81/262.80	   U104(x0, active(x1), x2)
743.81/262.80	   U104(x0, x1, active(x2))
743.81/262.80	   plus(mark(x0), x1)
743.81/262.80	   plus(x0, mark(x1))
743.81/262.80	   plus(active(x0), x1)
743.81/262.80	   plus(x0, active(x1))
743.81/262.80	   x(mark(x0), x1)
743.81/262.80	   x(x0, mark(x1))
743.81/262.80	   x(active(x0), x1)
743.81/262.80	   x(x0, active(x1))
743.81/262.80	   U11(mark(x0), x1, x2)
743.81/262.80	   U11(x0, mark(x1), x2)
743.81/262.80	   U11(x0, x1, mark(x2))
743.81/262.80	   U11(active(x0), x1, x2)
743.81/262.80	   U11(x0, active(x1), x2)
743.81/262.80	   U11(x0, x1, active(x2))
743.81/262.80	   U12(mark(x0), x1, x2)
743.81/262.80	   U12(x0, mark(x1), x2)
743.81/262.80	   U12(x0, x1, mark(x2))
743.81/262.80	   U12(active(x0), x1, x2)
743.81/262.80	   U12(x0, active(x1), x2)
743.81/262.80	   U12(x0, x1, active(x2))
743.81/262.80	   U13(mark(x0), x1, x2)
743.81/262.80	   U13(x0, mark(x1), x2)
743.81/262.80	   U13(x0, x1, mark(x2))
743.81/262.80	   U13(active(x0), x1, x2)
743.81/262.80	   U13(x0, active(x1), x2)
743.81/262.80	   U13(x0, x1, active(x2))
743.81/262.80	   U14(mark(x0), x1, x2)
743.81/262.80	   U14(x0, mark(x1), x2)
743.81/262.80	   U14(x0, x1, mark(x2))
743.81/262.80	   U14(active(x0), x1, x2)
743.81/262.80	   U14(x0, active(x1), x2)
743.81/262.80	   U14(x0, x1, active(x2))
743.81/262.80	   U15(mark(x0), x1)
743.81/262.80	   U15(x0, mark(x1))
743.81/262.80	   U15(active(x0), x1)
743.81/262.80	   U15(x0, active(x1))
743.81/262.80	   U16(mark(x0))
743.81/262.80	   U16(active(x0))
743.81/262.80	   U21(mark(x0), x1)
743.81/262.80	   U21(x0, mark(x1))
743.81/262.80	   U21(active(x0), x1)
743.81/262.80	   U21(x0, active(x1))
743.81/262.80	   U22(mark(x0), x1)
743.81/262.80	   U22(x0, mark(x1))
743.81/262.80	   U22(active(x0), x1)
743.81/262.80	   U22(x0, active(x1))
743.81/262.80	   U23(mark(x0))
743.81/262.80	   U23(active(x0))
743.81/262.80	   U31(mark(x0), x1, x2)
743.81/262.80	   U31(x0, mark(x1), x2)
743.81/262.80	   U31(x0, x1, mark(x2))
743.81/262.80	   U31(active(x0), x1, x2)
743.81/262.80	   U31(x0, active(x1), x2)
743.81/262.80	   U31(x0, x1, active(x2))
743.81/262.80	   U32(mark(x0), x1, x2)
743.81/262.80	   U32(x0, mark(x1), x2)
743.81/262.80	   U32(x0, x1, mark(x2))
743.81/262.80	   U32(active(x0), x1, x2)
743.81/262.80	   U32(x0, active(x1), x2)
743.81/262.80	   U32(x0, x1, active(x2))
743.81/262.80	   U33(mark(x0), x1, x2)
743.81/262.80	   U33(x0, mark(x1), x2)
743.81/262.80	   U33(x0, x1, mark(x2))
743.81/262.80	   U33(active(x0), x1, x2)
743.81/262.80	   U33(x0, active(x1), x2)
743.81/262.80	   U33(x0, x1, active(x2))
743.81/262.80	   U34(mark(x0), x1, x2)
743.81/262.80	   U34(x0, mark(x1), x2)
743.81/262.80	   U34(x0, x1, mark(x2))
743.81/262.80	   U34(active(x0), x1, x2)
743.81/262.80	   U34(x0, active(x1), x2)
743.81/262.80	   U34(x0, x1, active(x2))
743.81/262.80	   U35(mark(x0), x1)
743.81/262.80	   U35(x0, mark(x1))
743.81/262.80	   U35(active(x0), x1)
743.81/262.80	   U35(x0, active(x1))
743.81/262.80	   U36(mark(x0))
743.81/262.80	   U36(active(x0))
743.81/262.80	   U41(mark(x0), x1)
743.81/262.80	   U41(x0, mark(x1))
743.81/262.80	   U41(active(x0), x1)
743.81/262.80	   U41(x0, active(x1))
743.81/262.80	   U42(mark(x0))
743.81/262.80	   U42(active(x0))
743.81/262.80	   U51(mark(x0))
743.81/262.80	   U51(active(x0))
743.81/262.80	   U61(mark(x0), x1)
743.81/262.80	   U61(x0, mark(x1))
743.81/262.80	   U61(active(x0), x1)
743.81/262.80	   U61(x0, active(x1))
743.81/262.80	   U62(mark(x0))
743.81/262.80	   U62(active(x0))
743.81/262.80	   U71(mark(x0), x1)
743.81/262.80	   U71(x0, mark(x1))
743.81/262.80	   U71(active(x0), x1)
743.81/262.80	   U71(x0, active(x1))
743.81/262.80	   U72(mark(x0), x1)
743.81/262.80	   U72(x0, mark(x1))
743.81/262.80	   U72(active(x0), x1)
743.81/262.80	   U72(x0, active(x1))
743.81/262.80	   U81(mark(x0), x1, x2)
743.81/262.80	   U81(x0, mark(x1), x2)
743.81/262.80	   U81(x0, x1, mark(x2))
743.81/262.80	   U81(active(x0), x1, x2)
743.81/262.80	   U81(x0, active(x1), x2)
743.81/262.80	   U81(x0, x1, active(x2))
743.81/262.80	   U82(mark(x0), x1, x2)
743.81/262.80	   U82(x0, mark(x1), x2)
743.81/262.80	   U82(x0, x1, mark(x2))
743.81/262.80	   U82(active(x0), x1, x2)
743.81/262.80	   U82(x0, active(x1), x2)
743.81/262.80	   U82(x0, x1, active(x2))
743.81/262.80	   U83(mark(x0), x1, x2)
743.81/262.80	   U83(x0, mark(x1), x2)
743.81/262.80	   U83(x0, x1, mark(x2))
743.81/262.80	   U83(active(x0), x1, x2)
743.81/262.80	   U83(x0, active(x1), x2)
743.81/262.80	   U83(x0, x1, active(x2))
743.81/262.80	   U84(mark(x0), x1, x2)
743.81/262.80	   U84(x0, mark(x1), x2)
743.81/262.80	   U84(x0, x1, mark(x2))
743.81/262.80	   U84(active(x0), x1, x2)
743.81/262.80	   U84(x0, active(x1), x2)
743.81/262.80	   U84(x0, x1, active(x2))
743.81/262.80	   s(mark(x0))
743.81/262.80	   s(active(x0))
743.81/262.80	   U91(mark(x0), x1)
743.81/262.80	   U91(x0, mark(x1))
743.81/262.80	   U91(active(x0), x1)
743.81/262.80	   U91(x0, active(x1))
743.81/262.80	   U92(mark(x0))
743.81/262.80	   U92(active(x0))
743.81/262.80	
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(79)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U61^1(X1, mark(X2)) -> U61^1(X1, X2)
743.81/262.80	   U61^1(mark(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(active(X1), X2) -> U61^1(X1, X2)
743.81/262.80	   U61^1(X1, active(X2)) -> U61^1(X1, X2)
743.81/262.80	
743.81/262.80	R is empty.
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.80	   active(U103(tt, x0, x1))
743.81/262.80	   active(U104(tt, x0, x1))
743.81/262.80	   active(U11(tt, x0, x1))
743.81/262.80	   active(U12(tt, x0, x1))
743.81/262.80	   active(U13(tt, x0, x1))
743.81/262.80	   active(U14(tt, x0, x1))
743.81/262.80	   active(U15(tt, x0))
743.81/262.80	   active(U16(tt))
743.81/262.80	   active(U21(tt, x0))
743.81/262.80	   active(U22(tt, x0))
743.81/262.80	   active(U23(tt))
743.81/262.80	   active(U31(tt, x0, x1))
743.81/262.80	   active(U32(tt, x0, x1))
743.81/262.80	   active(U33(tt, x0, x1))
743.81/262.80	   active(U34(tt, x0, x1))
743.81/262.80	   active(U35(tt, x0))
743.81/262.80	   active(U36(tt))
743.81/262.80	   active(U41(tt, x0))
743.81/262.80	   active(U42(tt))
743.81/262.80	   active(U51(tt))
743.81/262.80	   active(U61(tt, x0))
743.81/262.80	   active(U62(tt))
743.81/262.80	   active(U71(tt, x0))
743.81/262.80	   active(U72(tt, x0))
743.81/262.80	   active(U81(tt, x0, x1))
743.81/262.80	   active(U82(tt, x0, x1))
743.81/262.80	   active(U83(tt, x0, x1))
743.81/262.80	   active(U84(tt, x0, x1))
743.81/262.80	   active(U91(tt, x0))
743.81/262.80	   active(U92(tt))
743.81/262.80	   active(isNat(0))
743.81/262.80	   active(isNat(plus(x0, x1)))
743.81/262.80	   active(isNat(s(x0)))
743.81/262.80	   active(isNat(x(x0, x1)))
743.81/262.80	   active(isNatKind(0))
743.81/262.80	   active(isNatKind(plus(x0, x1)))
743.81/262.80	   active(isNatKind(s(x0)))
743.81/262.80	   active(isNatKind(x(x0, x1)))
743.81/262.80	   active(plus(x0, 0))
743.81/262.80	   active(plus(x0, s(x1)))
743.81/262.80	   active(x(x0, 0))
743.81/262.80	   active(x(x0, s(x1)))
743.81/262.80	   mark(U101(x0, x1, x2))
743.81/262.80	   mark(tt)
743.81/262.80	   mark(U102(x0, x1, x2))
743.81/262.80	   mark(isNatKind(x0))
743.81/262.80	   mark(U103(x0, x1, x2))
743.81/262.80	   mark(isNat(x0))
743.81/262.80	   mark(U104(x0, x1, x2))
743.81/262.80	   mark(plus(x0, x1))
743.81/262.80	   mark(x(x0, x1))
743.81/262.80	   mark(U11(x0, x1, x2))
743.81/262.80	   mark(U12(x0, x1, x2))
743.81/262.80	   mark(U13(x0, x1, x2))
743.81/262.80	   mark(U14(x0, x1, x2))
743.81/262.80	   mark(U15(x0, x1))
743.81/262.80	   mark(U16(x0))
743.81/262.80	   mark(U21(x0, x1))
743.81/262.80	   mark(U22(x0, x1))
743.81/262.80	   mark(U23(x0))
743.81/262.80	   mark(U31(x0, x1, x2))
743.81/262.80	   mark(U32(x0, x1, x2))
743.81/262.80	   mark(U33(x0, x1, x2))
743.81/262.80	   mark(U34(x0, x1, x2))
743.81/262.80	   mark(U35(x0, x1))
743.81/262.80	   mark(U36(x0))
743.81/262.80	   mark(U41(x0, x1))
743.81/262.80	   mark(U42(x0))
743.81/262.80	   mark(U51(x0))
743.81/262.80	   mark(U61(x0, x1))
743.81/262.80	   mark(U62(x0))
743.81/262.80	   mark(U71(x0, x1))
743.81/262.80	   mark(U72(x0, x1))
743.81/262.80	   mark(U81(x0, x1, x2))
743.81/262.80	   mark(U82(x0, x1, x2))
743.81/262.80	   mark(U83(x0, x1, x2))
743.81/262.80	   mark(U84(x0, x1, x2))
743.81/262.80	   mark(s(x0))
743.81/262.80	   mark(U91(x0, x1))
743.81/262.80	   mark(U92(x0))
743.81/262.80	   mark(0)
743.81/262.80	
743.81/262.80	We have to consider all minimal (P,Q,R)-chains.
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(80) QDPSizeChangeProof (EQUIVALENT)
743.81/262.80	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. 
743.81/262.80	
743.81/262.80	From the DPs we obtained the following set of size-change graphs:
743.81/262.80	*U61^1(X1, mark(X2)) -> U61^1(X1, X2)
743.81/262.80	The graph contains the following edges 1 >= 1, 2 > 2
743.81/262.80	
743.81/262.80	
743.81/262.80	*U61^1(mark(X1), X2) -> U61^1(X1, X2)
743.81/262.80	The graph contains the following edges 1 > 1, 2 >= 2
743.81/262.80	
743.81/262.80	
743.81/262.80	*U61^1(active(X1), X2) -> U61^1(X1, X2)
743.81/262.80	The graph contains the following edges 1 > 1, 2 >= 2
743.81/262.80	
743.81/262.80	
743.81/262.80	*U61^1(X1, active(X2)) -> U61^1(X1, X2)
743.81/262.80	The graph contains the following edges 1 >= 1, 2 > 2
743.81/262.80	
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(81)
743.81/262.80	YES
743.81/262.80	
743.81/262.80	----------------------------------------
743.81/262.80	
743.81/262.80	(82)
743.81/262.80	Obligation:
743.81/262.80	Q DP problem:
743.81/262.80	The TRS P consists of the following rules:
743.81/262.80	
743.81/262.80	   U51^1(active(X)) -> U51^1(X)
743.81/262.80	   U51^1(mark(X)) -> U51^1(X)
743.81/262.80	
743.81/262.80	The TRS R consists of the following rules:
743.81/262.80	
743.81/262.80	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.81/262.80	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.81/262.80	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.81/262.80	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.81/262.80	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.81/262.80	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.81/262.80	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.81/262.80	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.81/262.80	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.81/262.80	   active(U16(tt)) -> mark(tt)
743.81/262.80	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.81/262.80	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.81/262.80	   active(U23(tt)) -> mark(tt)
743.81/262.80	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.81/262.80	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.81/262.80	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.81/262.80	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.81/262.80	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.81/262.80	   active(U36(tt)) -> mark(tt)
743.81/262.80	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.81/262.80	   active(U42(tt)) -> mark(tt)
743.81/262.80	   active(U51(tt)) -> mark(tt)
743.81/262.80	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.81/262.80	   active(U62(tt)) -> mark(tt)
743.81/262.80	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.81/262.80	   active(U72(tt, N)) -> mark(N)
743.81/262.80	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.81/262.80	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.81/262.80	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.81/262.80	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.81/262.80	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.81/262.80	   active(U92(tt)) -> mark(0)
743.81/262.80	   active(isNat(0)) -> mark(tt)
743.81/262.80	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.81/262.80	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.81/262.80	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.81/262.80	   active(isNatKind(0)) -> mark(tt)
743.81/262.80	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.81/262.80	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.81/262.80	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.81/262.80	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.81/262.80	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.81/262.80	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.81/262.80	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.81/262.80	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.81/262.80	   mark(tt) -> active(tt)
743.81/262.80	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.81/262.80	   mark(isNatKind(X)) -> active(isNatKind(X))
743.81/262.80	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.81/262.80	   mark(isNat(X)) -> active(isNat(X))
743.81/262.80	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.81/262.80	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.81/262.80	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.81/262.80	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.81/262.80	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.81/262.80	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.81/262.80	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.81/262.80	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.81/262.80	   mark(U16(X)) -> active(U16(mark(X)))
743.81/262.80	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.81/262.80	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.81/262.80	   mark(U23(X)) -> active(U23(mark(X)))
743.81/262.80	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.81/262.80	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.81/262.80	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.81/262.80	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.81/262.80	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.81/262.80	   mark(U36(X)) -> active(U36(mark(X)))
743.81/262.80	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.81/262.80	   mark(U42(X)) -> active(U42(mark(X)))
743.81/262.80	   mark(U51(X)) -> active(U51(mark(X)))
743.81/262.80	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.81/262.80	   mark(U62(X)) -> active(U62(mark(X)))
743.81/262.80	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.81/262.80	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.81/262.80	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.81/262.80	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.81/262.80	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.81/262.80	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.81/262.80	   mark(s(X)) -> active(s(mark(X)))
743.81/262.80	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.81/262.80	   mark(U92(X)) -> active(U92(mark(X)))
743.81/262.80	   mark(0) -> active(0)
743.81/262.80	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.81/262.80	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.81/262.80	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.81/262.80	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.81/262.80	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.81/262.80	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.81/262.80	   isNatKind(mark(X)) -> isNatKind(X)
743.81/262.80	   isNatKind(active(X)) -> isNatKind(X)
743.81/262.80	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.81/262.80	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.81/262.80	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.81/262.80	   isNat(mark(X)) -> isNat(X)
743.81/262.80	   isNat(active(X)) -> isNat(X)
743.81/262.80	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.81/262.80	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.81/262.80	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.81/262.80	   plus(mark(X1), X2) -> plus(X1, X2)
743.81/262.80	   plus(X1, mark(X2)) -> plus(X1, X2)
743.81/262.80	   plus(active(X1), X2) -> plus(X1, X2)
743.81/262.80	   plus(X1, active(X2)) -> plus(X1, X2)
743.81/262.80	   x(mark(X1), X2) -> x(X1, X2)
743.81/262.80	   x(X1, mark(X2)) -> x(X1, X2)
743.81/262.80	   x(active(X1), X2) -> x(X1, X2)
743.81/262.80	   x(X1, active(X2)) -> x(X1, X2)
743.81/262.80	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.81/262.80	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.81/262.80	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.81/262.80	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.81/262.80	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.81/262.80	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.81/262.80	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.81/262.80	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.81/262.80	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.81/262.80	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.81/262.80	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.81/262.80	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.81/262.80	   U15(mark(X1), X2) -> U15(X1, X2)
743.81/262.80	   U15(X1, mark(X2)) -> U15(X1, X2)
743.81/262.80	   U15(active(X1), X2) -> U15(X1, X2)
743.81/262.80	   U15(X1, active(X2)) -> U15(X1, X2)
743.81/262.80	   U16(mark(X)) -> U16(X)
743.81/262.80	   U16(active(X)) -> U16(X)
743.81/262.80	   U21(mark(X1), X2) -> U21(X1, X2)
743.81/262.80	   U21(X1, mark(X2)) -> U21(X1, X2)
743.81/262.80	   U21(active(X1), X2) -> U21(X1, X2)
743.81/262.80	   U21(X1, active(X2)) -> U21(X1, X2)
743.81/262.80	   U22(mark(X1), X2) -> U22(X1, X2)
743.81/262.80	   U22(X1, mark(X2)) -> U22(X1, X2)
743.81/262.80	   U22(active(X1), X2) -> U22(X1, X2)
743.81/262.80	   U22(X1, active(X2)) -> U22(X1, X2)
743.81/262.80	   U23(mark(X)) -> U23(X)
743.81/262.80	   U23(active(X)) -> U23(X)
743.81/262.80	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.81/262.80	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.81/262.80	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.81/262.80	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.81/262.80	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.81/262.80	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.81/262.80	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.81/262.80	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.81/262.80	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.81/262.80	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.81/262.80	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.81/262.80	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.81/262.80	   U35(mark(X1), X2) -> U35(X1, X2)
743.81/262.80	   U35(X1, mark(X2)) -> U35(X1, X2)
743.81/262.80	   U35(active(X1), X2) -> U35(X1, X2)
743.81/262.80	   U35(X1, active(X2)) -> U35(X1, X2)
743.81/262.80	   U36(mark(X)) -> U36(X)
743.81/262.80	   U36(active(X)) -> U36(X)
743.81/262.80	   U41(mark(X1), X2) -> U41(X1, X2)
743.81/262.80	   U41(X1, mark(X2)) -> U41(X1, X2)
743.81/262.80	   U41(active(X1), X2) -> U41(X1, X2)
743.81/262.80	   U41(X1, active(X2)) -> U41(X1, X2)
743.81/262.80	   U42(mark(X)) -> U42(X)
743.81/262.80	   U42(active(X)) -> U42(X)
743.81/262.80	   U51(mark(X)) -> U51(X)
743.81/262.80	   U51(active(X)) -> U51(X)
743.81/262.80	   U61(mark(X1), X2) -> U61(X1, X2)
743.81/262.80	   U61(X1, mark(X2)) -> U61(X1, X2)
743.81/262.80	   U61(active(X1), X2) -> U61(X1, X2)
743.81/262.80	   U61(X1, active(X2)) -> U61(X1, X2)
743.81/262.80	   U62(mark(X)) -> U62(X)
743.81/262.80	   U62(active(X)) -> U62(X)
743.81/262.80	   U71(mark(X1), X2) -> U71(X1, X2)
743.81/262.80	   U71(X1, mark(X2)) -> U71(X1, X2)
743.81/262.80	   U71(active(X1), X2) -> U71(X1, X2)
743.81/262.80	   U71(X1, active(X2)) -> U71(X1, X2)
743.81/262.80	   U72(mark(X1), X2) -> U72(X1, X2)
743.81/262.80	   U72(X1, mark(X2)) -> U72(X1, X2)
743.81/262.80	   U72(active(X1), X2) -> U72(X1, X2)
743.81/262.80	   U72(X1, active(X2)) -> U72(X1, X2)
743.81/262.80	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.81/262.80	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.81/262.80	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.81/262.80	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.81/262.80	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.81/262.80	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.81/262.80	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.81/262.80	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.81/262.80	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.81/262.80	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.81/262.80	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.81/262.80	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.81/262.80	   s(mark(X)) -> s(X)
743.81/262.80	   s(active(X)) -> s(X)
743.81/262.80	   U91(mark(X1), X2) -> U91(X1, X2)
743.81/262.80	   U91(X1, mark(X2)) -> U91(X1, X2)
743.81/262.80	   U91(active(X1), X2) -> U91(X1, X2)
743.81/262.80	   U91(X1, active(X2)) -> U91(X1, X2)
743.81/262.80	   U92(mark(X)) -> U92(X)
743.81/262.80	   U92(active(X)) -> U92(X)
743.81/262.80	
743.81/262.80	The set Q consists of the following terms:
743.81/262.80	
743.81/262.80	   active(U101(tt, x0, x1))
743.81/262.80	   active(U102(tt, x0, x1))
743.81/262.81	   active(U103(tt, x0, x1))
743.81/262.81	   active(U104(tt, x0, x1))
743.81/262.81	   active(U11(tt, x0, x1))
743.81/262.81	   active(U12(tt, x0, x1))
743.81/262.81	   active(U13(tt, x0, x1))
743.81/262.81	   active(U14(tt, x0, x1))
743.81/262.81	   active(U15(tt, x0))
743.81/262.81	   active(U16(tt))
743.81/262.81	   active(U21(tt, x0))
743.81/262.81	   active(U22(tt, x0))
743.81/262.81	   active(U23(tt))
743.81/262.81	   active(U31(tt, x0, x1))
743.81/262.81	   active(U32(tt, x0, x1))
743.81/262.81	   active(U33(tt, x0, x1))
743.81/262.81	   active(U34(tt, x0, x1))
743.81/262.81	   active(U35(tt, x0))
743.81/262.81	   active(U36(tt))
743.81/262.81	   active(U41(tt, x0))
743.81/262.81	   active(U42(tt))
743.81/262.81	   active(U51(tt))
743.81/262.81	   active(U61(tt, x0))
743.81/262.81	   active(U62(tt))
743.81/262.81	   active(U71(tt, x0))
743.81/262.81	   active(U72(tt, x0))
743.81/262.81	   active(U81(tt, x0, x1))
743.81/262.81	   active(U82(tt, x0, x1))
743.81/262.81	   active(U83(tt, x0, x1))
743.81/262.81	   active(U84(tt, x0, x1))
743.81/262.81	   active(U91(tt, x0))
743.81/262.81	   active(U92(tt))
743.81/262.81	   active(isNat(0))
743.81/262.81	   active(isNat(plus(x0, x1)))
743.81/262.81	   active(isNat(s(x0)))
743.81/262.81	   active(isNat(x(x0, x1)))
743.81/262.81	   active(isNatKind(0))
743.81/262.81	   active(isNatKind(plus(x0, x1)))
743.81/262.81	   active(isNatKind(s(x0)))
743.81/262.81	   active(isNatKind(x(x0, x1)))
743.81/262.81	   active(plus(x0, 0))
743.81/262.81	   active(plus(x0, s(x1)))
743.81/262.81	   active(x(x0, 0))
743.81/262.81	   active(x(x0, s(x1)))
743.81/262.81	   mark(U101(x0, x1, x2))
743.81/262.81	   mark(tt)
743.81/262.81	   mark(U102(x0, x1, x2))
743.81/262.81	   mark(isNatKind(x0))
743.81/262.81	   mark(U103(x0, x1, x2))
743.81/262.81	   mark(isNat(x0))
743.81/262.81	   mark(U104(x0, x1, x2))
743.81/262.81	   mark(plus(x0, x1))
743.81/262.81	   mark(x(x0, x1))
743.81/262.81	   mark(U11(x0, x1, x2))
743.81/262.81	   mark(U12(x0, x1, x2))
743.81/262.81	   mark(U13(x0, x1, x2))
743.81/262.81	   mark(U14(x0, x1, x2))
743.81/262.81	   mark(U15(x0, x1))
743.81/262.81	   mark(U16(x0))
743.81/262.81	   mark(U21(x0, x1))
743.81/262.81	   mark(U22(x0, x1))
743.81/262.81	   mark(U23(x0))
743.81/262.81	   mark(U31(x0, x1, x2))
743.81/262.81	   mark(U32(x0, x1, x2))
743.81/262.81	   mark(U33(x0, x1, x2))
743.81/262.81	   mark(U34(x0, x1, x2))
743.81/262.81	   mark(U35(x0, x1))
743.81/262.81	   mark(U36(x0))
743.81/262.81	   mark(U41(x0, x1))
743.81/262.81	   mark(U42(x0))
743.81/262.81	   mark(U51(x0))
743.81/262.81	   mark(U61(x0, x1))
743.81/262.81	   mark(U62(x0))
743.81/262.81	   mark(U71(x0, x1))
743.81/262.81	   mark(U72(x0, x1))
743.81/262.81	   mark(U81(x0, x1, x2))
743.81/262.81	   mark(U82(x0, x1, x2))
743.81/262.81	   mark(U83(x0, x1, x2))
743.81/262.81	   mark(U84(x0, x1, x2))
743.81/262.81	   mark(s(x0))
743.81/262.81	   mark(U91(x0, x1))
743.81/262.81	   mark(U92(x0))
743.81/262.81	   mark(0)
743.81/262.81	   U101(mark(x0), x1, x2)
743.81/262.81	   U101(x0, mark(x1), x2)
743.81/262.81	   U101(x0, x1, mark(x2))
743.81/262.81	   U101(active(x0), x1, x2)
743.81/262.81	   U101(x0, active(x1), x2)
743.81/262.81	   U101(x0, x1, active(x2))
743.81/262.81	   U102(mark(x0), x1, x2)
743.81/262.81	   U102(x0, mark(x1), x2)
743.81/262.81	   U102(x0, x1, mark(x2))
743.81/262.81	   U102(active(x0), x1, x2)
743.81/262.81	   U102(x0, active(x1), x2)
743.81/262.81	   U102(x0, x1, active(x2))
743.81/262.81	   isNatKind(mark(x0))
743.81/262.81	   isNatKind(active(x0))
743.81/262.81	   U103(mark(x0), x1, x2)
743.81/262.81	   U103(x0, mark(x1), x2)
743.81/262.81	   U103(x0, x1, mark(x2))
743.81/262.81	   U103(active(x0), x1, x2)
743.81/262.81	   U103(x0, active(x1), x2)
743.81/262.81	   U103(x0, x1, active(x2))
743.81/262.81	   isNat(mark(x0))
743.81/262.81	   isNat(active(x0))
743.81/262.81	   U104(mark(x0), x1, x2)
743.81/262.81	   U104(x0, mark(x1), x2)
743.81/262.81	   U104(x0, x1, mark(x2))
743.81/262.81	   U104(active(x0), x1, x2)
743.81/262.81	   U104(x0, active(x1), x2)
743.81/262.81	   U104(x0, x1, active(x2))
743.81/262.81	   plus(mark(x0), x1)
743.81/262.81	   plus(x0, mark(x1))
743.81/262.81	   plus(active(x0), x1)
743.81/262.81	   plus(x0, active(x1))
743.81/262.81	   x(mark(x0), x1)
743.81/262.81	   x(x0, mark(x1))
743.81/262.81	   x(active(x0), x1)
743.81/262.81	   x(x0, active(x1))
743.81/262.81	   U11(mark(x0), x1, x2)
743.81/262.81	   U11(x0, mark(x1), x2)
743.81/262.81	   U11(x0, x1, mark(x2))
743.81/262.81	   U11(active(x0), x1, x2)
743.81/262.81	   U11(x0, active(x1), x2)
743.81/262.81	   U11(x0, x1, active(x2))
743.81/262.81	   U12(mark(x0), x1, x2)
743.81/262.81	   U12(x0, mark(x1), x2)
743.81/262.81	   U12(x0, x1, mark(x2))
743.81/262.81	   U12(active(x0), x1, x2)
743.81/262.81	   U12(x0, active(x1), x2)
743.81/262.81	   U12(x0, x1, active(x2))
743.81/262.81	   U13(mark(x0), x1, x2)
743.81/262.81	   U13(x0, mark(x1), x2)
743.81/262.81	   U13(x0, x1, mark(x2))
743.81/262.81	   U13(active(x0), x1, x2)
743.81/262.81	   U13(x0, active(x1), x2)
743.81/262.81	   U13(x0, x1, active(x2))
743.81/262.81	   U14(mark(x0), x1, x2)
743.81/262.81	   U14(x0, mark(x1), x2)
743.81/262.81	   U14(x0, x1, mark(x2))
743.81/262.81	   U14(active(x0), x1, x2)
743.81/262.81	   U14(x0, active(x1), x2)
743.81/262.81	   U14(x0, x1, active(x2))
743.81/262.81	   U15(mark(x0), x1)
743.81/262.81	   U15(x0, mark(x1))
743.81/262.81	   U15(active(x0), x1)
743.81/262.81	   U15(x0, active(x1))
743.81/262.81	   U16(mark(x0))
743.81/262.81	   U16(active(x0))
743.81/262.81	   U21(mark(x0), x1)
743.81/262.81	   U21(x0, mark(x1))
743.81/262.81	   U21(active(x0), x1)
743.81/262.81	   U21(x0, active(x1))
743.81/262.81	   U22(mark(x0), x1)
743.81/262.81	   U22(x0, mark(x1))
743.81/262.81	   U22(active(x0), x1)
743.81/262.81	   U22(x0, active(x1))
743.81/262.81	   U23(mark(x0))
743.81/262.81	   U23(active(x0))
743.81/262.81	   U31(mark(x0), x1, x2)
743.81/262.81	   U31(x0, mark(x1), x2)
743.81/262.81	   U31(x0, x1, mark(x2))
743.81/262.81	   U31(active(x0), x1, x2)
743.81/262.81	   U31(x0, active(x1), x2)
743.81/262.81	   U31(x0, x1, active(x2))
743.81/262.81	   U32(mark(x0), x1, x2)
743.81/262.81	   U32(x0, mark(x1), x2)
743.81/262.81	   U32(x0, x1, mark(x2))
743.81/262.81	   U32(active(x0), x1, x2)
743.81/262.81	   U32(x0, active(x1), x2)
743.81/262.81	   U32(x0, x1, active(x2))
743.81/262.81	   U33(mark(x0), x1, x2)
743.81/262.81	   U33(x0, mark(x1), x2)
743.81/262.81	   U33(x0, x1, mark(x2))
743.81/262.81	   U33(active(x0), x1, x2)
743.81/262.81	   U33(x0, active(x1), x2)
743.81/262.81	   U33(x0, x1, active(x2))
743.81/262.81	   U34(mark(x0), x1, x2)
743.81/262.81	   U34(x0, mark(x1), x2)
743.81/262.81	   U34(x0, x1, mark(x2))
743.81/262.81	   U34(active(x0), x1, x2)
743.81/262.81	   U34(x0, active(x1), x2)
743.81/262.81	   U34(x0, x1, active(x2))
743.81/262.81	   U35(mark(x0), x1)
743.81/262.81	   U35(x0, mark(x1))
743.81/262.81	   U35(active(x0), x1)
743.81/262.81	   U35(x0, active(x1))
743.81/262.81	   U36(mark(x0))
743.81/262.81	   U36(active(x0))
743.81/262.81	   U41(mark(x0), x1)
743.81/262.81	   U41(x0, mark(x1))
743.81/262.81	   U41(active(x0), x1)
743.81/262.81	   U41(x0, active(x1))
743.81/262.81	   U42(mark(x0))
743.81/262.81	   U42(active(x0))
743.81/262.81	   U51(mark(x0))
743.81/262.81	   U51(active(x0))
743.81/262.81	   U61(mark(x0), x1)
743.81/262.81	   U61(x0, mark(x1))
743.81/262.81	   U61(active(x0), x1)
743.81/262.81	   U61(x0, active(x1))
743.81/262.81	   U62(mark(x0))
743.81/262.81	   U62(active(x0))
743.81/262.81	   U71(mark(x0), x1)
743.81/262.81	   U71(x0, mark(x1))
743.81/262.81	   U71(active(x0), x1)
743.81/262.81	   U71(x0, active(x1))
743.81/262.81	   U72(mark(x0), x1)
743.81/262.81	   U72(x0, mark(x1))
743.81/262.81	   U72(active(x0), x1)
743.81/262.81	   U72(x0, active(x1))
743.81/262.81	   U81(mark(x0), x1, x2)
743.81/262.81	   U81(x0, mark(x1), x2)
743.81/262.81	   U81(x0, x1, mark(x2))
743.81/262.81	   U81(active(x0), x1, x2)
743.81/262.81	   U81(x0, active(x1), x2)
743.81/262.81	   U81(x0, x1, active(x2))
743.81/262.81	   U82(mark(x0), x1, x2)
743.81/262.81	   U82(x0, mark(x1), x2)
743.81/262.81	   U82(x0, x1, mark(x2))
743.81/262.81	   U82(active(x0), x1, x2)
743.81/262.81	   U82(x0, active(x1), x2)
743.81/262.81	   U82(x0, x1, active(x2))
743.81/262.81	   U83(mark(x0), x1, x2)
743.81/262.81	   U83(x0, mark(x1), x2)
743.81/262.81	   U83(x0, x1, mark(x2))
743.81/262.81	   U83(active(x0), x1, x2)
743.81/262.81	   U83(x0, active(x1), x2)
743.81/262.81	   U83(x0, x1, active(x2))
743.81/262.81	   U84(mark(x0), x1, x2)
743.81/262.81	   U84(x0, mark(x1), x2)
743.81/262.81	   U84(x0, x1, mark(x2))
743.81/262.81	   U84(active(x0), x1, x2)
743.81/262.81	   U84(x0, active(x1), x2)
743.81/262.81	   U84(x0, x1, active(x2))
743.81/262.81	   s(mark(x0))
743.81/262.81	   s(active(x0))
743.81/262.81	   U91(mark(x0), x1)
743.81/262.81	   U91(x0, mark(x1))
743.81/262.81	   U91(active(x0), x1)
743.81/262.81	   U91(x0, active(x1))
743.81/262.81	   U92(mark(x0))
743.81/262.81	   U92(active(x0))
743.81/262.81	
743.81/262.81	We have to consider all minimal (P,Q,R)-chains.
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(83) UsableRulesProof (EQUIVALENT)
743.81/262.81	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.
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(84)
743.81/262.81	Obligation:
743.81/262.81	Q DP problem:
743.81/262.81	The TRS P consists of the following rules:
743.81/262.81	
743.81/262.81	   U51^1(active(X)) -> U51^1(X)
743.81/262.81	   U51^1(mark(X)) -> U51^1(X)
743.81/262.81	
743.81/262.81	R is empty.
743.81/262.81	The set Q consists of the following terms:
743.81/262.81	
743.81/262.81	   active(U101(tt, x0, x1))
743.81/262.81	   active(U102(tt, x0, x1))
743.81/262.81	   active(U103(tt, x0, x1))
743.81/262.81	   active(U104(tt, x0, x1))
743.81/262.81	   active(U11(tt, x0, x1))
743.81/262.81	   active(U12(tt, x0, x1))
743.81/262.81	   active(U13(tt, x0, x1))
743.81/262.81	   active(U14(tt, x0, x1))
743.81/262.81	   active(U15(tt, x0))
743.81/262.81	   active(U16(tt))
743.81/262.81	   active(U21(tt, x0))
743.81/262.81	   active(U22(tt, x0))
743.81/262.81	   active(U23(tt))
743.81/262.81	   active(U31(tt, x0, x1))
743.81/262.81	   active(U32(tt, x0, x1))
743.81/262.81	   active(U33(tt, x0, x1))
743.81/262.81	   active(U34(tt, x0, x1))
743.81/262.81	   active(U35(tt, x0))
743.81/262.81	   active(U36(tt))
743.81/262.81	   active(U41(tt, x0))
743.81/262.81	   active(U42(tt))
743.81/262.81	   active(U51(tt))
743.81/262.81	   active(U61(tt, x0))
743.81/262.81	   active(U62(tt))
743.81/262.81	   active(U71(tt, x0))
743.81/262.81	   active(U72(tt, x0))
743.81/262.81	   active(U81(tt, x0, x1))
743.81/262.81	   active(U82(tt, x0, x1))
743.81/262.81	   active(U83(tt, x0, x1))
743.81/262.81	   active(U84(tt, x0, x1))
743.81/262.81	   active(U91(tt, x0))
743.81/262.81	   active(U92(tt))
743.81/262.81	   active(isNat(0))
743.81/262.81	   active(isNat(plus(x0, x1)))
743.81/262.81	   active(isNat(s(x0)))
743.81/262.81	   active(isNat(x(x0, x1)))
743.81/262.81	   active(isNatKind(0))
743.81/262.81	   active(isNatKind(plus(x0, x1)))
743.81/262.81	   active(isNatKind(s(x0)))
743.81/262.81	   active(isNatKind(x(x0, x1)))
743.81/262.81	   active(plus(x0, 0))
743.81/262.81	   active(plus(x0, s(x1)))
743.81/262.81	   active(x(x0, 0))
743.81/262.81	   active(x(x0, s(x1)))
743.81/262.81	   mark(U101(x0, x1, x2))
743.81/262.81	   mark(tt)
743.81/262.81	   mark(U102(x0, x1, x2))
743.81/262.81	   mark(isNatKind(x0))
743.81/262.81	   mark(U103(x0, x1, x2))
743.81/262.81	   mark(isNat(x0))
743.81/262.81	   mark(U104(x0, x1, x2))
743.81/262.81	   mark(plus(x0, x1))
743.81/262.81	   mark(x(x0, x1))
743.81/262.81	   mark(U11(x0, x1, x2))
743.81/262.81	   mark(U12(x0, x1, x2))
743.81/262.81	   mark(U13(x0, x1, x2))
743.81/262.81	   mark(U14(x0, x1, x2))
743.81/262.81	   mark(U15(x0, x1))
743.81/262.81	   mark(U16(x0))
743.81/262.81	   mark(U21(x0, x1))
743.81/262.81	   mark(U22(x0, x1))
743.81/262.81	   mark(U23(x0))
743.81/262.81	   mark(U31(x0, x1, x2))
743.81/262.81	   mark(U32(x0, x1, x2))
743.81/262.81	   mark(U33(x0, x1, x2))
743.81/262.81	   mark(U34(x0, x1, x2))
743.81/262.81	   mark(U35(x0, x1))
743.81/262.81	   mark(U36(x0))
743.81/262.81	   mark(U41(x0, x1))
743.81/262.81	   mark(U42(x0))
743.81/262.81	   mark(U51(x0))
743.81/262.81	   mark(U61(x0, x1))
743.81/262.81	   mark(U62(x0))
743.81/262.81	   mark(U71(x0, x1))
743.81/262.81	   mark(U72(x0, x1))
743.81/262.81	   mark(U81(x0, x1, x2))
743.81/262.81	   mark(U82(x0, x1, x2))
743.81/262.81	   mark(U83(x0, x1, x2))
743.81/262.81	   mark(U84(x0, x1, x2))
743.81/262.81	   mark(s(x0))
743.81/262.81	   mark(U91(x0, x1))
743.81/262.81	   mark(U92(x0))
743.81/262.81	   mark(0)
743.81/262.81	   U101(mark(x0), x1, x2)
743.81/262.81	   U101(x0, mark(x1), x2)
743.81/262.81	   U101(x0, x1, mark(x2))
743.81/262.81	   U101(active(x0), x1, x2)
743.81/262.81	   U101(x0, active(x1), x2)
743.81/262.81	   U101(x0, x1, active(x2))
743.81/262.81	   U102(mark(x0), x1, x2)
743.81/262.81	   U102(x0, mark(x1), x2)
743.81/262.81	   U102(x0, x1, mark(x2))
743.81/262.81	   U102(active(x0), x1, x2)
743.81/262.81	   U102(x0, active(x1), x2)
743.81/262.81	   U102(x0, x1, active(x2))
743.81/262.81	   isNatKind(mark(x0))
743.81/262.81	   isNatKind(active(x0))
743.81/262.81	   U103(mark(x0), x1, x2)
743.81/262.81	   U103(x0, mark(x1), x2)
743.81/262.81	   U103(x0, x1, mark(x2))
743.81/262.81	   U103(active(x0), x1, x2)
743.81/262.81	   U103(x0, active(x1), x2)
743.81/262.81	   U103(x0, x1, active(x2))
743.81/262.81	   isNat(mark(x0))
743.81/262.81	   isNat(active(x0))
743.81/262.81	   U104(mark(x0), x1, x2)
743.81/262.81	   U104(x0, mark(x1), x2)
743.81/262.81	   U104(x0, x1, mark(x2))
743.81/262.81	   U104(active(x0), x1, x2)
743.81/262.81	   U104(x0, active(x1), x2)
743.81/262.81	   U104(x0, x1, active(x2))
743.81/262.81	   plus(mark(x0), x1)
743.81/262.81	   plus(x0, mark(x1))
743.81/262.81	   plus(active(x0), x1)
743.81/262.81	   plus(x0, active(x1))
743.81/262.81	   x(mark(x0), x1)
743.81/262.81	   x(x0, mark(x1))
743.81/262.81	   x(active(x0), x1)
743.81/262.81	   x(x0, active(x1))
743.81/262.81	   U11(mark(x0), x1, x2)
743.81/262.81	   U11(x0, mark(x1), x2)
743.81/262.81	   U11(x0, x1, mark(x2))
743.81/262.81	   U11(active(x0), x1, x2)
743.81/262.81	   U11(x0, active(x1), x2)
743.81/262.81	   U11(x0, x1, active(x2))
743.81/262.81	   U12(mark(x0), x1, x2)
743.81/262.81	   U12(x0, mark(x1), x2)
743.81/262.81	   U12(x0, x1, mark(x2))
743.81/262.81	   U12(active(x0), x1, x2)
743.81/262.81	   U12(x0, active(x1), x2)
743.81/262.81	   U12(x0, x1, active(x2))
743.81/262.81	   U13(mark(x0), x1, x2)
743.81/262.81	   U13(x0, mark(x1), x2)
743.81/262.81	   U13(x0, x1, mark(x2))
743.81/262.81	   U13(active(x0), x1, x2)
743.81/262.81	   U13(x0, active(x1), x2)
743.81/262.81	   U13(x0, x1, active(x2))
743.81/262.81	   U14(mark(x0), x1, x2)
743.81/262.81	   U14(x0, mark(x1), x2)
743.81/262.81	   U14(x0, x1, mark(x2))
743.81/262.81	   U14(active(x0), x1, x2)
743.81/262.81	   U14(x0, active(x1), x2)
743.81/262.81	   U14(x0, x1, active(x2))
743.81/262.81	   U15(mark(x0), x1)
743.81/262.81	   U15(x0, mark(x1))
743.81/262.81	   U15(active(x0), x1)
743.81/262.81	   U15(x0, active(x1))
743.81/262.81	   U16(mark(x0))
743.81/262.81	   U16(active(x0))
743.81/262.81	   U21(mark(x0), x1)
743.81/262.81	   U21(x0, mark(x1))
743.81/262.81	   U21(active(x0), x1)
743.81/262.81	   U21(x0, active(x1))
743.81/262.81	   U22(mark(x0), x1)
743.81/262.81	   U22(x0, mark(x1))
743.81/262.81	   U22(active(x0), x1)
743.81/262.81	   U22(x0, active(x1))
743.81/262.81	   U23(mark(x0))
743.81/262.81	   U23(active(x0))
743.81/262.81	   U31(mark(x0), x1, x2)
743.81/262.81	   U31(x0, mark(x1), x2)
743.81/262.81	   U31(x0, x1, mark(x2))
743.81/262.81	   U31(active(x0), x1, x2)
743.81/262.81	   U31(x0, active(x1), x2)
743.81/262.81	   U31(x0, x1, active(x2))
743.81/262.81	   U32(mark(x0), x1, x2)
743.81/262.81	   U32(x0, mark(x1), x2)
743.81/262.81	   U32(x0, x1, mark(x2))
743.81/262.81	   U32(active(x0), x1, x2)
743.81/262.81	   U32(x0, active(x1), x2)
743.81/262.81	   U32(x0, x1, active(x2))
743.81/262.81	   U33(mark(x0), x1, x2)
743.81/262.81	   U33(x0, mark(x1), x2)
743.81/262.81	   U33(x0, x1, mark(x2))
743.81/262.81	   U33(active(x0), x1, x2)
743.81/262.81	   U33(x0, active(x1), x2)
743.81/262.81	   U33(x0, x1, active(x2))
743.81/262.81	   U34(mark(x0), x1, x2)
743.81/262.81	   U34(x0, mark(x1), x2)
743.81/262.81	   U34(x0, x1, mark(x2))
743.81/262.81	   U34(active(x0), x1, x2)
743.81/262.81	   U34(x0, active(x1), x2)
743.81/262.81	   U34(x0, x1, active(x2))
743.81/262.81	   U35(mark(x0), x1)
743.81/262.81	   U35(x0, mark(x1))
743.81/262.81	   U35(active(x0), x1)
743.81/262.81	   U35(x0, active(x1))
743.81/262.81	   U36(mark(x0))
743.81/262.81	   U36(active(x0))
743.81/262.81	   U41(mark(x0), x1)
743.81/262.81	   U41(x0, mark(x1))
743.81/262.81	   U41(active(x0), x1)
743.81/262.81	   U41(x0, active(x1))
743.81/262.81	   U42(mark(x0))
743.81/262.81	   U42(active(x0))
743.81/262.81	   U51(mark(x0))
743.81/262.81	   U51(active(x0))
743.81/262.81	   U61(mark(x0), x1)
743.81/262.81	   U61(x0, mark(x1))
743.81/262.81	   U61(active(x0), x1)
743.81/262.81	   U61(x0, active(x1))
743.81/262.81	   U62(mark(x0))
743.81/262.81	   U62(active(x0))
743.81/262.81	   U71(mark(x0), x1)
743.81/262.81	   U71(x0, mark(x1))
743.81/262.81	   U71(active(x0), x1)
743.81/262.81	   U71(x0, active(x1))
743.81/262.81	   U72(mark(x0), x1)
743.81/262.81	   U72(x0, mark(x1))
743.81/262.81	   U72(active(x0), x1)
743.81/262.81	   U72(x0, active(x1))
743.81/262.81	   U81(mark(x0), x1, x2)
743.81/262.81	   U81(x0, mark(x1), x2)
743.81/262.81	   U81(x0, x1, mark(x2))
743.81/262.81	   U81(active(x0), x1, x2)
743.81/262.81	   U81(x0, active(x1), x2)
743.81/262.81	   U81(x0, x1, active(x2))
743.81/262.81	   U82(mark(x0), x1, x2)
743.81/262.81	   U82(x0, mark(x1), x2)
743.81/262.81	   U82(x0, x1, mark(x2))
743.81/262.81	   U82(active(x0), x1, x2)
743.81/262.81	   U82(x0, active(x1), x2)
743.81/262.81	   U82(x0, x1, active(x2))
743.81/262.81	   U83(mark(x0), x1, x2)
743.81/262.81	   U83(x0, mark(x1), x2)
743.81/262.81	   U83(x0, x1, mark(x2))
743.81/262.81	   U83(active(x0), x1, x2)
743.81/262.81	   U83(x0, active(x1), x2)
743.81/262.81	   U83(x0, x1, active(x2))
743.81/262.81	   U84(mark(x0), x1, x2)
743.81/262.81	   U84(x0, mark(x1), x2)
743.81/262.81	   U84(x0, x1, mark(x2))
743.81/262.81	   U84(active(x0), x1, x2)
743.81/262.81	   U84(x0, active(x1), x2)
743.81/262.81	   U84(x0, x1, active(x2))
743.81/262.81	   s(mark(x0))
743.81/262.81	   s(active(x0))
743.81/262.81	   U91(mark(x0), x1)
743.81/262.81	   U91(x0, mark(x1))
743.81/262.81	   U91(active(x0), x1)
743.81/262.81	   U91(x0, active(x1))
743.81/262.81	   U92(mark(x0))
743.81/262.81	   U92(active(x0))
743.81/262.81	
743.81/262.81	We have to consider all minimal (P,Q,R)-chains.
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(85) QReductionProof (EQUIVALENT)
743.81/262.81	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.81/262.81	
743.81/262.81	   U101(mark(x0), x1, x2)
743.81/262.81	   U101(x0, mark(x1), x2)
743.81/262.81	   U101(x0, x1, mark(x2))
743.81/262.81	   U101(active(x0), x1, x2)
743.81/262.81	   U101(x0, active(x1), x2)
743.81/262.81	   U101(x0, x1, active(x2))
743.81/262.81	   U102(mark(x0), x1, x2)
743.81/262.81	   U102(x0, mark(x1), x2)
743.81/262.81	   U102(x0, x1, mark(x2))
743.81/262.81	   U102(active(x0), x1, x2)
743.81/262.81	   U102(x0, active(x1), x2)
743.81/262.81	   U102(x0, x1, active(x2))
743.81/262.81	   isNatKind(mark(x0))
743.81/262.81	   isNatKind(active(x0))
743.81/262.81	   U103(mark(x0), x1, x2)
743.81/262.81	   U103(x0, mark(x1), x2)
743.81/262.81	   U103(x0, x1, mark(x2))
743.81/262.81	   U103(active(x0), x1, x2)
743.81/262.81	   U103(x0, active(x1), x2)
743.81/262.81	   U103(x0, x1, active(x2))
743.81/262.81	   isNat(mark(x0))
743.81/262.81	   isNat(active(x0))
743.81/262.81	   U104(mark(x0), x1, x2)
743.81/262.81	   U104(x0, mark(x1), x2)
743.81/262.81	   U104(x0, x1, mark(x2))
743.81/262.81	   U104(active(x0), x1, x2)
743.81/262.81	   U104(x0, active(x1), x2)
743.81/262.81	   U104(x0, x1, active(x2))
743.81/262.81	   plus(mark(x0), x1)
743.81/262.81	   plus(x0, mark(x1))
743.81/262.81	   plus(active(x0), x1)
743.81/262.81	   plus(x0, active(x1))
743.81/262.81	   x(mark(x0), x1)
743.81/262.81	   x(x0, mark(x1))
743.81/262.81	   x(active(x0), x1)
743.81/262.81	   x(x0, active(x1))
743.81/262.81	   U11(mark(x0), x1, x2)
743.81/262.81	   U11(x0, mark(x1), x2)
743.81/262.81	   U11(x0, x1, mark(x2))
743.81/262.81	   U11(active(x0), x1, x2)
743.81/262.81	   U11(x0, active(x1), x2)
743.81/262.81	   U11(x0, x1, active(x2))
743.81/262.81	   U12(mark(x0), x1, x2)
743.81/262.81	   U12(x0, mark(x1), x2)
743.81/262.81	   U12(x0, x1, mark(x2))
743.81/262.81	   U12(active(x0), x1, x2)
743.81/262.81	   U12(x0, active(x1), x2)
743.81/262.81	   U12(x0, x1, active(x2))
743.81/262.81	   U13(mark(x0), x1, x2)
743.81/262.81	   U13(x0, mark(x1), x2)
743.81/262.81	   U13(x0, x1, mark(x2))
743.81/262.81	   U13(active(x0), x1, x2)
743.81/262.81	   U13(x0, active(x1), x2)
743.81/262.81	   U13(x0, x1, active(x2))
743.81/262.81	   U14(mark(x0), x1, x2)
743.81/262.81	   U14(x0, mark(x1), x2)
743.81/262.81	   U14(x0, x1, mark(x2))
743.81/262.81	   U14(active(x0), x1, x2)
743.81/262.81	   U14(x0, active(x1), x2)
743.81/262.81	   U14(x0, x1, active(x2))
743.81/262.81	   U15(mark(x0), x1)
743.81/262.81	   U15(x0, mark(x1))
743.81/262.81	   U15(active(x0), x1)
743.81/262.81	   U15(x0, active(x1))
743.81/262.81	   U16(mark(x0))
743.81/262.81	   U16(active(x0))
743.81/262.81	   U21(mark(x0), x1)
743.81/262.81	   U21(x0, mark(x1))
743.81/262.81	   U21(active(x0), x1)
743.81/262.81	   U21(x0, active(x1))
743.81/262.81	   U22(mark(x0), x1)
743.81/262.81	   U22(x0, mark(x1))
743.81/262.81	   U22(active(x0), x1)
743.81/262.81	   U22(x0, active(x1))
743.81/262.81	   U23(mark(x0))
743.81/262.81	   U23(active(x0))
743.81/262.81	   U31(mark(x0), x1, x2)
743.81/262.81	   U31(x0, mark(x1), x2)
743.81/262.81	   U31(x0, x1, mark(x2))
743.81/262.81	   U31(active(x0), x1, x2)
743.81/262.81	   U31(x0, active(x1), x2)
743.81/262.81	   U31(x0, x1, active(x2))
743.81/262.81	   U32(mark(x0), x1, x2)
743.81/262.81	   U32(x0, mark(x1), x2)
743.81/262.81	   U32(x0, x1, mark(x2))
743.81/262.81	   U32(active(x0), x1, x2)
743.81/262.81	   U32(x0, active(x1), x2)
743.81/262.81	   U32(x0, x1, active(x2))
743.81/262.81	   U33(mark(x0), x1, x2)
743.81/262.81	   U33(x0, mark(x1), x2)
743.81/262.81	   U33(x0, x1, mark(x2))
743.81/262.81	   U33(active(x0), x1, x2)
743.81/262.81	   U33(x0, active(x1), x2)
743.81/262.81	   U33(x0, x1, active(x2))
743.81/262.81	   U34(mark(x0), x1, x2)
743.81/262.81	   U34(x0, mark(x1), x2)
743.81/262.81	   U34(x0, x1, mark(x2))
743.81/262.81	   U34(active(x0), x1, x2)
743.81/262.81	   U34(x0, active(x1), x2)
743.81/262.81	   U34(x0, x1, active(x2))
743.81/262.81	   U35(mark(x0), x1)
743.81/262.81	   U35(x0, mark(x1))
743.81/262.81	   U35(active(x0), x1)
743.81/262.81	   U35(x0, active(x1))
743.81/262.81	   U36(mark(x0))
743.81/262.81	   U36(active(x0))
743.81/262.81	   U41(mark(x0), x1)
743.81/262.81	   U41(x0, mark(x1))
743.81/262.81	   U41(active(x0), x1)
743.81/262.81	   U41(x0, active(x1))
743.81/262.81	   U42(mark(x0))
743.81/262.81	   U42(active(x0))
743.81/262.81	   U51(mark(x0))
743.81/262.81	   U51(active(x0))
743.81/262.81	   U61(mark(x0), x1)
743.81/262.81	   U61(x0, mark(x1))
743.81/262.81	   U61(active(x0), x1)
743.81/262.81	   U61(x0, active(x1))
743.81/262.81	   U62(mark(x0))
743.81/262.81	   U62(active(x0))
743.81/262.81	   U71(mark(x0), x1)
743.81/262.81	   U71(x0, mark(x1))
743.81/262.81	   U71(active(x0), x1)
743.81/262.81	   U71(x0, active(x1))
743.81/262.81	   U72(mark(x0), x1)
743.81/262.81	   U72(x0, mark(x1))
743.81/262.81	   U72(active(x0), x1)
743.81/262.81	   U72(x0, active(x1))
743.81/262.81	   U81(mark(x0), x1, x2)
743.81/262.81	   U81(x0, mark(x1), x2)
743.81/262.81	   U81(x0, x1, mark(x2))
743.81/262.81	   U81(active(x0), x1, x2)
743.81/262.81	   U81(x0, active(x1), x2)
743.81/262.81	   U81(x0, x1, active(x2))
743.81/262.81	   U82(mark(x0), x1, x2)
743.81/262.81	   U82(x0, mark(x1), x2)
743.81/262.81	   U82(x0, x1, mark(x2))
743.81/262.81	   U82(active(x0), x1, x2)
743.81/262.81	   U82(x0, active(x1), x2)
743.81/262.81	   U82(x0, x1, active(x2))
743.81/262.81	   U83(mark(x0), x1, x2)
743.81/262.81	   U83(x0, mark(x1), x2)
743.81/262.81	   U83(x0, x1, mark(x2))
743.81/262.81	   U83(active(x0), x1, x2)
743.81/262.81	   U83(x0, active(x1), x2)
743.81/262.81	   U83(x0, x1, active(x2))
743.81/262.81	   U84(mark(x0), x1, x2)
743.81/262.81	   U84(x0, mark(x1), x2)
743.81/262.81	   U84(x0, x1, mark(x2))
743.81/262.81	   U84(active(x0), x1, x2)
743.81/262.81	   U84(x0, active(x1), x2)
743.81/262.81	   U84(x0, x1, active(x2))
743.81/262.81	   s(mark(x0))
743.81/262.81	   s(active(x0))
743.81/262.81	   U91(mark(x0), x1)
743.81/262.81	   U91(x0, mark(x1))
743.81/262.81	   U91(active(x0), x1)
743.81/262.81	   U91(x0, active(x1))
743.81/262.81	   U92(mark(x0))
743.81/262.81	   U92(active(x0))
743.81/262.81	
743.81/262.81	
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(86)
743.81/262.81	Obligation:
743.81/262.81	Q DP problem:
743.81/262.81	The TRS P consists of the following rules:
743.81/262.81	
743.81/262.81	   U51^1(active(X)) -> U51^1(X)
743.81/262.81	   U51^1(mark(X)) -> U51^1(X)
743.81/262.81	
743.81/262.81	R is empty.
743.81/262.81	The set Q consists of the following terms:
743.81/262.81	
743.81/262.81	   active(U101(tt, x0, x1))
743.81/262.81	   active(U102(tt, x0, x1))
743.81/262.81	   active(U103(tt, x0, x1))
743.81/262.81	   active(U104(tt, x0, x1))
743.81/262.81	   active(U11(tt, x0, x1))
743.81/262.81	   active(U12(tt, x0, x1))
743.81/262.81	   active(U13(tt, x0, x1))
743.81/262.81	   active(U14(tt, x0, x1))
743.81/262.81	   active(U15(tt, x0))
743.81/262.81	   active(U16(tt))
743.81/262.81	   active(U21(tt, x0))
743.81/262.81	   active(U22(tt, x0))
743.81/262.81	   active(U23(tt))
743.81/262.81	   active(U31(tt, x0, x1))
743.81/262.81	   active(U32(tt, x0, x1))
743.81/262.81	   active(U33(tt, x0, x1))
743.81/262.81	   active(U34(tt, x0, x1))
743.81/262.81	   active(U35(tt, x0))
743.81/262.81	   active(U36(tt))
743.81/262.81	   active(U41(tt, x0))
743.81/262.81	   active(U42(tt))
743.81/262.81	   active(U51(tt))
743.81/262.81	   active(U61(tt, x0))
743.81/262.81	   active(U62(tt))
743.81/262.81	   active(U71(tt, x0))
743.81/262.81	   active(U72(tt, x0))
743.81/262.81	   active(U81(tt, x0, x1))
743.81/262.81	   active(U82(tt, x0, x1))
743.81/262.81	   active(U83(tt, x0, x1))
743.81/262.81	   active(U84(tt, x0, x1))
743.81/262.81	   active(U91(tt, x0))
743.81/262.81	   active(U92(tt))
743.81/262.81	   active(isNat(0))
743.81/262.81	   active(isNat(plus(x0, x1)))
743.81/262.81	   active(isNat(s(x0)))
743.81/262.81	   active(isNat(x(x0, x1)))
743.81/262.81	   active(isNatKind(0))
743.81/262.81	   active(isNatKind(plus(x0, x1)))
743.81/262.81	   active(isNatKind(s(x0)))
743.81/262.81	   active(isNatKind(x(x0, x1)))
743.81/262.81	   active(plus(x0, 0))
743.81/262.81	   active(plus(x0, s(x1)))
743.81/262.81	   active(x(x0, 0))
743.81/262.81	   active(x(x0, s(x1)))
743.81/262.81	   mark(U101(x0, x1, x2))
743.81/262.81	   mark(tt)
743.81/262.81	   mark(U102(x0, x1, x2))
743.81/262.81	   mark(isNatKind(x0))
743.81/262.81	   mark(U103(x0, x1, x2))
743.81/262.81	   mark(isNat(x0))
743.81/262.81	   mark(U104(x0, x1, x2))
743.81/262.81	   mark(plus(x0, x1))
743.81/262.81	   mark(x(x0, x1))
743.81/262.81	   mark(U11(x0, x1, x2))
743.81/262.81	   mark(U12(x0, x1, x2))
743.81/262.81	   mark(U13(x0, x1, x2))
743.81/262.81	   mark(U14(x0, x1, x2))
743.81/262.81	   mark(U15(x0, x1))
743.81/262.81	   mark(U16(x0))
743.81/262.81	   mark(U21(x0, x1))
743.81/262.81	   mark(U22(x0, x1))
743.81/262.81	   mark(U23(x0))
743.81/262.81	   mark(U31(x0, x1, x2))
743.81/262.81	   mark(U32(x0, x1, x2))
743.81/262.81	   mark(U33(x0, x1, x2))
743.81/262.81	   mark(U34(x0, x1, x2))
743.81/262.81	   mark(U35(x0, x1))
743.81/262.81	   mark(U36(x0))
743.81/262.81	   mark(U41(x0, x1))
743.81/262.81	   mark(U42(x0))
743.81/262.81	   mark(U51(x0))
743.81/262.81	   mark(U61(x0, x1))
743.81/262.81	   mark(U62(x0))
743.81/262.81	   mark(U71(x0, x1))
743.81/262.81	   mark(U72(x0, x1))
743.81/262.81	   mark(U81(x0, x1, x2))
743.81/262.81	   mark(U82(x0, x1, x2))
743.81/262.81	   mark(U83(x0, x1, x2))
743.81/262.81	   mark(U84(x0, x1, x2))
743.81/262.81	   mark(s(x0))
743.81/262.81	   mark(U91(x0, x1))
743.81/262.81	   mark(U92(x0))
743.81/262.81	   mark(0)
743.81/262.81	
743.81/262.81	We have to consider all minimal (P,Q,R)-chains.
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(87) QDPSizeChangeProof (EQUIVALENT)
743.81/262.81	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
743.81/262.81	
743.81/262.81	From the DPs we obtained the following set of size-change graphs:
743.81/262.81	*U51^1(active(X)) -> U51^1(X)
743.81/262.81	The graph contains the following edges 1 > 1
743.81/262.81	
743.81/262.81	
743.81/262.81	*U51^1(mark(X)) -> U51^1(X)
743.81/262.81	The graph contains the following edges 1 > 1
743.81/262.81	
743.81/262.81	
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(88)
743.81/262.81	YES
743.81/262.81	
743.81/262.81	----------------------------------------
743.81/262.81	
743.81/262.81	(89)
743.81/262.81	Obligation:
743.81/262.81	Q DP problem:
743.81/262.81	The TRS P consists of the following rules:
743.81/262.81	
743.81/262.81	   U42^1(active(X)) -> U42^1(X)
743.81/262.81	   U42^1(mark(X)) -> U42^1(X)
743.81/262.81	
743.81/262.81	The TRS R consists of the following rules:
743.81/262.81	
743.81/262.81	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.81/262.81	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.81/262.81	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.81/262.81	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.81/262.81	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.81/262.81	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.81/262.81	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.81/262.81	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.81/262.81	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.81/262.81	   active(U16(tt)) -> mark(tt)
743.81/262.81	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.81/262.81	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.81/262.81	   active(U23(tt)) -> mark(tt)
743.81/262.81	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.81/262.81	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.81/262.81	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.81/262.81	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.81/262.81	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.81/262.81	   active(U36(tt)) -> mark(tt)
743.81/262.81	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.81/262.81	   active(U42(tt)) -> mark(tt)
743.81/262.81	   active(U51(tt)) -> mark(tt)
743.81/262.81	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.81/262.81	   active(U62(tt)) -> mark(tt)
743.81/262.81	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.81/262.81	   active(U72(tt, N)) -> mark(N)
743.81/262.81	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.81/262.81	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.81/262.81	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.81/262.81	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.81/262.81	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.81/262.81	   active(U92(tt)) -> mark(0)
743.81/262.81	   active(isNat(0)) -> mark(tt)
743.81/262.81	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.81/262.81	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.81/262.81	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.81/262.81	   active(isNatKind(0)) -> mark(tt)
743.81/262.81	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.81/262.81	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.81/262.81	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.81/262.81	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.81/262.81	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.81/262.81	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.81/262.81	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.81/262.81	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.81/262.81	   mark(tt) -> active(tt)
743.81/262.81	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.81/262.81	   mark(isNatKind(X)) -> active(isNatKind(X))
743.81/262.81	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.81/262.81	   mark(isNat(X)) -> active(isNat(X))
743.81/262.81	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.81/262.81	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.81/262.81	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.81/262.81	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.81/262.81	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.81/262.81	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.81/262.81	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.81/262.81	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.81/262.81	   mark(U16(X)) -> active(U16(mark(X)))
743.81/262.81	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.81/262.81	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.81/262.81	   mark(U23(X)) -> active(U23(mark(X)))
743.81/262.81	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.81/262.81	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.81/262.81	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.81/262.81	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.81/262.81	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.81/262.81	   mark(U36(X)) -> active(U36(mark(X)))
743.81/262.81	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.81/262.81	   mark(U42(X)) -> active(U42(mark(X)))
743.81/262.81	   mark(U51(X)) -> active(U51(mark(X)))
743.81/262.81	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.81/262.81	   mark(U62(X)) -> active(U62(mark(X)))
743.81/262.81	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.81/262.81	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.81/262.81	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.81/262.81	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.81/262.81	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.81/262.81	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.81/262.81	   mark(s(X)) -> active(s(mark(X)))
743.81/262.81	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.81/262.81	   mark(U92(X)) -> active(U92(mark(X)))
743.81/262.81	   mark(0) -> active(0)
743.81/262.81	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.81	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.81/262.81	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.81/262.81	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.81	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.81/262.81	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.81/262.81	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.81	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.81/262.81	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.81/262.81	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.81	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.81/262.81	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.81/262.81	   isNatKind(mark(X)) -> isNatKind(X)
743.81/262.81	   isNatKind(active(X)) -> isNatKind(X)
743.81/262.81	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.81	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.81/262.81	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.81/262.81	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.81	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.81/262.81	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.81/262.81	   isNat(mark(X)) -> isNat(X)
743.81/262.81	   isNat(active(X)) -> isNat(X)
743.81/262.81	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.81	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.81/262.81	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.81/262.81	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.81	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.81/262.81	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.81/262.81	   plus(mark(X1), X2) -> plus(X1, X2)
743.81/262.81	   plus(X1, mark(X2)) -> plus(X1, X2)
743.81/262.81	   plus(active(X1), X2) -> plus(X1, X2)
743.81/262.81	   plus(X1, active(X2)) -> plus(X1, X2)
743.81/262.81	   x(mark(X1), X2) -> x(X1, X2)
743.81/262.81	   x(X1, mark(X2)) -> x(X1, X2)
743.81/262.81	   x(active(X1), X2) -> x(X1, X2)
743.81/262.81	   x(X1, active(X2)) -> x(X1, X2)
743.81/262.81	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.81	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.81/262.81	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.81/262.81	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.81	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.81/262.81	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.81/262.81	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.81	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.81/262.81	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.81/262.81	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.81	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.81/262.81	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.81/262.81	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.81	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.81/262.81	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.81/262.81	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.81	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.81/262.81	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.81/262.81	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.81	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.81/262.81	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.81/262.81	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.81	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.81/262.81	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.81/262.81	   U15(mark(X1), X2) -> U15(X1, X2)
743.81/262.81	   U15(X1, mark(X2)) -> U15(X1, X2)
743.81/262.81	   U15(active(X1), X2) -> U15(X1, X2)
743.81/262.81	   U15(X1, active(X2)) -> U15(X1, X2)
743.81/262.81	   U16(mark(X)) -> U16(X)
743.81/262.81	   U16(active(X)) -> U16(X)
743.81/262.81	   U21(mark(X1), X2) -> U21(X1, X2)
743.81/262.81	   U21(X1, mark(X2)) -> U21(X1, X2)
743.81/262.81	   U21(active(X1), X2) -> U21(X1, X2)
743.81/262.81	   U21(X1, active(X2)) -> U21(X1, X2)
743.81/262.81	   U22(mark(X1), X2) -> U22(X1, X2)
743.81/262.81	   U22(X1, mark(X2)) -> U22(X1, X2)
743.81/262.81	   U22(active(X1), X2) -> U22(X1, X2)
743.81/262.81	   U22(X1, active(X2)) -> U22(X1, X2)
743.81/262.81	   U23(mark(X)) -> U23(X)
743.81/262.81	   U23(active(X)) -> U23(X)
743.81/262.81	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.81	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.81/262.81	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.81/262.81	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.81	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.81/262.81	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.81/262.81	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.81	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.81/262.81	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.81/262.81	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.81	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.81/262.81	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.81/262.81	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.81	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.81/262.81	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.81/262.81	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.81	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.81/262.81	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.81/262.81	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.81	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.81/262.81	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.81/262.81	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.81	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.81/262.81	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.81/262.81	   U35(mark(X1), X2) -> U35(X1, X2)
743.81/262.81	   U35(X1, mark(X2)) -> U35(X1, X2)
743.81/262.81	   U35(active(X1), X2) -> U35(X1, X2)
743.81/262.81	   U35(X1, active(X2)) -> U35(X1, X2)
743.81/262.81	   U36(mark(X)) -> U36(X)
743.81/262.81	   U36(active(X)) -> U36(X)
743.81/262.81	   U41(mark(X1), X2) -> U41(X1, X2)
743.81/262.81	   U41(X1, mark(X2)) -> U41(X1, X2)
743.81/262.81	   U41(active(X1), X2) -> U41(X1, X2)
743.81/262.81	   U41(X1, active(X2)) -> U41(X1, X2)
743.81/262.81	   U42(mark(X)) -> U42(X)
743.81/262.81	   U42(active(X)) -> U42(X)
743.81/262.81	   U51(mark(X)) -> U51(X)
743.81/262.81	   U51(active(X)) -> U51(X)
743.81/262.81	   U61(mark(X1), X2) -> U61(X1, X2)
743.81/262.81	   U61(X1, mark(X2)) -> U61(X1, X2)
743.81/262.81	   U61(active(X1), X2) -> U61(X1, X2)
743.81/262.81	   U61(X1, active(X2)) -> U61(X1, X2)
743.81/262.81	   U62(mark(X)) -> U62(X)
743.81/262.81	   U62(active(X)) -> U62(X)
743.81/262.81	   U71(mark(X1), X2) -> U71(X1, X2)
743.81/262.81	   U71(X1, mark(X2)) -> U71(X1, X2)
743.81/262.81	   U71(active(X1), X2) -> U71(X1, X2)
743.81/262.81	   U71(X1, active(X2)) -> U71(X1, X2)
743.81/262.81	   U72(mark(X1), X2) -> U72(X1, X2)
743.81/262.81	   U72(X1, mark(X2)) -> U72(X1, X2)
743.81/262.81	   U72(active(X1), X2) -> U72(X1, X2)
743.81/262.81	   U72(X1, active(X2)) -> U72(X1, X2)
743.81/262.81	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.81	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.81/262.81	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.81/262.81	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.81	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.81/262.81	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.81/262.81	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.81	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.81/262.81	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.81/262.81	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.81	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.81/262.81	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.81/262.81	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.81	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.81/262.81	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.81/262.81	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.81	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.81/262.81	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.81/262.81	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.81	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.81/262.81	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.81/262.81	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.81	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.81/262.81	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.81/262.81	   s(mark(X)) -> s(X)
743.81/262.81	   s(active(X)) -> s(X)
743.81/262.81	   U91(mark(X1), X2) -> U91(X1, X2)
743.81/262.81	   U91(X1, mark(X2)) -> U91(X1, X2)
743.81/262.81	   U91(active(X1), X2) -> U91(X1, X2)
743.81/262.81	   U91(X1, active(X2)) -> U91(X1, X2)
743.81/262.81	   U92(mark(X)) -> U92(X)
743.81/262.81	   U92(active(X)) -> U92(X)
743.81/262.81	
743.81/262.81	The set Q consists of the following terms:
743.81/262.81	
743.81/262.81	   active(U101(tt, x0, x1))
743.81/262.81	   active(U102(tt, x0, x1))
743.81/262.81	   active(U103(tt, x0, x1))
743.81/262.81	   active(U104(tt, x0, x1))
743.81/262.81	   active(U11(tt, x0, x1))
743.81/262.81	   active(U12(tt, x0, x1))
743.81/262.81	   active(U13(tt, x0, x1))
743.81/262.81	   active(U14(tt, x0, x1))
743.81/262.81	   active(U15(tt, x0))
743.81/262.81	   active(U16(tt))
743.81/262.81	   active(U21(tt, x0))
743.81/262.81	   active(U22(tt, x0))
743.81/262.81	   active(U23(tt))
743.81/262.81	   active(U31(tt, x0, x1))
743.81/262.81	   active(U32(tt, x0, x1))
743.81/262.81	   active(U33(tt, x0, x1))
743.81/262.81	   active(U34(tt, x0, x1))
743.81/262.81	   active(U35(tt, x0))
743.81/262.81	   active(U36(tt))
743.81/262.81	   active(U41(tt, x0))
743.81/262.81	   active(U42(tt))
743.81/262.81	   active(U51(tt))
743.81/262.81	   active(U61(tt, x0))
743.81/262.81	   active(U62(tt))
743.81/262.81	   active(U71(tt, x0))
743.81/262.81	   active(U72(tt, x0))
743.81/262.81	   active(U81(tt, x0, x1))
743.81/262.81	   active(U82(tt, x0, x1))
743.81/262.81	   active(U83(tt, x0, x1))
743.81/262.81	   active(U84(tt, x0, x1))
743.81/262.81	   active(U91(tt, x0))
743.81/262.81	   active(U92(tt))
743.81/262.81	   active(isNat(0))
743.81/262.81	   active(isNat(plus(x0, x1)))
743.81/262.81	   active(isNat(s(x0)))
743.81/262.81	   active(isNat(x(x0, x1)))
743.81/262.81	   active(isNatKind(0))
743.81/262.81	   active(isNatKind(plus(x0, x1)))
743.81/262.81	   active(isNatKind(s(x0)))
743.81/262.81	   active(isNatKind(x(x0, x1)))
743.81/262.81	   active(plus(x0, 0))
743.81/262.81	   active(plus(x0, s(x1)))
743.81/262.81	   active(x(x0, 0))
743.81/262.81	   active(x(x0, s(x1)))
743.81/262.81	   mark(U101(x0, x1, x2))
743.81/262.81	   mark(tt)
743.81/262.81	   mark(U102(x0, x1, x2))
743.81/262.81	   mark(isNatKind(x0))
743.81/262.81	   mark(U103(x0, x1, x2))
743.81/262.81	   mark(isNat(x0))
743.81/262.81	   mark(U104(x0, x1, x2))
743.81/262.81	   mark(plus(x0, x1))
743.81/262.81	   mark(x(x0, x1))
743.81/262.81	   mark(U11(x0, x1, x2))
743.81/262.81	   mark(U12(x0, x1, x2))
743.81/262.81	   mark(U13(x0, x1, x2))
743.81/262.81	   mark(U14(x0, x1, x2))
743.81/262.81	   mark(U15(x0, x1))
743.81/262.81	   mark(U16(x0))
743.81/262.81	   mark(U21(x0, x1))
743.81/262.81	   mark(U22(x0, x1))
743.81/262.81	   mark(U23(x0))
743.81/262.81	   mark(U31(x0, x1, x2))
743.81/262.81	   mark(U32(x0, x1, x2))
743.81/262.81	   mark(U33(x0, x1, x2))
743.81/262.81	   mark(U34(x0, x1, x2))
743.81/262.81	   mark(U35(x0, x1))
743.81/262.81	   mark(U36(x0))
743.81/262.81	   mark(U41(x0, x1))
743.81/262.81	   mark(U42(x0))
743.81/262.81	   mark(U51(x0))
743.81/262.81	   mark(U61(x0, x1))
743.81/262.81	   mark(U62(x0))
743.81/262.81	   mark(U71(x0, x1))
743.81/262.81	   mark(U72(x0, x1))
743.81/262.81	   mark(U81(x0, x1, x2))
743.81/262.81	   mark(U82(x0, x1, x2))
743.81/262.81	   mark(U83(x0, x1, x2))
743.81/262.81	   mark(U84(x0, x1, x2))
743.81/262.81	   mark(s(x0))
743.81/262.83	   mark(U91(x0, x1))
743.81/262.83	   mark(U92(x0))
743.81/262.83	   mark(0)
743.81/262.83	   U101(mark(x0), x1, x2)
743.81/262.83	   U101(x0, mark(x1), x2)
743.81/262.83	   U101(x0, x1, mark(x2))
743.81/262.83	   U101(active(x0), x1, x2)
743.81/262.83	   U101(x0, active(x1), x2)
743.81/262.83	   U101(x0, x1, active(x2))
743.81/262.83	   U102(mark(x0), x1, x2)
743.81/262.83	   U102(x0, mark(x1), x2)
743.81/262.83	   U102(x0, x1, mark(x2))
743.81/262.83	   U102(active(x0), x1, x2)
743.81/262.83	   U102(x0, active(x1), x2)
743.81/262.83	   U102(x0, x1, active(x2))
743.81/262.83	   isNatKind(mark(x0))
743.81/262.83	   isNatKind(active(x0))
743.81/262.83	   U103(mark(x0), x1, x2)
743.81/262.83	   U103(x0, mark(x1), x2)
743.81/262.83	   U103(x0, x1, mark(x2))
743.81/262.83	   U103(active(x0), x1, x2)
743.81/262.83	   U103(x0, active(x1), x2)
743.81/262.83	   U103(x0, x1, active(x2))
743.81/262.83	   isNat(mark(x0))
743.81/262.83	   isNat(active(x0))
743.81/262.83	   U104(mark(x0), x1, x2)
743.81/262.83	   U104(x0, mark(x1), x2)
743.81/262.83	   U104(x0, x1, mark(x2))
743.81/262.83	   U104(active(x0), x1, x2)
743.81/262.83	   U104(x0, active(x1), x2)
743.81/262.83	   U104(x0, x1, active(x2))
743.81/262.83	   plus(mark(x0), x1)
743.81/262.83	   plus(x0, mark(x1))
743.81/262.83	   plus(active(x0), x1)
743.81/262.83	   plus(x0, active(x1))
743.81/262.83	   x(mark(x0), x1)
743.81/262.83	   x(x0, mark(x1))
743.81/262.83	   x(active(x0), x1)
743.81/262.83	   x(x0, active(x1))
743.81/262.83	   U11(mark(x0), x1, x2)
743.81/262.83	   U11(x0, mark(x1), x2)
743.81/262.83	   U11(x0, x1, mark(x2))
743.81/262.83	   U11(active(x0), x1, x2)
743.81/262.83	   U11(x0, active(x1), x2)
743.81/262.83	   U11(x0, x1, active(x2))
743.81/262.83	   U12(mark(x0), x1, x2)
743.81/262.83	   U12(x0, mark(x1), x2)
743.81/262.83	   U12(x0, x1, mark(x2))
743.81/262.83	   U12(active(x0), x1, x2)
743.81/262.83	   U12(x0, active(x1), x2)
743.81/262.83	   U12(x0, x1, active(x2))
743.81/262.83	   U13(mark(x0), x1, x2)
743.81/262.83	   U13(x0, mark(x1), x2)
743.81/262.83	   U13(x0, x1, mark(x2))
743.81/262.83	   U13(active(x0), x1, x2)
743.81/262.83	   U13(x0, active(x1), x2)
743.81/262.83	   U13(x0, x1, active(x2))
743.81/262.83	   U14(mark(x0), x1, x2)
743.81/262.83	   U14(x0, mark(x1), x2)
743.81/262.83	   U14(x0, x1, mark(x2))
743.81/262.83	   U14(active(x0), x1, x2)
743.81/262.83	   U14(x0, active(x1), x2)
743.81/262.83	   U14(x0, x1, active(x2))
743.81/262.83	   U15(mark(x0), x1)
743.81/262.83	   U15(x0, mark(x1))
743.81/262.83	   U15(active(x0), x1)
743.81/262.83	   U15(x0, active(x1))
743.81/262.83	   U16(mark(x0))
743.81/262.83	   U16(active(x0))
743.81/262.83	   U21(mark(x0), x1)
743.81/262.83	   U21(x0, mark(x1))
743.81/262.83	   U21(active(x0), x1)
743.81/262.83	   U21(x0, active(x1))
743.81/262.83	   U22(mark(x0), x1)
743.81/262.83	   U22(x0, mark(x1))
743.81/262.83	   U22(active(x0), x1)
743.81/262.83	   U22(x0, active(x1))
743.81/262.83	   U23(mark(x0))
743.81/262.83	   U23(active(x0))
743.81/262.83	   U31(mark(x0), x1, x2)
743.81/262.83	   U31(x0, mark(x1), x2)
743.81/262.83	   U31(x0, x1, mark(x2))
743.81/262.83	   U31(active(x0), x1, x2)
743.81/262.83	   U31(x0, active(x1), x2)
743.81/262.83	   U31(x0, x1, active(x2))
743.81/262.83	   U32(mark(x0), x1, x2)
743.81/262.83	   U32(x0, mark(x1), x2)
743.81/262.83	   U32(x0, x1, mark(x2))
743.81/262.83	   U32(active(x0), x1, x2)
743.81/262.83	   U32(x0, active(x1), x2)
743.81/262.83	   U32(x0, x1, active(x2))
743.81/262.83	   U33(mark(x0), x1, x2)
743.81/262.83	   U33(x0, mark(x1), x2)
743.81/262.83	   U33(x0, x1, mark(x2))
743.81/262.83	   U33(active(x0), x1, x2)
743.81/262.83	   U33(x0, active(x1), x2)
743.81/262.83	   U33(x0, x1, active(x2))
743.81/262.83	   U34(mark(x0), x1, x2)
743.81/262.83	   U34(x0, mark(x1), x2)
743.81/262.83	   U34(x0, x1, mark(x2))
743.81/262.83	   U34(active(x0), x1, x2)
743.81/262.83	   U34(x0, active(x1), x2)
743.81/262.83	   U34(x0, x1, active(x2))
743.81/262.83	   U35(mark(x0), x1)
743.81/262.83	   U35(x0, mark(x1))
743.81/262.83	   U35(active(x0), x1)
743.81/262.83	   U35(x0, active(x1))
743.81/262.83	   U36(mark(x0))
743.81/262.83	   U36(active(x0))
743.81/262.83	   U41(mark(x0), x1)
743.81/262.83	   U41(x0, mark(x1))
743.81/262.83	   U41(active(x0), x1)
743.81/262.83	   U41(x0, active(x1))
743.81/262.83	   U42(mark(x0))
743.81/262.83	   U42(active(x0))
743.81/262.83	   U51(mark(x0))
743.81/262.83	   U51(active(x0))
743.81/262.83	   U61(mark(x0), x1)
743.81/262.83	   U61(x0, mark(x1))
743.81/262.83	   U61(active(x0), x1)
743.81/262.83	   U61(x0, active(x1))
743.81/262.83	   U62(mark(x0))
743.81/262.83	   U62(active(x0))
743.81/262.83	   U71(mark(x0), x1)
743.81/262.83	   U71(x0, mark(x1))
743.81/262.83	   U71(active(x0), x1)
743.81/262.83	   U71(x0, active(x1))
743.81/262.83	   U72(mark(x0), x1)
743.81/262.83	   U72(x0, mark(x1))
743.81/262.83	   U72(active(x0), x1)
743.81/262.83	   U72(x0, active(x1))
743.81/262.83	   U81(mark(x0), x1, x2)
743.81/262.83	   U81(x0, mark(x1), x2)
743.81/262.83	   U81(x0, x1, mark(x2))
743.81/262.83	   U81(active(x0), x1, x2)
743.81/262.83	   U81(x0, active(x1), x2)
743.81/262.83	   U81(x0, x1, active(x2))
743.81/262.83	   U82(mark(x0), x1, x2)
743.81/262.83	   U82(x0, mark(x1), x2)
743.81/262.83	   U82(x0, x1, mark(x2))
743.81/262.83	   U82(active(x0), x1, x2)
743.81/262.83	   U82(x0, active(x1), x2)
743.81/262.83	   U82(x0, x1, active(x2))
743.81/262.83	   U83(mark(x0), x1, x2)
743.81/262.83	   U83(x0, mark(x1), x2)
743.81/262.83	   U83(x0, x1, mark(x2))
743.81/262.83	   U83(active(x0), x1, x2)
743.81/262.83	   U83(x0, active(x1), x2)
743.81/262.83	   U83(x0, x1, active(x2))
743.81/262.83	   U84(mark(x0), x1, x2)
743.81/262.83	   U84(x0, mark(x1), x2)
743.81/262.83	   U84(x0, x1, mark(x2))
743.81/262.83	   U84(active(x0), x1, x2)
743.81/262.83	   U84(x0, active(x1), x2)
743.81/262.83	   U84(x0, x1, active(x2))
743.81/262.83	   s(mark(x0))
743.81/262.83	   s(active(x0))
743.81/262.83	   U91(mark(x0), x1)
743.81/262.83	   U91(x0, mark(x1))
743.81/262.83	   U91(active(x0), x1)
743.81/262.83	   U91(x0, active(x1))
743.81/262.83	   U92(mark(x0))
743.81/262.83	   U92(active(x0))
743.81/262.83	
743.81/262.83	We have to consider all minimal (P,Q,R)-chains.
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(90) UsableRulesProof (EQUIVALENT)
743.81/262.83	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.
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(91)
743.81/262.83	Obligation:
743.81/262.83	Q DP problem:
743.81/262.83	The TRS P consists of the following rules:
743.81/262.83	
743.81/262.83	   U42^1(active(X)) -> U42^1(X)
743.81/262.83	   U42^1(mark(X)) -> U42^1(X)
743.81/262.83	
743.81/262.83	R is empty.
743.81/262.83	The set Q consists of the following terms:
743.81/262.83	
743.81/262.83	   active(U101(tt, x0, x1))
743.81/262.83	   active(U102(tt, x0, x1))
743.81/262.83	   active(U103(tt, x0, x1))
743.81/262.83	   active(U104(tt, x0, x1))
743.81/262.83	   active(U11(tt, x0, x1))
743.81/262.83	   active(U12(tt, x0, x1))
743.81/262.83	   active(U13(tt, x0, x1))
743.81/262.83	   active(U14(tt, x0, x1))
743.81/262.83	   active(U15(tt, x0))
743.81/262.83	   active(U16(tt))
743.81/262.83	   active(U21(tt, x0))
743.81/262.83	   active(U22(tt, x0))
743.81/262.83	   active(U23(tt))
743.81/262.83	   active(U31(tt, x0, x1))
743.81/262.83	   active(U32(tt, x0, x1))
743.81/262.83	   active(U33(tt, x0, x1))
743.81/262.83	   active(U34(tt, x0, x1))
743.81/262.83	   active(U35(tt, x0))
743.81/262.83	   active(U36(tt))
743.81/262.83	   active(U41(tt, x0))
743.81/262.83	   active(U42(tt))
743.81/262.83	   active(U51(tt))
743.81/262.83	   active(U61(tt, x0))
743.81/262.83	   active(U62(tt))
743.81/262.83	   active(U71(tt, x0))
743.81/262.83	   active(U72(tt, x0))
743.81/262.83	   active(U81(tt, x0, x1))
743.81/262.83	   active(U82(tt, x0, x1))
743.81/262.83	   active(U83(tt, x0, x1))
743.81/262.83	   active(U84(tt, x0, x1))
743.81/262.83	   active(U91(tt, x0))
743.81/262.83	   active(U92(tt))
743.81/262.83	   active(isNat(0))
743.81/262.83	   active(isNat(plus(x0, x1)))
743.81/262.83	   active(isNat(s(x0)))
743.81/262.83	   active(isNat(x(x0, x1)))
743.81/262.83	   active(isNatKind(0))
743.81/262.83	   active(isNatKind(plus(x0, x1)))
743.81/262.83	   active(isNatKind(s(x0)))
743.81/262.83	   active(isNatKind(x(x0, x1)))
743.81/262.83	   active(plus(x0, 0))
743.81/262.83	   active(plus(x0, s(x1)))
743.81/262.83	   active(x(x0, 0))
743.81/262.83	   active(x(x0, s(x1)))
743.81/262.83	   mark(U101(x0, x1, x2))
743.81/262.83	   mark(tt)
743.81/262.83	   mark(U102(x0, x1, x2))
743.81/262.83	   mark(isNatKind(x0))
743.81/262.83	   mark(U103(x0, x1, x2))
743.81/262.83	   mark(isNat(x0))
743.81/262.83	   mark(U104(x0, x1, x2))
743.81/262.83	   mark(plus(x0, x1))
743.81/262.83	   mark(x(x0, x1))
743.81/262.83	   mark(U11(x0, x1, x2))
743.81/262.83	   mark(U12(x0, x1, x2))
743.81/262.83	   mark(U13(x0, x1, x2))
743.81/262.83	   mark(U14(x0, x1, x2))
743.81/262.83	   mark(U15(x0, x1))
743.81/262.83	   mark(U16(x0))
743.81/262.83	   mark(U21(x0, x1))
743.81/262.83	   mark(U22(x0, x1))
743.81/262.83	   mark(U23(x0))
743.81/262.83	   mark(U31(x0, x1, x2))
743.81/262.83	   mark(U32(x0, x1, x2))
743.81/262.83	   mark(U33(x0, x1, x2))
743.81/262.83	   mark(U34(x0, x1, x2))
743.81/262.83	   mark(U35(x0, x1))
743.81/262.83	   mark(U36(x0))
743.81/262.83	   mark(U41(x0, x1))
743.81/262.83	   mark(U42(x0))
743.81/262.83	   mark(U51(x0))
743.81/262.83	   mark(U61(x0, x1))
743.81/262.83	   mark(U62(x0))
743.81/262.83	   mark(U71(x0, x1))
743.81/262.83	   mark(U72(x0, x1))
743.81/262.83	   mark(U81(x0, x1, x2))
743.81/262.83	   mark(U82(x0, x1, x2))
743.81/262.83	   mark(U83(x0, x1, x2))
743.81/262.83	   mark(U84(x0, x1, x2))
743.81/262.83	   mark(s(x0))
743.81/262.83	   mark(U91(x0, x1))
743.81/262.83	   mark(U92(x0))
743.81/262.83	   mark(0)
743.81/262.83	   U101(mark(x0), x1, x2)
743.81/262.83	   U101(x0, mark(x1), x2)
743.81/262.83	   U101(x0, x1, mark(x2))
743.81/262.83	   U101(active(x0), x1, x2)
743.81/262.83	   U101(x0, active(x1), x2)
743.81/262.83	   U101(x0, x1, active(x2))
743.81/262.83	   U102(mark(x0), x1, x2)
743.81/262.83	   U102(x0, mark(x1), x2)
743.81/262.83	   U102(x0, x1, mark(x2))
743.81/262.83	   U102(active(x0), x1, x2)
743.81/262.83	   U102(x0, active(x1), x2)
743.81/262.83	   U102(x0, x1, active(x2))
743.81/262.83	   isNatKind(mark(x0))
743.81/262.83	   isNatKind(active(x0))
743.81/262.83	   U103(mark(x0), x1, x2)
743.81/262.83	   U103(x0, mark(x1), x2)
743.81/262.83	   U103(x0, x1, mark(x2))
743.81/262.83	   U103(active(x0), x1, x2)
743.81/262.83	   U103(x0, active(x1), x2)
743.81/262.83	   U103(x0, x1, active(x2))
743.81/262.83	   isNat(mark(x0))
743.81/262.83	   isNat(active(x0))
743.81/262.83	   U104(mark(x0), x1, x2)
743.81/262.83	   U104(x0, mark(x1), x2)
743.81/262.83	   U104(x0, x1, mark(x2))
743.81/262.83	   U104(active(x0), x1, x2)
743.81/262.83	   U104(x0, active(x1), x2)
743.81/262.83	   U104(x0, x1, active(x2))
743.81/262.83	   plus(mark(x0), x1)
743.81/262.83	   plus(x0, mark(x1))
743.81/262.83	   plus(active(x0), x1)
743.81/262.83	   plus(x0, active(x1))
743.81/262.83	   x(mark(x0), x1)
743.81/262.83	   x(x0, mark(x1))
743.81/262.83	   x(active(x0), x1)
743.81/262.83	   x(x0, active(x1))
743.81/262.83	   U11(mark(x0), x1, x2)
743.81/262.83	   U11(x0, mark(x1), x2)
743.81/262.83	   U11(x0, x1, mark(x2))
743.81/262.83	   U11(active(x0), x1, x2)
743.81/262.83	   U11(x0, active(x1), x2)
743.81/262.83	   U11(x0, x1, active(x2))
743.81/262.83	   U12(mark(x0), x1, x2)
743.81/262.83	   U12(x0, mark(x1), x2)
743.81/262.83	   U12(x0, x1, mark(x2))
743.81/262.83	   U12(active(x0), x1, x2)
743.81/262.83	   U12(x0, active(x1), x2)
743.81/262.83	   U12(x0, x1, active(x2))
743.81/262.83	   U13(mark(x0), x1, x2)
743.81/262.83	   U13(x0, mark(x1), x2)
743.81/262.83	   U13(x0, x1, mark(x2))
743.81/262.83	   U13(active(x0), x1, x2)
743.81/262.83	   U13(x0, active(x1), x2)
743.81/262.83	   U13(x0, x1, active(x2))
743.81/262.83	   U14(mark(x0), x1, x2)
743.81/262.83	   U14(x0, mark(x1), x2)
743.81/262.83	   U14(x0, x1, mark(x2))
743.81/262.83	   U14(active(x0), x1, x2)
743.81/262.83	   U14(x0, active(x1), x2)
743.81/262.83	   U14(x0, x1, active(x2))
743.81/262.83	   U15(mark(x0), x1)
743.81/262.83	   U15(x0, mark(x1))
743.81/262.83	   U15(active(x0), x1)
743.81/262.83	   U15(x0, active(x1))
743.81/262.83	   U16(mark(x0))
743.81/262.83	   U16(active(x0))
743.81/262.83	   U21(mark(x0), x1)
743.81/262.83	   U21(x0, mark(x1))
743.81/262.83	   U21(active(x0), x1)
743.81/262.83	   U21(x0, active(x1))
743.81/262.83	   U22(mark(x0), x1)
743.81/262.83	   U22(x0, mark(x1))
743.81/262.83	   U22(active(x0), x1)
743.81/262.83	   U22(x0, active(x1))
743.81/262.83	   U23(mark(x0))
743.81/262.83	   U23(active(x0))
743.81/262.83	   U31(mark(x0), x1, x2)
743.81/262.83	   U31(x0, mark(x1), x2)
743.81/262.83	   U31(x0, x1, mark(x2))
743.81/262.83	   U31(active(x0), x1, x2)
743.81/262.83	   U31(x0, active(x1), x2)
743.81/262.83	   U31(x0, x1, active(x2))
743.81/262.83	   U32(mark(x0), x1, x2)
743.81/262.83	   U32(x0, mark(x1), x2)
743.81/262.83	   U32(x0, x1, mark(x2))
743.81/262.83	   U32(active(x0), x1, x2)
743.81/262.83	   U32(x0, active(x1), x2)
743.81/262.83	   U32(x0, x1, active(x2))
743.81/262.83	   U33(mark(x0), x1, x2)
743.81/262.83	   U33(x0, mark(x1), x2)
743.81/262.83	   U33(x0, x1, mark(x2))
743.81/262.83	   U33(active(x0), x1, x2)
743.81/262.83	   U33(x0, active(x1), x2)
743.81/262.83	   U33(x0, x1, active(x2))
743.81/262.83	   U34(mark(x0), x1, x2)
743.81/262.83	   U34(x0, mark(x1), x2)
743.81/262.83	   U34(x0, x1, mark(x2))
743.81/262.83	   U34(active(x0), x1, x2)
743.81/262.83	   U34(x0, active(x1), x2)
743.81/262.83	   U34(x0, x1, active(x2))
743.81/262.83	   U35(mark(x0), x1)
743.81/262.83	   U35(x0, mark(x1))
743.81/262.83	   U35(active(x0), x1)
743.81/262.83	   U35(x0, active(x1))
743.81/262.83	   U36(mark(x0))
743.81/262.83	   U36(active(x0))
743.81/262.83	   U41(mark(x0), x1)
743.81/262.83	   U41(x0, mark(x1))
743.81/262.83	   U41(active(x0), x1)
743.81/262.83	   U41(x0, active(x1))
743.81/262.83	   U42(mark(x0))
743.81/262.83	   U42(active(x0))
743.81/262.83	   U51(mark(x0))
743.81/262.83	   U51(active(x0))
743.81/262.83	   U61(mark(x0), x1)
743.81/262.83	   U61(x0, mark(x1))
743.81/262.83	   U61(active(x0), x1)
743.81/262.83	   U61(x0, active(x1))
743.81/262.83	   U62(mark(x0))
743.81/262.83	   U62(active(x0))
743.81/262.83	   U71(mark(x0), x1)
743.81/262.83	   U71(x0, mark(x1))
743.81/262.83	   U71(active(x0), x1)
743.81/262.83	   U71(x0, active(x1))
743.81/262.83	   U72(mark(x0), x1)
743.81/262.83	   U72(x0, mark(x1))
743.81/262.83	   U72(active(x0), x1)
743.81/262.83	   U72(x0, active(x1))
743.81/262.83	   U81(mark(x0), x1, x2)
743.81/262.83	   U81(x0, mark(x1), x2)
743.81/262.83	   U81(x0, x1, mark(x2))
743.81/262.83	   U81(active(x0), x1, x2)
743.81/262.83	   U81(x0, active(x1), x2)
743.81/262.83	   U81(x0, x1, active(x2))
743.81/262.83	   U82(mark(x0), x1, x2)
743.81/262.83	   U82(x0, mark(x1), x2)
743.81/262.83	   U82(x0, x1, mark(x2))
743.81/262.83	   U82(active(x0), x1, x2)
743.81/262.83	   U82(x0, active(x1), x2)
743.81/262.83	   U82(x0, x1, active(x2))
743.81/262.83	   U83(mark(x0), x1, x2)
743.81/262.83	   U83(x0, mark(x1), x2)
743.81/262.83	   U83(x0, x1, mark(x2))
743.81/262.83	   U83(active(x0), x1, x2)
743.81/262.83	   U83(x0, active(x1), x2)
743.81/262.83	   U83(x0, x1, active(x2))
743.81/262.83	   U84(mark(x0), x1, x2)
743.81/262.83	   U84(x0, mark(x1), x2)
743.81/262.83	   U84(x0, x1, mark(x2))
743.81/262.83	   U84(active(x0), x1, x2)
743.81/262.83	   U84(x0, active(x1), x2)
743.81/262.83	   U84(x0, x1, active(x2))
743.81/262.83	   s(mark(x0))
743.81/262.83	   s(active(x0))
743.81/262.83	   U91(mark(x0), x1)
743.81/262.83	   U91(x0, mark(x1))
743.81/262.83	   U91(active(x0), x1)
743.81/262.83	   U91(x0, active(x1))
743.81/262.83	   U92(mark(x0))
743.81/262.83	   U92(active(x0))
743.81/262.83	
743.81/262.83	We have to consider all minimal (P,Q,R)-chains.
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(92) QReductionProof (EQUIVALENT)
743.81/262.83	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.81/262.83	
743.81/262.83	   U101(mark(x0), x1, x2)
743.81/262.83	   U101(x0, mark(x1), x2)
743.81/262.83	   U101(x0, x1, mark(x2))
743.81/262.83	   U101(active(x0), x1, x2)
743.81/262.83	   U101(x0, active(x1), x2)
743.81/262.83	   U101(x0, x1, active(x2))
743.81/262.83	   U102(mark(x0), x1, x2)
743.81/262.83	   U102(x0, mark(x1), x2)
743.81/262.83	   U102(x0, x1, mark(x2))
743.81/262.83	   U102(active(x0), x1, x2)
743.81/262.83	   U102(x0, active(x1), x2)
743.81/262.83	   U102(x0, x1, active(x2))
743.81/262.83	   isNatKind(mark(x0))
743.81/262.83	   isNatKind(active(x0))
743.81/262.83	   U103(mark(x0), x1, x2)
743.81/262.83	   U103(x0, mark(x1), x2)
743.81/262.83	   U103(x0, x1, mark(x2))
743.81/262.83	   U103(active(x0), x1, x2)
743.81/262.83	   U103(x0, active(x1), x2)
743.81/262.83	   U103(x0, x1, active(x2))
743.81/262.83	   isNat(mark(x0))
743.81/262.83	   isNat(active(x0))
743.81/262.83	   U104(mark(x0), x1, x2)
743.81/262.83	   U104(x0, mark(x1), x2)
743.81/262.83	   U104(x0, x1, mark(x2))
743.81/262.83	   U104(active(x0), x1, x2)
743.81/262.83	   U104(x0, active(x1), x2)
743.81/262.83	   U104(x0, x1, active(x2))
743.81/262.83	   plus(mark(x0), x1)
743.81/262.83	   plus(x0, mark(x1))
743.81/262.83	   plus(active(x0), x1)
743.81/262.83	   plus(x0, active(x1))
743.81/262.83	   x(mark(x0), x1)
743.81/262.83	   x(x0, mark(x1))
743.81/262.83	   x(active(x0), x1)
743.81/262.83	   x(x0, active(x1))
743.81/262.83	   U11(mark(x0), x1, x2)
743.81/262.83	   U11(x0, mark(x1), x2)
743.81/262.83	   U11(x0, x1, mark(x2))
743.81/262.83	   U11(active(x0), x1, x2)
743.81/262.83	   U11(x0, active(x1), x2)
743.81/262.83	   U11(x0, x1, active(x2))
743.81/262.83	   U12(mark(x0), x1, x2)
743.81/262.83	   U12(x0, mark(x1), x2)
743.81/262.83	   U12(x0, x1, mark(x2))
743.81/262.83	   U12(active(x0), x1, x2)
743.81/262.83	   U12(x0, active(x1), x2)
743.81/262.83	   U12(x0, x1, active(x2))
743.81/262.83	   U13(mark(x0), x1, x2)
743.81/262.83	   U13(x0, mark(x1), x2)
743.81/262.83	   U13(x0, x1, mark(x2))
743.81/262.83	   U13(active(x0), x1, x2)
743.81/262.83	   U13(x0, active(x1), x2)
743.81/262.83	   U13(x0, x1, active(x2))
743.81/262.83	   U14(mark(x0), x1, x2)
743.81/262.83	   U14(x0, mark(x1), x2)
743.81/262.83	   U14(x0, x1, mark(x2))
743.81/262.83	   U14(active(x0), x1, x2)
743.81/262.83	   U14(x0, active(x1), x2)
743.81/262.83	   U14(x0, x1, active(x2))
743.81/262.83	   U15(mark(x0), x1)
743.81/262.83	   U15(x0, mark(x1))
743.81/262.83	   U15(active(x0), x1)
743.81/262.83	   U15(x0, active(x1))
743.81/262.83	   U16(mark(x0))
743.81/262.83	   U16(active(x0))
743.81/262.83	   U21(mark(x0), x1)
743.81/262.83	   U21(x0, mark(x1))
743.81/262.83	   U21(active(x0), x1)
743.81/262.83	   U21(x0, active(x1))
743.81/262.83	   U22(mark(x0), x1)
743.81/262.83	   U22(x0, mark(x1))
743.81/262.83	   U22(active(x0), x1)
743.81/262.83	   U22(x0, active(x1))
743.81/262.83	   U23(mark(x0))
743.81/262.83	   U23(active(x0))
743.81/262.83	   U31(mark(x0), x1, x2)
743.81/262.83	   U31(x0, mark(x1), x2)
743.81/262.83	   U31(x0, x1, mark(x2))
743.81/262.83	   U31(active(x0), x1, x2)
743.81/262.83	   U31(x0, active(x1), x2)
743.81/262.83	   U31(x0, x1, active(x2))
743.81/262.83	   U32(mark(x0), x1, x2)
743.81/262.83	   U32(x0, mark(x1), x2)
743.81/262.83	   U32(x0, x1, mark(x2))
743.81/262.83	   U32(active(x0), x1, x2)
743.81/262.83	   U32(x0, active(x1), x2)
743.81/262.83	   U32(x0, x1, active(x2))
743.81/262.83	   U33(mark(x0), x1, x2)
743.81/262.83	   U33(x0, mark(x1), x2)
743.81/262.83	   U33(x0, x1, mark(x2))
743.81/262.83	   U33(active(x0), x1, x2)
743.81/262.83	   U33(x0, active(x1), x2)
743.81/262.83	   U33(x0, x1, active(x2))
743.81/262.83	   U34(mark(x0), x1, x2)
743.81/262.83	   U34(x0, mark(x1), x2)
743.81/262.83	   U34(x0, x1, mark(x2))
743.81/262.83	   U34(active(x0), x1, x2)
743.81/262.83	   U34(x0, active(x1), x2)
743.81/262.83	   U34(x0, x1, active(x2))
743.81/262.83	   U35(mark(x0), x1)
743.81/262.83	   U35(x0, mark(x1))
743.81/262.83	   U35(active(x0), x1)
743.81/262.83	   U35(x0, active(x1))
743.81/262.83	   U36(mark(x0))
743.81/262.83	   U36(active(x0))
743.81/262.83	   U41(mark(x0), x1)
743.81/262.83	   U41(x0, mark(x1))
743.81/262.83	   U41(active(x0), x1)
743.81/262.83	   U41(x0, active(x1))
743.81/262.83	   U42(mark(x0))
743.81/262.83	   U42(active(x0))
743.81/262.83	   U51(mark(x0))
743.81/262.83	   U51(active(x0))
743.81/262.83	   U61(mark(x0), x1)
743.81/262.83	   U61(x0, mark(x1))
743.81/262.83	   U61(active(x0), x1)
743.81/262.83	   U61(x0, active(x1))
743.81/262.83	   U62(mark(x0))
743.81/262.83	   U62(active(x0))
743.81/262.83	   U71(mark(x0), x1)
743.81/262.83	   U71(x0, mark(x1))
743.81/262.83	   U71(active(x0), x1)
743.81/262.83	   U71(x0, active(x1))
743.81/262.83	   U72(mark(x0), x1)
743.81/262.83	   U72(x0, mark(x1))
743.81/262.83	   U72(active(x0), x1)
743.81/262.83	   U72(x0, active(x1))
743.81/262.83	   U81(mark(x0), x1, x2)
743.81/262.83	   U81(x0, mark(x1), x2)
743.81/262.83	   U81(x0, x1, mark(x2))
743.81/262.83	   U81(active(x0), x1, x2)
743.81/262.83	   U81(x0, active(x1), x2)
743.81/262.83	   U81(x0, x1, active(x2))
743.81/262.83	   U82(mark(x0), x1, x2)
743.81/262.83	   U82(x0, mark(x1), x2)
743.81/262.83	   U82(x0, x1, mark(x2))
743.81/262.83	   U82(active(x0), x1, x2)
743.81/262.83	   U82(x0, active(x1), x2)
743.81/262.83	   U82(x0, x1, active(x2))
743.81/262.83	   U83(mark(x0), x1, x2)
743.81/262.83	   U83(x0, mark(x1), x2)
743.81/262.83	   U83(x0, x1, mark(x2))
743.81/262.83	   U83(active(x0), x1, x2)
743.81/262.83	   U83(x0, active(x1), x2)
743.81/262.83	   U83(x0, x1, active(x2))
743.81/262.83	   U84(mark(x0), x1, x2)
743.81/262.83	   U84(x0, mark(x1), x2)
743.81/262.83	   U84(x0, x1, mark(x2))
743.81/262.83	   U84(active(x0), x1, x2)
743.81/262.83	   U84(x0, active(x1), x2)
743.81/262.83	   U84(x0, x1, active(x2))
743.81/262.83	   s(mark(x0))
743.81/262.83	   s(active(x0))
743.81/262.83	   U91(mark(x0), x1)
743.81/262.83	   U91(x0, mark(x1))
743.81/262.83	   U91(active(x0), x1)
743.81/262.83	   U91(x0, active(x1))
743.81/262.83	   U92(mark(x0))
743.81/262.83	   U92(active(x0))
743.81/262.83	
743.81/262.83	
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(93)
743.81/262.83	Obligation:
743.81/262.83	Q DP problem:
743.81/262.83	The TRS P consists of the following rules:
743.81/262.83	
743.81/262.83	   U42^1(active(X)) -> U42^1(X)
743.81/262.83	   U42^1(mark(X)) -> U42^1(X)
743.81/262.83	
743.81/262.83	R is empty.
743.81/262.83	The set Q consists of the following terms:
743.81/262.83	
743.81/262.83	   active(U101(tt, x0, x1))
743.81/262.83	   active(U102(tt, x0, x1))
743.81/262.83	   active(U103(tt, x0, x1))
743.81/262.83	   active(U104(tt, x0, x1))
743.81/262.83	   active(U11(tt, x0, x1))
743.81/262.83	   active(U12(tt, x0, x1))
743.81/262.83	   active(U13(tt, x0, x1))
743.81/262.83	   active(U14(tt, x0, x1))
743.81/262.83	   active(U15(tt, x0))
743.81/262.83	   active(U16(tt))
743.81/262.83	   active(U21(tt, x0))
743.81/262.83	   active(U22(tt, x0))
743.81/262.83	   active(U23(tt))
743.81/262.83	   active(U31(tt, x0, x1))
743.81/262.83	   active(U32(tt, x0, x1))
743.81/262.83	   active(U33(tt, x0, x1))
743.81/262.83	   active(U34(tt, x0, x1))
743.81/262.83	   active(U35(tt, x0))
743.81/262.83	   active(U36(tt))
743.81/262.83	   active(U41(tt, x0))
743.81/262.83	   active(U42(tt))
743.81/262.83	   active(U51(tt))
743.81/262.83	   active(U61(tt, x0))
743.81/262.83	   active(U62(tt))
743.81/262.83	   active(U71(tt, x0))
743.81/262.83	   active(U72(tt, x0))
743.81/262.83	   active(U81(tt, x0, x1))
743.81/262.83	   active(U82(tt, x0, x1))
743.81/262.83	   active(U83(tt, x0, x1))
743.81/262.83	   active(U84(tt, x0, x1))
743.81/262.83	   active(U91(tt, x0))
743.81/262.83	   active(U92(tt))
743.81/262.83	   active(isNat(0))
743.81/262.83	   active(isNat(plus(x0, x1)))
743.81/262.83	   active(isNat(s(x0)))
743.81/262.83	   active(isNat(x(x0, x1)))
743.81/262.83	   active(isNatKind(0))
743.81/262.83	   active(isNatKind(plus(x0, x1)))
743.81/262.83	   active(isNatKind(s(x0)))
743.81/262.83	   active(isNatKind(x(x0, x1)))
743.81/262.83	   active(plus(x0, 0))
743.81/262.83	   active(plus(x0, s(x1)))
743.81/262.83	   active(x(x0, 0))
743.81/262.83	   active(x(x0, s(x1)))
743.81/262.83	   mark(U101(x0, x1, x2))
743.81/262.83	   mark(tt)
743.81/262.83	   mark(U102(x0, x1, x2))
743.81/262.83	   mark(isNatKind(x0))
743.81/262.83	   mark(U103(x0, x1, x2))
743.81/262.83	   mark(isNat(x0))
743.81/262.83	   mark(U104(x0, x1, x2))
743.81/262.83	   mark(plus(x0, x1))
743.81/262.83	   mark(x(x0, x1))
743.81/262.83	   mark(U11(x0, x1, x2))
743.81/262.83	   mark(U12(x0, x1, x2))
743.81/262.83	   mark(U13(x0, x1, x2))
743.81/262.83	   mark(U14(x0, x1, x2))
743.81/262.83	   mark(U15(x0, x1))
743.81/262.83	   mark(U16(x0))
743.81/262.83	   mark(U21(x0, x1))
743.81/262.83	   mark(U22(x0, x1))
743.81/262.83	   mark(U23(x0))
743.81/262.83	   mark(U31(x0, x1, x2))
743.81/262.83	   mark(U32(x0, x1, x2))
743.81/262.83	   mark(U33(x0, x1, x2))
743.81/262.83	   mark(U34(x0, x1, x2))
743.81/262.83	   mark(U35(x0, x1))
743.81/262.83	   mark(U36(x0))
743.81/262.83	   mark(U41(x0, x1))
743.81/262.83	   mark(U42(x0))
743.81/262.83	   mark(U51(x0))
743.81/262.83	   mark(U61(x0, x1))
743.81/262.83	   mark(U62(x0))
743.81/262.83	   mark(U71(x0, x1))
743.81/262.83	   mark(U72(x0, x1))
743.81/262.83	   mark(U81(x0, x1, x2))
743.81/262.83	   mark(U82(x0, x1, x2))
743.81/262.83	   mark(U83(x0, x1, x2))
743.81/262.83	   mark(U84(x0, x1, x2))
743.81/262.83	   mark(s(x0))
743.81/262.83	   mark(U91(x0, x1))
743.81/262.83	   mark(U92(x0))
743.81/262.83	   mark(0)
743.81/262.83	
743.81/262.83	We have to consider all minimal (P,Q,R)-chains.
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(94) QDPSizeChangeProof (EQUIVALENT)
743.81/262.83	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. 
743.81/262.83	
743.81/262.83	From the DPs we obtained the following set of size-change graphs:
743.81/262.83	*U42^1(active(X)) -> U42^1(X)
743.81/262.83	The graph contains the following edges 1 > 1
743.81/262.83	
743.81/262.83	
743.81/262.83	*U42^1(mark(X)) -> U42^1(X)
743.81/262.83	The graph contains the following edges 1 > 1
743.81/262.83	
743.81/262.83	
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(95)
743.81/262.83	YES
743.81/262.83	
743.81/262.83	----------------------------------------
743.81/262.83	
743.81/262.83	(96)
743.81/262.83	Obligation:
743.81/262.83	Q DP problem:
743.81/262.83	The TRS P consists of the following rules:
743.81/262.83	
743.81/262.83	   U41^1(X1, mark(X2)) -> U41^1(X1, X2)
743.81/262.83	   U41^1(mark(X1), X2) -> U41^1(X1, X2)
743.81/262.83	   U41^1(active(X1), X2) -> U41^1(X1, X2)
743.81/262.83	   U41^1(X1, active(X2)) -> U41^1(X1, X2)
743.81/262.83	
743.81/262.83	The TRS R consists of the following rules:
743.81/262.83	
743.81/262.83	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.81/262.83	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.81/262.83	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.81/262.83	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.81/262.83	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.81/262.83	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.81/262.83	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.81/262.83	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.81/262.83	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.81/262.83	   active(U16(tt)) -> mark(tt)
743.81/262.83	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.81/262.83	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.81/262.83	   active(U23(tt)) -> mark(tt)
743.81/262.83	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.81/262.83	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.81/262.83	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.81/262.83	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.81/262.83	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.81/262.83	   active(U36(tt)) -> mark(tt)
743.81/262.83	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.81/262.83	   active(U42(tt)) -> mark(tt)
743.81/262.83	   active(U51(tt)) -> mark(tt)
743.81/262.83	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.81/262.83	   active(U62(tt)) -> mark(tt)
743.81/262.83	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.81/262.83	   active(U72(tt, N)) -> mark(N)
743.81/262.83	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.81/262.83	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.81/262.83	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.81/262.83	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.81/262.83	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.81/262.83	   active(U92(tt)) -> mark(0)
743.81/262.83	   active(isNat(0)) -> mark(tt)
743.81/262.83	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.81/262.83	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.81/262.83	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.81/262.83	   active(isNatKind(0)) -> mark(tt)
743.81/262.83	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.81/262.83	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.81/262.83	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.81/262.83	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.81/262.83	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.81/262.83	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.81/262.83	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.81/262.83	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.81/262.83	   mark(tt) -> active(tt)
743.81/262.83	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.81/262.83	   mark(isNatKind(X)) -> active(isNatKind(X))
743.81/262.83	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.81/262.83	   mark(isNat(X)) -> active(isNat(X))
743.81/262.83	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.81/262.83	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.81/262.83	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.81/262.83	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.81/262.83	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.81/262.83	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.81/262.83	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.81/262.83	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.81/262.83	   mark(U16(X)) -> active(U16(mark(X)))
743.81/262.83	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.81/262.83	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.81/262.83	   mark(U23(X)) -> active(U23(mark(X)))
743.81/262.83	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.81/262.83	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.81/262.83	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.81/262.83	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.81/262.83	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.81/262.83	   mark(U36(X)) -> active(U36(mark(X)))
743.81/262.83	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.81/262.83	   mark(U42(X)) -> active(U42(mark(X)))
743.81/262.83	   mark(U51(X)) -> active(U51(mark(X)))
743.81/262.83	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.81/262.83	   mark(U62(X)) -> active(U62(mark(X)))
743.81/262.83	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.81/262.83	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.81/262.83	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.81/262.83	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.81/262.83	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.81/262.83	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.81/262.83	   mark(s(X)) -> active(s(mark(X)))
743.81/262.83	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.81/262.83	   mark(U92(X)) -> active(U92(mark(X)))
743.81/262.83	   mark(0) -> active(0)
743.81/262.83	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.83	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.81/262.83	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.81/262.83	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.83	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.81/262.83	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.81/262.83	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.83	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.81/262.83	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.81/262.83	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.83	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.81/262.83	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.81/262.83	   isNatKind(mark(X)) -> isNatKind(X)
743.81/262.83	   isNatKind(active(X)) -> isNatKind(X)
743.81/262.83	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.83	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.81/262.83	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.81/262.83	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.83	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.81/262.83	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.81/262.83	   isNat(mark(X)) -> isNat(X)
743.81/262.83	   isNat(active(X)) -> isNat(X)
743.81/262.83	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.83	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.81/262.83	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.81/262.83	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.83	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.81/262.83	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.81/262.83	   plus(mark(X1), X2) -> plus(X1, X2)
743.81/262.83	   plus(X1, mark(X2)) -> plus(X1, X2)
743.81/262.83	   plus(active(X1), X2) -> plus(X1, X2)
743.81/262.83	   plus(X1, active(X2)) -> plus(X1, X2)
743.81/262.83	   x(mark(X1), X2) -> x(X1, X2)
743.81/262.83	   x(X1, mark(X2)) -> x(X1, X2)
743.81/262.83	   x(active(X1), X2) -> x(X1, X2)
743.81/262.83	   x(X1, active(X2)) -> x(X1, X2)
743.81/262.83	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.83	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.81/262.83	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.81/262.83	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.83	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.81/262.83	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.81/262.83	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.83	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.81/262.83	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.81/262.83	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.83	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.81/262.83	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.81/262.83	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.83	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.81/262.83	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.81/262.83	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.83	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.81/262.83	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.81/262.83	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.83	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.81/262.83	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.81/262.83	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.83	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.81/262.83	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.81/262.83	   U15(mark(X1), X2) -> U15(X1, X2)
743.81/262.83	   U15(X1, mark(X2)) -> U15(X1, X2)
743.81/262.83	   U15(active(X1), X2) -> U15(X1, X2)
743.81/262.83	   U15(X1, active(X2)) -> U15(X1, X2)
743.81/262.83	   U16(mark(X)) -> U16(X)
743.81/262.83	   U16(active(X)) -> U16(X)
743.81/262.83	   U21(mark(X1), X2) -> U21(X1, X2)
743.81/262.83	   U21(X1, mark(X2)) -> U21(X1, X2)
743.81/262.83	   U21(active(X1), X2) -> U21(X1, X2)
743.81/262.83	   U21(X1, active(X2)) -> U21(X1, X2)
743.81/262.83	   U22(mark(X1), X2) -> U22(X1, X2)
743.81/262.83	   U22(X1, mark(X2)) -> U22(X1, X2)
743.81/262.83	   U22(active(X1), X2) -> U22(X1, X2)
743.81/262.83	   U22(X1, active(X2)) -> U22(X1, X2)
743.81/262.83	   U23(mark(X)) -> U23(X)
743.81/262.83	   U23(active(X)) -> U23(X)
743.81/262.83	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.83	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.81/262.83	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.81/262.83	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.83	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.81/262.83	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.81/262.83	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.83	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.81/262.83	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.81/262.83	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.83	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.81/262.83	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.81/262.83	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.83	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.81/262.83	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.81/262.83	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.83	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.81/262.83	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.81/262.83	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.83	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.81/262.83	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.81/262.83	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.83	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.81/262.83	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.81/262.83	   U35(mark(X1), X2) -> U35(X1, X2)
743.81/262.83	   U35(X1, mark(X2)) -> U35(X1, X2)
743.81/262.83	   U35(active(X1), X2) -> U35(X1, X2)
743.81/262.83	   U35(X1, active(X2)) -> U35(X1, X2)
743.81/262.83	   U36(mark(X)) -> U36(X)
743.81/262.83	   U36(active(X)) -> U36(X)
743.81/262.83	   U41(mark(X1), X2) -> U41(X1, X2)
743.81/262.83	   U41(X1, mark(X2)) -> U41(X1, X2)
743.81/262.83	   U41(active(X1), X2) -> U41(X1, X2)
743.81/262.83	   U41(X1, active(X2)) -> U41(X1, X2)
743.81/262.83	   U42(mark(X)) -> U42(X)
743.81/262.83	   U42(active(X)) -> U42(X)
743.81/262.83	   U51(mark(X)) -> U51(X)
743.81/262.83	   U51(active(X)) -> U51(X)
743.81/262.83	   U61(mark(X1), X2) -> U61(X1, X2)
743.81/262.83	   U61(X1, mark(X2)) -> U61(X1, X2)
743.81/262.83	   U61(active(X1), X2) -> U61(X1, X2)
743.81/262.83	   U61(X1, active(X2)) -> U61(X1, X2)
743.81/262.83	   U62(mark(X)) -> U62(X)
743.81/262.83	   U62(active(X)) -> U62(X)
743.81/262.83	   U71(mark(X1), X2) -> U71(X1, X2)
743.81/262.83	   U71(X1, mark(X2)) -> U71(X1, X2)
743.81/262.83	   U71(active(X1), X2) -> U71(X1, X2)
743.81/262.83	   U71(X1, active(X2)) -> U71(X1, X2)
743.81/262.83	   U72(mark(X1), X2) -> U72(X1, X2)
743.81/262.83	   U72(X1, mark(X2)) -> U72(X1, X2)
743.81/262.83	   U72(active(X1), X2) -> U72(X1, X2)
743.81/262.83	   U72(X1, active(X2)) -> U72(X1, X2)
743.81/262.83	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.83	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.81/262.83	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.81/262.83	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.83	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.81/262.83	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.81/262.83	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.83	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.81/262.83	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.81/262.83	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.83	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.81/262.83	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.81/262.83	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.83	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.81/262.83	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.81/262.83	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.83	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.81/262.83	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.81/262.83	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.83	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.81/262.83	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.81/262.83	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.83	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.81/262.83	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.81/262.83	   s(mark(X)) -> s(X)
743.81/262.83	   s(active(X)) -> s(X)
743.81/262.83	   U91(mark(X1), X2) -> U91(X1, X2)
743.81/262.83	   U91(X1, mark(X2)) -> U91(X1, X2)
743.81/262.83	   U91(active(X1), X2) -> U91(X1, X2)
743.81/262.83	   U91(X1, active(X2)) -> U91(X1, X2)
743.81/262.83	   U92(mark(X)) -> U92(X)
743.81/262.83	   U92(active(X)) -> U92(X)
743.81/262.83	
743.81/262.83	The set Q consists of the following terms:
743.81/262.83	
743.81/262.83	   active(U101(tt, x0, x1))
743.81/262.83	   active(U102(tt, x0, x1))
743.81/262.83	   active(U103(tt, x0, x1))
743.81/262.83	   active(U104(tt, x0, x1))
743.81/262.83	   active(U11(tt, x0, x1))
743.81/262.83	   active(U12(tt, x0, x1))
743.81/262.83	   active(U13(tt, x0, x1))
743.81/262.83	   active(U14(tt, x0, x1))
743.81/262.83	   active(U15(tt, x0))
743.81/262.83	   active(U16(tt))
743.81/262.83	   active(U21(tt, x0))
743.81/262.83	   active(U22(tt, x0))
743.81/262.83	   active(U23(tt))
743.81/262.83	   active(U31(tt, x0, x1))
743.81/262.83	   active(U32(tt, x0, x1))
743.81/262.83	   active(U33(tt, x0, x1))
743.81/262.83	   active(U34(tt, x0, x1))
743.81/262.83	   active(U35(tt, x0))
743.81/262.83	   active(U36(tt))
743.81/262.83	   active(U41(tt, x0))
743.81/262.83	   active(U42(tt))
743.81/262.83	   active(U51(tt))
743.81/262.83	   active(U61(tt, x0))
743.81/262.83	   active(U62(tt))
743.81/262.83	   active(U71(tt, x0))
743.81/262.83	   active(U72(tt, x0))
743.81/262.83	   active(U81(tt, x0, x1))
743.81/262.83	   active(U82(tt, x0, x1))
743.81/262.83	   active(U83(tt, x0, x1))
743.81/262.83	   active(U84(tt, x0, x1))
743.81/262.83	   active(U91(tt, x0))
743.81/262.83	   active(U92(tt))
743.81/262.83	   active(isNat(0))
743.81/262.83	   active(isNat(plus(x0, x1)))
743.81/262.83	   active(isNat(s(x0)))
743.81/262.83	   active(isNat(x(x0, x1)))
743.81/262.83	   active(isNatKind(0))
743.81/262.83	   active(isNatKind(plus(x0, x1)))
743.81/262.83	   active(isNatKind(s(x0)))
743.81/262.83	   active(isNatKind(x(x0, x1)))
743.81/262.83	   active(plus(x0, 0))
743.81/262.83	   active(plus(x0, s(x1)))
743.81/262.83	   active(x(x0, 0))
743.81/262.83	   active(x(x0, s(x1)))
743.81/262.83	   mark(U101(x0, x1, x2))
743.81/262.83	   mark(tt)
743.81/262.83	   mark(U102(x0, x1, x2))
743.81/262.83	   mark(isNatKind(x0))
743.81/262.83	   mark(U103(x0, x1, x2))
743.81/262.83	   mark(isNat(x0))
743.81/262.83	   mark(U104(x0, x1, x2))
743.81/262.83	   mark(plus(x0, x1))
743.81/262.83	   mark(x(x0, x1))
743.81/262.83	   mark(U11(x0, x1, x2))
743.81/262.83	   mark(U12(x0, x1, x2))
743.81/262.83	   mark(U13(x0, x1, x2))
743.81/262.83	   mark(U14(x0, x1, x2))
743.81/262.83	   mark(U15(x0, x1))
743.81/262.83	   mark(U16(x0))
743.81/262.83	   mark(U21(x0, x1))
743.81/262.83	   mark(U22(x0, x1))
743.81/262.83	   mark(U23(x0))
743.81/262.83	   mark(U31(x0, x1, x2))
743.81/262.83	   mark(U32(x0, x1, x2))
743.81/262.84	   mark(U33(x0, x1, x2))
743.81/262.84	   mark(U34(x0, x1, x2))
743.81/262.84	   mark(U35(x0, x1))
743.81/262.84	   mark(U36(x0))
743.81/262.84	   mark(U41(x0, x1))
743.81/262.84	   mark(U42(x0))
743.81/262.84	   mark(U51(x0))
743.81/262.84	   mark(U61(x0, x1))
743.81/262.84	   mark(U62(x0))
743.81/262.84	   mark(U71(x0, x1))
743.81/262.84	   mark(U72(x0, x1))
743.81/262.84	   mark(U81(x0, x1, x2))
743.81/262.84	   mark(U82(x0, x1, x2))
743.81/262.84	   mark(U83(x0, x1, x2))
743.81/262.84	   mark(U84(x0, x1, x2))
743.81/262.84	   mark(s(x0))
743.81/262.84	   mark(U91(x0, x1))
743.81/262.84	   mark(U92(x0))
743.81/262.84	   mark(0)
743.81/262.84	   U101(mark(x0), x1, x2)
743.81/262.84	   U101(x0, mark(x1), x2)
743.81/262.84	   U101(x0, x1, mark(x2))
743.81/262.84	   U101(active(x0), x1, x2)
743.81/262.84	   U101(x0, active(x1), x2)
743.81/262.84	   U101(x0, x1, active(x2))
743.81/262.84	   U102(mark(x0), x1, x2)
743.81/262.84	   U102(x0, mark(x1), x2)
743.81/262.84	   U102(x0, x1, mark(x2))
743.81/262.84	   U102(active(x0), x1, x2)
743.81/262.84	   U102(x0, active(x1), x2)
743.81/262.84	   U102(x0, x1, active(x2))
743.81/262.84	   isNatKind(mark(x0))
743.81/262.84	   isNatKind(active(x0))
743.81/262.84	   U103(mark(x0), x1, x2)
743.81/262.84	   U103(x0, mark(x1), x2)
743.81/262.84	   U103(x0, x1, mark(x2))
743.81/262.84	   U103(active(x0), x1, x2)
743.81/262.84	   U103(x0, active(x1), x2)
743.81/262.84	   U103(x0, x1, active(x2))
743.81/262.84	   isNat(mark(x0))
743.81/262.84	   isNat(active(x0))
743.81/262.84	   U104(mark(x0), x1, x2)
743.81/262.84	   U104(x0, mark(x1), x2)
743.81/262.84	   U104(x0, x1, mark(x2))
743.81/262.84	   U104(active(x0), x1, x2)
743.81/262.84	   U104(x0, active(x1), x2)
743.81/262.84	   U104(x0, x1, active(x2))
743.81/262.84	   plus(mark(x0), x1)
743.81/262.84	   plus(x0, mark(x1))
743.81/262.84	   plus(active(x0), x1)
743.81/262.84	   plus(x0, active(x1))
743.81/262.84	   x(mark(x0), x1)
743.81/262.84	   x(x0, mark(x1))
743.81/262.84	   x(active(x0), x1)
743.81/262.84	   x(x0, active(x1))
743.81/262.84	   U11(mark(x0), x1, x2)
743.81/262.84	   U11(x0, mark(x1), x2)
743.81/262.84	   U11(x0, x1, mark(x2))
743.81/262.84	   U11(active(x0), x1, x2)
743.81/262.84	   U11(x0, active(x1), x2)
743.81/262.84	   U11(x0, x1, active(x2))
743.81/262.84	   U12(mark(x0), x1, x2)
743.81/262.84	   U12(x0, mark(x1), x2)
743.81/262.84	   U12(x0, x1, mark(x2))
743.81/262.84	   U12(active(x0), x1, x2)
743.81/262.84	   U12(x0, active(x1), x2)
743.81/262.84	   U12(x0, x1, active(x2))
743.81/262.84	   U13(mark(x0), x1, x2)
743.81/262.84	   U13(x0, mark(x1), x2)
743.81/262.84	   U13(x0, x1, mark(x2))
743.81/262.84	   U13(active(x0), x1, x2)
743.81/262.84	   U13(x0, active(x1), x2)
743.81/262.84	   U13(x0, x1, active(x2))
743.81/262.84	   U14(mark(x0), x1, x2)
743.81/262.84	   U14(x0, mark(x1), x2)
743.81/262.84	   U14(x0, x1, mark(x2))
743.81/262.84	   U14(active(x0), x1, x2)
743.81/262.84	   U14(x0, active(x1), x2)
743.81/262.84	   U14(x0, x1, active(x2))
743.81/262.84	   U15(mark(x0), x1)
743.81/262.84	   U15(x0, mark(x1))
743.81/262.84	   U15(active(x0), x1)
743.81/262.84	   U15(x0, active(x1))
743.81/262.84	   U16(mark(x0))
743.81/262.84	   U16(active(x0))
743.81/262.84	   U21(mark(x0), x1)
743.81/262.84	   U21(x0, mark(x1))
743.81/262.84	   U21(active(x0), x1)
743.81/262.84	   U21(x0, active(x1))
743.81/262.84	   U22(mark(x0), x1)
743.81/262.84	   U22(x0, mark(x1))
743.81/262.84	   U22(active(x0), x1)
743.81/262.84	   U22(x0, active(x1))
743.81/262.84	   U23(mark(x0))
743.81/262.84	   U23(active(x0))
743.81/262.84	   U31(mark(x0), x1, x2)
743.81/262.84	   U31(x0, mark(x1), x2)
743.81/262.84	   U31(x0, x1, mark(x2))
743.81/262.84	   U31(active(x0), x1, x2)
743.81/262.84	   U31(x0, active(x1), x2)
743.81/262.84	   U31(x0, x1, active(x2))
743.81/262.84	   U32(mark(x0), x1, x2)
743.81/262.84	   U32(x0, mark(x1), x2)
743.81/262.84	   U32(x0, x1, mark(x2))
743.81/262.84	   U32(active(x0), x1, x2)
743.81/262.84	   U32(x0, active(x1), x2)
743.81/262.84	   U32(x0, x1, active(x2))
743.81/262.84	   U33(mark(x0), x1, x2)
743.81/262.84	   U33(x0, mark(x1), x2)
743.81/262.84	   U33(x0, x1, mark(x2))
743.81/262.84	   U33(active(x0), x1, x2)
743.81/262.84	   U33(x0, active(x1), x2)
743.81/262.84	   U33(x0, x1, active(x2))
743.81/262.84	   U34(mark(x0), x1, x2)
743.81/262.84	   U34(x0, mark(x1), x2)
743.81/262.84	   U34(x0, x1, mark(x2))
743.81/262.84	   U34(active(x0), x1, x2)
743.81/262.84	   U34(x0, active(x1), x2)
743.81/262.84	   U34(x0, x1, active(x2))
743.81/262.84	   U35(mark(x0), x1)
743.81/262.84	   U35(x0, mark(x1))
743.81/262.84	   U35(active(x0), x1)
743.81/262.84	   U35(x0, active(x1))
743.81/262.84	   U36(mark(x0))
743.81/262.84	   U36(active(x0))
743.81/262.84	   U41(mark(x0), x1)
743.81/262.84	   U41(x0, mark(x1))
743.81/262.84	   U41(active(x0), x1)
743.81/262.84	   U41(x0, active(x1))
743.81/262.84	   U42(mark(x0))
743.81/262.84	   U42(active(x0))
743.81/262.84	   U51(mark(x0))
743.81/262.84	   U51(active(x0))
743.81/262.84	   U61(mark(x0), x1)
743.81/262.84	   U61(x0, mark(x1))
743.81/262.84	   U61(active(x0), x1)
743.81/262.84	   U61(x0, active(x1))
743.81/262.84	   U62(mark(x0))
743.81/262.84	   U62(active(x0))
743.81/262.84	   U71(mark(x0), x1)
743.81/262.84	   U71(x0, mark(x1))
743.81/262.84	   U71(active(x0), x1)
743.81/262.84	   U71(x0, active(x1))
743.81/262.84	   U72(mark(x0), x1)
743.81/262.84	   U72(x0, mark(x1))
743.81/262.84	   U72(active(x0), x1)
743.81/262.84	   U72(x0, active(x1))
743.81/262.84	   U81(mark(x0), x1, x2)
743.81/262.84	   U81(x0, mark(x1), x2)
743.81/262.84	   U81(x0, x1, mark(x2))
743.81/262.84	   U81(active(x0), x1, x2)
743.81/262.84	   U81(x0, active(x1), x2)
743.81/262.84	   U81(x0, x1, active(x2))
743.81/262.84	   U82(mark(x0), x1, x2)
743.81/262.84	   U82(x0, mark(x1), x2)
743.81/262.84	   U82(x0, x1, mark(x2))
743.81/262.84	   U82(active(x0), x1, x2)
743.81/262.84	   U82(x0, active(x1), x2)
743.81/262.84	   U82(x0, x1, active(x2))
743.81/262.84	   U83(mark(x0), x1, x2)
743.81/262.84	   U83(x0, mark(x1), x2)
743.81/262.84	   U83(x0, x1, mark(x2))
743.81/262.84	   U83(active(x0), x1, x2)
743.81/262.84	   U83(x0, active(x1), x2)
743.81/262.84	   U83(x0, x1, active(x2))
743.81/262.84	   U84(mark(x0), x1, x2)
743.81/262.84	   U84(x0, mark(x1), x2)
743.81/262.84	   U84(x0, x1, mark(x2))
743.81/262.84	   U84(active(x0), x1, x2)
743.81/262.84	   U84(x0, active(x1), x2)
743.81/262.84	   U84(x0, x1, active(x2))
743.81/262.84	   s(mark(x0))
743.81/262.84	   s(active(x0))
743.81/262.84	   U91(mark(x0), x1)
743.81/262.84	   U91(x0, mark(x1))
743.81/262.84	   U91(active(x0), x1)
743.81/262.84	   U91(x0, active(x1))
743.81/262.84	   U92(mark(x0))
743.81/262.84	   U92(active(x0))
743.81/262.84	
743.81/262.84	We have to consider all minimal (P,Q,R)-chains.
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(97) UsableRulesProof (EQUIVALENT)
743.81/262.84	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.
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(98)
743.81/262.84	Obligation:
743.81/262.84	Q DP problem:
743.81/262.84	The TRS P consists of the following rules:
743.81/262.84	
743.81/262.84	   U41^1(X1, mark(X2)) -> U41^1(X1, X2)
743.81/262.84	   U41^1(mark(X1), X2) -> U41^1(X1, X2)
743.81/262.84	   U41^1(active(X1), X2) -> U41^1(X1, X2)
743.81/262.84	   U41^1(X1, active(X2)) -> U41^1(X1, X2)
743.81/262.84	
743.81/262.84	R is empty.
743.81/262.84	The set Q consists of the following terms:
743.81/262.84	
743.81/262.84	   active(U101(tt, x0, x1))
743.81/262.84	   active(U102(tt, x0, x1))
743.81/262.84	   active(U103(tt, x0, x1))
743.81/262.84	   active(U104(tt, x0, x1))
743.81/262.84	   active(U11(tt, x0, x1))
743.81/262.84	   active(U12(tt, x0, x1))
743.81/262.84	   active(U13(tt, x0, x1))
743.81/262.84	   active(U14(tt, x0, x1))
743.81/262.84	   active(U15(tt, x0))
743.81/262.84	   active(U16(tt))
743.81/262.84	   active(U21(tt, x0))
743.81/262.84	   active(U22(tt, x0))
743.81/262.84	   active(U23(tt))
743.81/262.84	   active(U31(tt, x0, x1))
743.81/262.84	   active(U32(tt, x0, x1))
743.81/262.84	   active(U33(tt, x0, x1))
743.81/262.84	   active(U34(tt, x0, x1))
743.81/262.84	   active(U35(tt, x0))
743.81/262.84	   active(U36(tt))
743.81/262.84	   active(U41(tt, x0))
743.81/262.84	   active(U42(tt))
743.81/262.84	   active(U51(tt))
743.81/262.84	   active(U61(tt, x0))
743.81/262.84	   active(U62(tt))
743.81/262.84	   active(U71(tt, x0))
743.81/262.84	   active(U72(tt, x0))
743.81/262.84	   active(U81(tt, x0, x1))
743.81/262.84	   active(U82(tt, x0, x1))
743.81/262.84	   active(U83(tt, x0, x1))
743.81/262.84	   active(U84(tt, x0, x1))
743.81/262.84	   active(U91(tt, x0))
743.81/262.84	   active(U92(tt))
743.81/262.84	   active(isNat(0))
743.81/262.84	   active(isNat(plus(x0, x1)))
743.81/262.84	   active(isNat(s(x0)))
743.81/262.84	   active(isNat(x(x0, x1)))
743.81/262.84	   active(isNatKind(0))
743.81/262.84	   active(isNatKind(plus(x0, x1)))
743.81/262.84	   active(isNatKind(s(x0)))
743.81/262.84	   active(isNatKind(x(x0, x1)))
743.81/262.84	   active(plus(x0, 0))
743.81/262.84	   active(plus(x0, s(x1)))
743.81/262.84	   active(x(x0, 0))
743.81/262.84	   active(x(x0, s(x1)))
743.81/262.84	   mark(U101(x0, x1, x2))
743.81/262.84	   mark(tt)
743.81/262.84	   mark(U102(x0, x1, x2))
743.81/262.84	   mark(isNatKind(x0))
743.81/262.84	   mark(U103(x0, x1, x2))
743.81/262.84	   mark(isNat(x0))
743.81/262.84	   mark(U104(x0, x1, x2))
743.81/262.84	   mark(plus(x0, x1))
743.81/262.84	   mark(x(x0, x1))
743.81/262.84	   mark(U11(x0, x1, x2))
743.81/262.84	   mark(U12(x0, x1, x2))
743.81/262.84	   mark(U13(x0, x1, x2))
743.81/262.84	   mark(U14(x0, x1, x2))
743.81/262.84	   mark(U15(x0, x1))
743.81/262.84	   mark(U16(x0))
743.81/262.84	   mark(U21(x0, x1))
743.81/262.84	   mark(U22(x0, x1))
743.81/262.84	   mark(U23(x0))
743.81/262.84	   mark(U31(x0, x1, x2))
743.81/262.84	   mark(U32(x0, x1, x2))
743.81/262.84	   mark(U33(x0, x1, x2))
743.81/262.84	   mark(U34(x0, x1, x2))
743.81/262.84	   mark(U35(x0, x1))
743.81/262.84	   mark(U36(x0))
743.81/262.84	   mark(U41(x0, x1))
743.81/262.84	   mark(U42(x0))
743.81/262.84	   mark(U51(x0))
743.81/262.84	   mark(U61(x0, x1))
743.81/262.84	   mark(U62(x0))
743.81/262.84	   mark(U71(x0, x1))
743.81/262.84	   mark(U72(x0, x1))
743.81/262.84	   mark(U81(x0, x1, x2))
743.81/262.84	   mark(U82(x0, x1, x2))
743.81/262.84	   mark(U83(x0, x1, x2))
743.81/262.84	   mark(U84(x0, x1, x2))
743.81/262.84	   mark(s(x0))
743.81/262.84	   mark(U91(x0, x1))
743.81/262.84	   mark(U92(x0))
743.81/262.84	   mark(0)
743.81/262.84	   U101(mark(x0), x1, x2)
743.81/262.84	   U101(x0, mark(x1), x2)
743.81/262.84	   U101(x0, x1, mark(x2))
743.81/262.84	   U101(active(x0), x1, x2)
743.81/262.84	   U101(x0, active(x1), x2)
743.81/262.84	   U101(x0, x1, active(x2))
743.81/262.84	   U102(mark(x0), x1, x2)
743.81/262.84	   U102(x0, mark(x1), x2)
743.81/262.84	   U102(x0, x1, mark(x2))
743.81/262.84	   U102(active(x0), x1, x2)
743.81/262.84	   U102(x0, active(x1), x2)
743.81/262.84	   U102(x0, x1, active(x2))
743.81/262.84	   isNatKind(mark(x0))
743.81/262.84	   isNatKind(active(x0))
743.81/262.84	   U103(mark(x0), x1, x2)
743.81/262.84	   U103(x0, mark(x1), x2)
743.81/262.84	   U103(x0, x1, mark(x2))
743.81/262.84	   U103(active(x0), x1, x2)
743.81/262.84	   U103(x0, active(x1), x2)
743.81/262.84	   U103(x0, x1, active(x2))
743.81/262.84	   isNat(mark(x0))
743.81/262.84	   isNat(active(x0))
743.81/262.84	   U104(mark(x0), x1, x2)
743.81/262.84	   U104(x0, mark(x1), x2)
743.81/262.84	   U104(x0, x1, mark(x2))
743.81/262.84	   U104(active(x0), x1, x2)
743.81/262.84	   U104(x0, active(x1), x2)
743.81/262.84	   U104(x0, x1, active(x2))
743.81/262.84	   plus(mark(x0), x1)
743.81/262.84	   plus(x0, mark(x1))
743.81/262.84	   plus(active(x0), x1)
743.81/262.84	   plus(x0, active(x1))
743.81/262.84	   x(mark(x0), x1)
743.81/262.84	   x(x0, mark(x1))
743.81/262.84	   x(active(x0), x1)
743.81/262.84	   x(x0, active(x1))
743.81/262.84	   U11(mark(x0), x1, x2)
743.81/262.84	   U11(x0, mark(x1), x2)
743.81/262.84	   U11(x0, x1, mark(x2))
743.81/262.84	   U11(active(x0), x1, x2)
743.81/262.84	   U11(x0, active(x1), x2)
743.81/262.84	   U11(x0, x1, active(x2))
743.81/262.84	   U12(mark(x0), x1, x2)
743.81/262.84	   U12(x0, mark(x1), x2)
743.81/262.84	   U12(x0, x1, mark(x2))
743.81/262.84	   U12(active(x0), x1, x2)
743.81/262.84	   U12(x0, active(x1), x2)
743.81/262.84	   U12(x0, x1, active(x2))
743.81/262.84	   U13(mark(x0), x1, x2)
743.81/262.84	   U13(x0, mark(x1), x2)
743.81/262.84	   U13(x0, x1, mark(x2))
743.81/262.84	   U13(active(x0), x1, x2)
743.81/262.84	   U13(x0, active(x1), x2)
743.81/262.84	   U13(x0, x1, active(x2))
743.81/262.84	   U14(mark(x0), x1, x2)
743.81/262.84	   U14(x0, mark(x1), x2)
743.81/262.84	   U14(x0, x1, mark(x2))
743.81/262.84	   U14(active(x0), x1, x2)
743.81/262.84	   U14(x0, active(x1), x2)
743.81/262.84	   U14(x0, x1, active(x2))
743.81/262.84	   U15(mark(x0), x1)
743.81/262.84	   U15(x0, mark(x1))
743.81/262.84	   U15(active(x0), x1)
743.81/262.84	   U15(x0, active(x1))
743.81/262.84	   U16(mark(x0))
743.81/262.84	   U16(active(x0))
743.81/262.84	   U21(mark(x0), x1)
743.81/262.84	   U21(x0, mark(x1))
743.81/262.84	   U21(active(x0), x1)
743.81/262.84	   U21(x0, active(x1))
743.81/262.84	   U22(mark(x0), x1)
743.81/262.84	   U22(x0, mark(x1))
743.81/262.84	   U22(active(x0), x1)
743.81/262.84	   U22(x0, active(x1))
743.81/262.84	   U23(mark(x0))
743.81/262.84	   U23(active(x0))
743.81/262.84	   U31(mark(x0), x1, x2)
743.81/262.84	   U31(x0, mark(x1), x2)
743.81/262.84	   U31(x0, x1, mark(x2))
743.81/262.84	   U31(active(x0), x1, x2)
743.81/262.84	   U31(x0, active(x1), x2)
743.81/262.84	   U31(x0, x1, active(x2))
743.81/262.84	   U32(mark(x0), x1, x2)
743.81/262.84	   U32(x0, mark(x1), x2)
743.81/262.84	   U32(x0, x1, mark(x2))
743.81/262.84	   U32(active(x0), x1, x2)
743.81/262.84	   U32(x0, active(x1), x2)
743.81/262.84	   U32(x0, x1, active(x2))
743.81/262.84	   U33(mark(x0), x1, x2)
743.81/262.84	   U33(x0, mark(x1), x2)
743.81/262.84	   U33(x0, x1, mark(x2))
743.81/262.84	   U33(active(x0), x1, x2)
743.81/262.84	   U33(x0, active(x1), x2)
743.81/262.84	   U33(x0, x1, active(x2))
743.81/262.84	   U34(mark(x0), x1, x2)
743.81/262.84	   U34(x0, mark(x1), x2)
743.81/262.84	   U34(x0, x1, mark(x2))
743.81/262.84	   U34(active(x0), x1, x2)
743.81/262.84	   U34(x0, active(x1), x2)
743.81/262.84	   U34(x0, x1, active(x2))
743.81/262.84	   U35(mark(x0), x1)
743.81/262.84	   U35(x0, mark(x1))
743.81/262.84	   U35(active(x0), x1)
743.81/262.84	   U35(x0, active(x1))
743.81/262.84	   U36(mark(x0))
743.81/262.84	   U36(active(x0))
743.81/262.84	   U41(mark(x0), x1)
743.81/262.84	   U41(x0, mark(x1))
743.81/262.84	   U41(active(x0), x1)
743.81/262.84	   U41(x0, active(x1))
743.81/262.84	   U42(mark(x0))
743.81/262.84	   U42(active(x0))
743.81/262.84	   U51(mark(x0))
743.81/262.84	   U51(active(x0))
743.81/262.84	   U61(mark(x0), x1)
743.81/262.84	   U61(x0, mark(x1))
743.81/262.84	   U61(active(x0), x1)
743.81/262.84	   U61(x0, active(x1))
743.81/262.84	   U62(mark(x0))
743.81/262.84	   U62(active(x0))
743.81/262.84	   U71(mark(x0), x1)
743.81/262.84	   U71(x0, mark(x1))
743.81/262.84	   U71(active(x0), x1)
743.81/262.84	   U71(x0, active(x1))
743.81/262.84	   U72(mark(x0), x1)
743.81/262.84	   U72(x0, mark(x1))
743.81/262.84	   U72(active(x0), x1)
743.81/262.84	   U72(x0, active(x1))
743.81/262.84	   U81(mark(x0), x1, x2)
743.81/262.84	   U81(x0, mark(x1), x2)
743.81/262.84	   U81(x0, x1, mark(x2))
743.81/262.84	   U81(active(x0), x1, x2)
743.81/262.84	   U81(x0, active(x1), x2)
743.81/262.84	   U81(x0, x1, active(x2))
743.81/262.84	   U82(mark(x0), x1, x2)
743.81/262.84	   U82(x0, mark(x1), x2)
743.81/262.84	   U82(x0, x1, mark(x2))
743.81/262.84	   U82(active(x0), x1, x2)
743.81/262.84	   U82(x0, active(x1), x2)
743.81/262.84	   U82(x0, x1, active(x2))
743.81/262.84	   U83(mark(x0), x1, x2)
743.81/262.84	   U83(x0, mark(x1), x2)
743.81/262.84	   U83(x0, x1, mark(x2))
743.81/262.84	   U83(active(x0), x1, x2)
743.81/262.84	   U83(x0, active(x1), x2)
743.81/262.84	   U83(x0, x1, active(x2))
743.81/262.84	   U84(mark(x0), x1, x2)
743.81/262.84	   U84(x0, mark(x1), x2)
743.81/262.84	   U84(x0, x1, mark(x2))
743.81/262.84	   U84(active(x0), x1, x2)
743.81/262.84	   U84(x0, active(x1), x2)
743.81/262.84	   U84(x0, x1, active(x2))
743.81/262.84	   s(mark(x0))
743.81/262.84	   s(active(x0))
743.81/262.84	   U91(mark(x0), x1)
743.81/262.84	   U91(x0, mark(x1))
743.81/262.84	   U91(active(x0), x1)
743.81/262.84	   U91(x0, active(x1))
743.81/262.84	   U92(mark(x0))
743.81/262.84	   U92(active(x0))
743.81/262.84	
743.81/262.84	We have to consider all minimal (P,Q,R)-chains.
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(99) QReductionProof (EQUIVALENT)
743.81/262.84	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
743.81/262.84	
743.81/262.84	   U101(mark(x0), x1, x2)
743.81/262.84	   U101(x0, mark(x1), x2)
743.81/262.84	   U101(x0, x1, mark(x2))
743.81/262.84	   U101(active(x0), x1, x2)
743.81/262.84	   U101(x0, active(x1), x2)
743.81/262.84	   U101(x0, x1, active(x2))
743.81/262.84	   U102(mark(x0), x1, x2)
743.81/262.84	   U102(x0, mark(x1), x2)
743.81/262.84	   U102(x0, x1, mark(x2))
743.81/262.84	   U102(active(x0), x1, x2)
743.81/262.84	   U102(x0, active(x1), x2)
743.81/262.84	   U102(x0, x1, active(x2))
743.81/262.84	   isNatKind(mark(x0))
743.81/262.84	   isNatKind(active(x0))
743.81/262.84	   U103(mark(x0), x1, x2)
743.81/262.84	   U103(x0, mark(x1), x2)
743.81/262.84	   U103(x0, x1, mark(x2))
743.81/262.84	   U103(active(x0), x1, x2)
743.81/262.84	   U103(x0, active(x1), x2)
743.81/262.84	   U103(x0, x1, active(x2))
743.81/262.84	   isNat(mark(x0))
743.81/262.84	   isNat(active(x0))
743.81/262.84	   U104(mark(x0), x1, x2)
743.81/262.84	   U104(x0, mark(x1), x2)
743.81/262.84	   U104(x0, x1, mark(x2))
743.81/262.84	   U104(active(x0), x1, x2)
743.81/262.84	   U104(x0, active(x1), x2)
743.81/262.84	   U104(x0, x1, active(x2))
743.81/262.84	   plus(mark(x0), x1)
743.81/262.84	   plus(x0, mark(x1))
743.81/262.84	   plus(active(x0), x1)
743.81/262.84	   plus(x0, active(x1))
743.81/262.84	   x(mark(x0), x1)
743.81/262.84	   x(x0, mark(x1))
743.81/262.84	   x(active(x0), x1)
743.81/262.84	   x(x0, active(x1))
743.81/262.84	   U11(mark(x0), x1, x2)
743.81/262.84	   U11(x0, mark(x1), x2)
743.81/262.84	   U11(x0, x1, mark(x2))
743.81/262.84	   U11(active(x0), x1, x2)
743.81/262.84	   U11(x0, active(x1), x2)
743.81/262.84	   U11(x0, x1, active(x2))
743.81/262.84	   U12(mark(x0), x1, x2)
743.81/262.84	   U12(x0, mark(x1), x2)
743.81/262.84	   U12(x0, x1, mark(x2))
743.81/262.84	   U12(active(x0), x1, x2)
743.81/262.84	   U12(x0, active(x1), x2)
743.81/262.84	   U12(x0, x1, active(x2))
743.81/262.84	   U13(mark(x0), x1, x2)
743.81/262.84	   U13(x0, mark(x1), x2)
743.81/262.84	   U13(x0, x1, mark(x2))
743.81/262.84	   U13(active(x0), x1, x2)
743.81/262.84	   U13(x0, active(x1), x2)
743.81/262.84	   U13(x0, x1, active(x2))
743.81/262.84	   U14(mark(x0), x1, x2)
743.81/262.84	   U14(x0, mark(x1), x2)
743.81/262.84	   U14(x0, x1, mark(x2))
743.81/262.84	   U14(active(x0), x1, x2)
743.81/262.84	   U14(x0, active(x1), x2)
743.81/262.84	   U14(x0, x1, active(x2))
743.81/262.84	   U15(mark(x0), x1)
743.81/262.84	   U15(x0, mark(x1))
743.81/262.84	   U15(active(x0), x1)
743.81/262.84	   U15(x0, active(x1))
743.81/262.84	   U16(mark(x0))
743.81/262.84	   U16(active(x0))
743.81/262.84	   U21(mark(x0), x1)
743.81/262.84	   U21(x0, mark(x1))
743.81/262.84	   U21(active(x0), x1)
743.81/262.84	   U21(x0, active(x1))
743.81/262.84	   U22(mark(x0), x1)
743.81/262.84	   U22(x0, mark(x1))
743.81/262.84	   U22(active(x0), x1)
743.81/262.84	   U22(x0, active(x1))
743.81/262.84	   U23(mark(x0))
743.81/262.84	   U23(active(x0))
743.81/262.84	   U31(mark(x0), x1, x2)
743.81/262.84	   U31(x0, mark(x1), x2)
743.81/262.84	   U31(x0, x1, mark(x2))
743.81/262.84	   U31(active(x0), x1, x2)
743.81/262.84	   U31(x0, active(x1), x2)
743.81/262.84	   U31(x0, x1, active(x2))
743.81/262.84	   U32(mark(x0), x1, x2)
743.81/262.84	   U32(x0, mark(x1), x2)
743.81/262.84	   U32(x0, x1, mark(x2))
743.81/262.84	   U32(active(x0), x1, x2)
743.81/262.84	   U32(x0, active(x1), x2)
743.81/262.84	   U32(x0, x1, active(x2))
743.81/262.84	   U33(mark(x0), x1, x2)
743.81/262.84	   U33(x0, mark(x1), x2)
743.81/262.84	   U33(x0, x1, mark(x2))
743.81/262.84	   U33(active(x0), x1, x2)
743.81/262.84	   U33(x0, active(x1), x2)
743.81/262.84	   U33(x0, x1, active(x2))
743.81/262.84	   U34(mark(x0), x1, x2)
743.81/262.84	   U34(x0, mark(x1), x2)
743.81/262.84	   U34(x0, x1, mark(x2))
743.81/262.84	   U34(active(x0), x1, x2)
743.81/262.84	   U34(x0, active(x1), x2)
743.81/262.84	   U34(x0, x1, active(x2))
743.81/262.84	   U35(mark(x0), x1)
743.81/262.84	   U35(x0, mark(x1))
743.81/262.84	   U35(active(x0), x1)
743.81/262.84	   U35(x0, active(x1))
743.81/262.84	   U36(mark(x0))
743.81/262.84	   U36(active(x0))
743.81/262.84	   U41(mark(x0), x1)
743.81/262.84	   U41(x0, mark(x1))
743.81/262.84	   U41(active(x0), x1)
743.81/262.84	   U41(x0, active(x1))
743.81/262.84	   U42(mark(x0))
743.81/262.84	   U42(active(x0))
743.81/262.84	   U51(mark(x0))
743.81/262.84	   U51(active(x0))
743.81/262.84	   U61(mark(x0), x1)
743.81/262.84	   U61(x0, mark(x1))
743.81/262.84	   U61(active(x0), x1)
743.81/262.84	   U61(x0, active(x1))
743.81/262.84	   U62(mark(x0))
743.81/262.84	   U62(active(x0))
743.81/262.84	   U71(mark(x0), x1)
743.81/262.84	   U71(x0, mark(x1))
743.81/262.84	   U71(active(x0), x1)
743.81/262.84	   U71(x0, active(x1))
743.81/262.84	   U72(mark(x0), x1)
743.81/262.84	   U72(x0, mark(x1))
743.81/262.84	   U72(active(x0), x1)
743.81/262.84	   U72(x0, active(x1))
743.81/262.84	   U81(mark(x0), x1, x2)
743.81/262.84	   U81(x0, mark(x1), x2)
743.81/262.84	   U81(x0, x1, mark(x2))
743.81/262.84	   U81(active(x0), x1, x2)
743.81/262.84	   U81(x0, active(x1), x2)
743.81/262.84	   U81(x0, x1, active(x2))
743.81/262.84	   U82(mark(x0), x1, x2)
743.81/262.84	   U82(x0, mark(x1), x2)
743.81/262.84	   U82(x0, x1, mark(x2))
743.81/262.84	   U82(active(x0), x1, x2)
743.81/262.84	   U82(x0, active(x1), x2)
743.81/262.84	   U82(x0, x1, active(x2))
743.81/262.84	   U83(mark(x0), x1, x2)
743.81/262.84	   U83(x0, mark(x1), x2)
743.81/262.84	   U83(x0, x1, mark(x2))
743.81/262.84	   U83(active(x0), x1, x2)
743.81/262.84	   U83(x0, active(x1), x2)
743.81/262.84	   U83(x0, x1, active(x2))
743.81/262.84	   U84(mark(x0), x1, x2)
743.81/262.84	   U84(x0, mark(x1), x2)
743.81/262.84	   U84(x0, x1, mark(x2))
743.81/262.84	   U84(active(x0), x1, x2)
743.81/262.84	   U84(x0, active(x1), x2)
743.81/262.84	   U84(x0, x1, active(x2))
743.81/262.84	   s(mark(x0))
743.81/262.84	   s(active(x0))
743.81/262.84	   U91(mark(x0), x1)
743.81/262.84	   U91(x0, mark(x1))
743.81/262.84	   U91(active(x0), x1)
743.81/262.84	   U91(x0, active(x1))
743.81/262.84	   U92(mark(x0))
743.81/262.84	   U92(active(x0))
743.81/262.84	
743.81/262.84	
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(100)
743.81/262.84	Obligation:
743.81/262.84	Q DP problem:
743.81/262.84	The TRS P consists of the following rules:
743.81/262.84	
743.81/262.84	   U41^1(X1, mark(X2)) -> U41^1(X1, X2)
743.81/262.84	   U41^1(mark(X1), X2) -> U41^1(X1, X2)
743.81/262.84	   U41^1(active(X1), X2) -> U41^1(X1, X2)
743.81/262.84	   U41^1(X1, active(X2)) -> U41^1(X1, X2)
743.81/262.84	
743.81/262.84	R is empty.
743.81/262.84	The set Q consists of the following terms:
743.81/262.84	
743.81/262.84	   active(U101(tt, x0, x1))
743.81/262.84	   active(U102(tt, x0, x1))
743.81/262.84	   active(U103(tt, x0, x1))
743.81/262.84	   active(U104(tt, x0, x1))
743.81/262.84	   active(U11(tt, x0, x1))
743.81/262.84	   active(U12(tt, x0, x1))
743.81/262.84	   active(U13(tt, x0, x1))
743.81/262.84	   active(U14(tt, x0, x1))
743.81/262.84	   active(U15(tt, x0))
743.81/262.84	   active(U16(tt))
743.81/262.84	   active(U21(tt, x0))
743.81/262.84	   active(U22(tt, x0))
743.81/262.84	   active(U23(tt))
743.81/262.84	   active(U31(tt, x0, x1))
743.81/262.84	   active(U32(tt, x0, x1))
743.81/262.84	   active(U33(tt, x0, x1))
743.81/262.84	   active(U34(tt, x0, x1))
743.81/262.84	   active(U35(tt, x0))
743.81/262.84	   active(U36(tt))
743.81/262.84	   active(U41(tt, x0))
743.81/262.84	   active(U42(tt))
743.81/262.84	   active(U51(tt))
743.81/262.84	   active(U61(tt, x0))
743.81/262.84	   active(U62(tt))
743.81/262.84	   active(U71(tt, x0))
743.81/262.84	   active(U72(tt, x0))
743.81/262.84	   active(U81(tt, x0, x1))
743.81/262.84	   active(U82(tt, x0, x1))
743.81/262.84	   active(U83(tt, x0, x1))
743.81/262.84	   active(U84(tt, x0, x1))
743.81/262.84	   active(U91(tt, x0))
743.81/262.84	   active(U92(tt))
743.81/262.84	   active(isNat(0))
743.81/262.84	   active(isNat(plus(x0, x1)))
743.81/262.84	   active(isNat(s(x0)))
743.81/262.84	   active(isNat(x(x0, x1)))
743.81/262.84	   active(isNatKind(0))
743.81/262.84	   active(isNatKind(plus(x0, x1)))
743.81/262.84	   active(isNatKind(s(x0)))
743.81/262.84	   active(isNatKind(x(x0, x1)))
743.81/262.84	   active(plus(x0, 0))
743.81/262.84	   active(plus(x0, s(x1)))
743.81/262.84	   active(x(x0, 0))
743.81/262.84	   active(x(x0, s(x1)))
743.81/262.84	   mark(U101(x0, x1, x2))
743.81/262.84	   mark(tt)
743.81/262.84	   mark(U102(x0, x1, x2))
743.81/262.84	   mark(isNatKind(x0))
743.81/262.84	   mark(U103(x0, x1, x2))
743.81/262.84	   mark(isNat(x0))
743.81/262.84	   mark(U104(x0, x1, x2))
743.81/262.84	   mark(plus(x0, x1))
743.81/262.84	   mark(x(x0, x1))
743.81/262.84	   mark(U11(x0, x1, x2))
743.81/262.84	   mark(U12(x0, x1, x2))
743.81/262.84	   mark(U13(x0, x1, x2))
743.81/262.84	   mark(U14(x0, x1, x2))
743.81/262.84	   mark(U15(x0, x1))
743.81/262.84	   mark(U16(x0))
743.81/262.84	   mark(U21(x0, x1))
743.81/262.84	   mark(U22(x0, x1))
743.81/262.84	   mark(U23(x0))
743.81/262.84	   mark(U31(x0, x1, x2))
743.81/262.84	   mark(U32(x0, x1, x2))
743.81/262.84	   mark(U33(x0, x1, x2))
743.81/262.84	   mark(U34(x0, x1, x2))
743.81/262.84	   mark(U35(x0, x1))
743.81/262.84	   mark(U36(x0))
743.81/262.84	   mark(U41(x0, x1))
743.81/262.84	   mark(U42(x0))
743.81/262.84	   mark(U51(x0))
743.81/262.84	   mark(U61(x0, x1))
743.81/262.84	   mark(U62(x0))
743.81/262.84	   mark(U71(x0, x1))
743.81/262.84	   mark(U72(x0, x1))
743.81/262.84	   mark(U81(x0, x1, x2))
743.81/262.84	   mark(U82(x0, x1, x2))
743.81/262.84	   mark(U83(x0, x1, x2))
743.81/262.84	   mark(U84(x0, x1, x2))
743.81/262.84	   mark(s(x0))
743.81/262.84	   mark(U91(x0, x1))
743.81/262.84	   mark(U92(x0))
743.81/262.84	   mark(0)
743.81/262.84	
743.81/262.84	We have to consider all minimal (P,Q,R)-chains.
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(101) QDPSizeChangeProof (EQUIVALENT)
743.81/262.84	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. 
743.81/262.84	
743.81/262.84	From the DPs we obtained the following set of size-change graphs:
743.81/262.84	*U41^1(X1, mark(X2)) -> U41^1(X1, X2)
743.81/262.84	The graph contains the following edges 1 >= 1, 2 > 2
743.81/262.84	
743.81/262.84	
743.81/262.84	*U41^1(mark(X1), X2) -> U41^1(X1, X2)
743.81/262.84	The graph contains the following edges 1 > 1, 2 >= 2
743.81/262.84	
743.81/262.84	
743.81/262.84	*U41^1(active(X1), X2) -> U41^1(X1, X2)
743.81/262.84	The graph contains the following edges 1 > 1, 2 >= 2
743.81/262.84	
743.81/262.84	
743.81/262.84	*U41^1(X1, active(X2)) -> U41^1(X1, X2)
743.81/262.84	The graph contains the following edges 1 >= 1, 2 > 2
743.81/262.84	
743.81/262.84	
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(102)
743.81/262.84	YES
743.81/262.84	
743.81/262.84	----------------------------------------
743.81/262.84	
743.81/262.84	(103)
743.81/262.84	Obligation:
743.81/262.84	Q DP problem:
743.81/262.84	The TRS P consists of the following rules:
743.81/262.84	
743.81/262.84	   U36^1(active(X)) -> U36^1(X)
743.81/262.84	   U36^1(mark(X)) -> U36^1(X)
743.81/262.84	
743.81/262.84	The TRS R consists of the following rules:
743.81/262.84	
743.81/262.84	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
743.81/262.84	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
743.81/262.84	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
743.81/262.84	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
743.81/262.84	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
743.81/262.84	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
743.81/262.84	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
743.81/262.84	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
743.81/262.84	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
743.81/262.84	   active(U16(tt)) -> mark(tt)
743.81/262.84	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
743.81/262.84	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
743.81/262.84	   active(U23(tt)) -> mark(tt)
743.81/262.84	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
743.81/262.84	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
743.81/262.84	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
743.81/262.84	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
743.81/262.84	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
743.81/262.84	   active(U36(tt)) -> mark(tt)
743.81/262.84	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
743.81/262.84	   active(U42(tt)) -> mark(tt)
743.81/262.84	   active(U51(tt)) -> mark(tt)
743.81/262.84	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
743.81/262.84	   active(U62(tt)) -> mark(tt)
743.81/262.84	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
743.81/262.84	   active(U72(tt, N)) -> mark(N)
743.81/262.84	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
743.81/262.84	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
743.81/262.84	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
743.81/262.84	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
743.81/262.84	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
743.81/262.84	   active(U92(tt)) -> mark(0)
743.81/262.84	   active(isNat(0)) -> mark(tt)
743.81/262.84	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
743.81/262.84	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
743.81/262.84	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
743.81/262.84	   active(isNatKind(0)) -> mark(tt)
743.81/262.84	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
743.81/262.84	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
743.81/262.84	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
743.81/262.84	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
743.81/262.84	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
743.81/262.84	   active(x(N, 0)) -> mark(U91(isNat(N), N))
743.81/262.84	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
743.81/262.84	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
743.81/262.84	   mark(tt) -> active(tt)
743.81/262.84	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
743.81/262.84	   mark(isNatKind(X)) -> active(isNatKind(X))
743.81/262.84	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
743.81/262.84	   mark(isNat(X)) -> active(isNat(X))
743.81/262.84	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
743.81/262.84	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
743.81/262.84	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
743.81/262.84	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
743.81/262.84	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
743.81/262.84	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
743.81/262.84	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
743.81/262.84	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
743.81/262.84	   mark(U16(X)) -> active(U16(mark(X)))
743.81/262.84	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
743.81/262.84	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
743.81/262.84	   mark(U23(X)) -> active(U23(mark(X)))
743.81/262.84	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
743.81/262.84	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
743.81/262.84	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
743.81/262.84	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
743.81/262.84	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
743.81/262.84	   mark(U36(X)) -> active(U36(mark(X)))
743.81/262.84	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
743.81/262.84	   mark(U42(X)) -> active(U42(mark(X)))
743.81/262.84	   mark(U51(X)) -> active(U51(mark(X)))
743.81/262.84	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
743.81/262.84	   mark(U62(X)) -> active(U62(mark(X)))
743.81/262.84	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
743.81/262.84	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
743.81/262.84	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
743.81/262.84	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
743.81/262.84	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
743.81/262.84	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
743.81/262.84	   mark(s(X)) -> active(s(mark(X)))
743.81/262.84	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
743.81/262.84	   mark(U92(X)) -> active(U92(mark(X)))
743.81/262.84	   mark(0) -> active(0)
743.81/262.84	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.84	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
743.81/262.84	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
743.81/262.84	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
743.81/262.84	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
743.81/262.84	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
743.81/262.84	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.84	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
743.81/262.84	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
743.81/262.84	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
743.81/262.84	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
743.81/262.84	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
743.81/262.84	   isNatKind(mark(X)) -> isNatKind(X)
743.81/262.84	   isNatKind(active(X)) -> isNatKind(X)
743.81/262.84	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.84	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
743.81/262.84	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
743.81/262.84	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
743.81/262.84	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
743.81/262.84	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
743.81/262.84	   isNat(mark(X)) -> isNat(X)
743.81/262.84	   isNat(active(X)) -> isNat(X)
743.81/262.84	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.84	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
743.81/262.84	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
743.81/262.84	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
743.81/262.84	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
743.81/262.84	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
743.81/262.84	   plus(mark(X1), X2) -> plus(X1, X2)
743.81/262.84	   plus(X1, mark(X2)) -> plus(X1, X2)
743.81/262.84	   plus(active(X1), X2) -> plus(X1, X2)
743.81/262.84	   plus(X1, active(X2)) -> plus(X1, X2)
743.81/262.84	   x(mark(X1), X2) -> x(X1, X2)
743.81/262.84	   x(X1, mark(X2)) -> x(X1, X2)
743.81/262.84	   x(active(X1), X2) -> x(X1, X2)
743.81/262.84	   x(X1, active(X2)) -> x(X1, X2)
743.81/262.84	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.84	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
743.81/262.84	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
743.81/262.84	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
743.81/262.84	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
743.81/262.84	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
743.81/262.84	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.84	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
743.81/262.84	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
743.81/262.84	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
743.81/262.84	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
743.81/262.84	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
743.81/262.84	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.84	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
743.81/262.84	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
743.81/262.84	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
743.81/262.84	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
743.81/262.84	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
743.81/262.84	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.84	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
743.81/262.84	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
743.81/262.84	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
743.81/262.84	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
743.81/262.84	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
743.81/262.84	   U15(mark(X1), X2) -> U15(X1, X2)
743.81/262.84	   U15(X1, mark(X2)) -> U15(X1, X2)
743.81/262.84	   U15(active(X1), X2) -> U15(X1, X2)
743.81/262.84	   U15(X1, active(X2)) -> U15(X1, X2)
743.81/262.84	   U16(mark(X)) -> U16(X)
743.81/262.84	   U16(active(X)) -> U16(X)
743.81/262.84	   U21(mark(X1), X2) -> U21(X1, X2)
743.81/262.84	   U21(X1, mark(X2)) -> U21(X1, X2)
743.81/262.84	   U21(active(X1), X2) -> U21(X1, X2)
743.81/262.84	   U21(X1, active(X2)) -> U21(X1, X2)
743.81/262.84	   U22(mark(X1), X2) -> U22(X1, X2)
743.81/262.84	   U22(X1, mark(X2)) -> U22(X1, X2)
743.81/262.84	   U22(active(X1), X2) -> U22(X1, X2)
743.81/262.84	   U22(X1, active(X2)) -> U22(X1, X2)
743.81/262.84	   U23(mark(X)) -> U23(X)
743.81/262.84	   U23(active(X)) -> U23(X)
743.81/262.84	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.84	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
743.81/262.84	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
743.81/262.84	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
743.81/262.84	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
743.81/262.84	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
743.81/262.84	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.84	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
743.81/262.84	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
743.81/262.84	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
743.81/262.84	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
743.81/262.84	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
743.81/262.84	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.84	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
743.81/262.84	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
743.81/262.84	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
743.81/262.84	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
743.81/262.84	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
743.81/262.84	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.84	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
743.81/262.84	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
743.81/262.84	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
743.81/262.84	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
743.81/262.84	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
743.81/262.84	   U35(mark(X1), X2) -> U35(X1, X2)
743.81/262.84	   U35(X1, mark(X2)) -> U35(X1, X2)
743.81/262.84	   U35(active(X1), X2) -> U35(X1, X2)
743.81/262.84	   U35(X1, active(X2)) -> U35(X1, X2)
743.81/262.84	   U36(mark(X)) -> U36(X)
743.81/262.84	   U36(active(X)) -> U36(X)
743.81/262.84	   U41(mark(X1), X2) -> U41(X1, X2)
743.81/262.84	   U41(X1, mark(X2)) -> U41(X1, X2)
743.81/262.84	   U41(active(X1), X2) -> U41(X1, X2)
743.81/262.84	   U41(X1, active(X2)) -> U41(X1, X2)
743.81/262.84	   U42(mark(X)) -> U42(X)
743.81/262.84	   U42(active(X)) -> U42(X)
743.81/262.84	   U51(mark(X)) -> U51(X)
743.81/262.84	   U51(active(X)) -> U51(X)
743.81/262.84	   U61(mark(X1), X2) -> U61(X1, X2)
743.81/262.84	   U61(X1, mark(X2)) -> U61(X1, X2)
743.81/262.84	   U61(active(X1), X2) -> U61(X1, X2)
743.81/262.84	   U61(X1, active(X2)) -> U61(X1, X2)
743.81/262.84	   U62(mark(X)) -> U62(X)
743.81/262.84	   U62(active(X)) -> U62(X)
743.81/262.84	   U71(mark(X1), X2) -> U71(X1, X2)
743.81/262.84	   U71(X1, mark(X2)) -> U71(X1, X2)
743.81/262.84	   U71(active(X1), X2) -> U71(X1, X2)
743.81/262.84	   U71(X1, active(X2)) -> U71(X1, X2)
743.81/262.84	   U72(mark(X1), X2) -> U72(X1, X2)
743.81/262.84	   U72(X1, mark(X2)) -> U72(X1, X2)
743.81/262.84	   U72(active(X1), X2) -> U72(X1, X2)
743.81/262.84	   U72(X1, active(X2)) -> U72(X1, X2)
743.81/262.84	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.84	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
743.81/262.84	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
743.81/262.84	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
743.81/262.84	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
743.81/262.84	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
743.81/262.84	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.84	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
743.81/262.84	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
743.81/262.84	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
743.81/262.84	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
743.81/262.84	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
743.81/262.84	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.84	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
743.81/262.84	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
743.81/262.84	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
743.81/262.84	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
743.81/262.84	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
743.81/262.84	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.84	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
743.81/262.84	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
743.81/262.84	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
743.81/262.84	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
743.81/262.84	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
743.81/262.84	   s(mark(X)) -> s(X)
743.81/262.84	   s(active(X)) -> s(X)
743.81/262.84	   U91(mark(X1), X2) -> U91(X1, X2)
743.81/262.84	   U91(X1, mark(X2)) -> U91(X1, X2)
743.81/262.84	   U91(active(X1), X2) -> U91(X1, X2)
743.81/262.84	   U91(X1, active(X2)) -> U91(X1, X2)
743.81/262.84	   U92(mark(X)) -> U92(X)
743.81/262.84	   U92(active(X)) -> U92(X)
743.81/262.84	
743.81/262.84	The set Q consists of the following terms:
743.81/262.84	
743.81/262.84	   active(U101(tt, x0, x1))
743.81/262.84	   active(U102(tt, x0, x1))
743.81/262.84	   active(U103(tt, x0, x1))
743.81/262.84	   active(U104(tt, x0, x1))
743.81/262.84	   active(U11(tt, x0, x1))
743.81/262.84	   active(U12(tt, x0, x1))
743.81/262.84	   active(U13(tt, x0, x1))
743.81/262.84	   active(U14(tt, x0, x1))
743.81/262.84	   active(U15(tt, x0))
743.81/262.84	   active(U16(tt))
743.81/262.84	   active(U21(tt, x0))
743.81/262.84	   active(U22(tt, x0))
743.81/262.84	   active(U23(tt))
743.81/262.84	   active(U31(tt, x0, x1))
743.81/262.84	   active(U32(tt, x0, x1))
743.81/262.84	   active(U33(tt, x0, x1))
743.81/262.84	   active(U34(tt, x0, x1))
743.81/262.84	   active(U35(tt, x0))
743.81/262.84	   active(U36(tt))
743.81/262.84	   active(U41(tt, x0))
743.81/262.84	   active(U42(tt))
743.81/262.84	   active(U51(tt))
743.81/262.84	   active(U61(tt, x0))
743.81/262.84	   active(U62(tt))
743.81/262.84	   active(U71(tt, x0))
743.81/262.84	   active(U72(tt, x0))
743.81/262.84	   active(U81(tt, x0, x1))
743.81/262.84	   active(U82(tt, x0, x1))
743.81/262.84	   active(U83(tt, x0, x1))
743.81/262.84	   active(U84(tt, x0, x1))
743.81/262.84	   active(U91(tt, x0))
743.81/262.84	   active(U92(tt))
743.81/262.84	   active(isNat(0))
743.81/262.84	   active(isNat(plus(x0, x1)))
743.81/262.84	   active(isNat(s(x0)))
743.81/262.84	   active(isNat(x(x0, x1)))
743.81/262.84	   active(isNatKind(0))
743.81/262.84	   active(isNatKind(plus(x0, x1)))
743.81/262.84	   active(isNatKind(s(x0)))
743.81/262.84	   active(isNatKind(x(x0, x1)))
743.81/262.84	   active(plus(x0, 0))
743.81/262.84	   active(plus(x0, s(x1)))
743.81/262.84	   active(x(x0, 0))
743.81/262.84	   active(x(x0, s(x1)))
743.81/262.84	   mark(U101(x0, x1, x2))
743.81/262.84	   mark(tt)
743.81/262.84	   mark(U102(x0, x1, x2))
743.81/262.84	   mark(isNatKind(x0))
743.81/262.84	   mark(U103(x0, x1, x2))
743.81/262.84	   mark(isNat(x0))
743.81/262.84	   mark(U104(x0, x1, x2))
743.81/262.84	   mark(plus(x0, x1))
743.81/262.84	   mark(x(x0, x1))
743.81/262.84	   mark(U11(x0, x1, x2))
743.81/262.84	   mark(U12(x0, x1, x2))
743.81/262.84	   mark(U13(x0, x1, x2))
743.81/262.84	   mark(U14(x0, x1, x2))
743.81/262.84	   mark(U15(x0, x1))
743.81/262.84	   mark(U16(x0))
743.81/262.84	   mark(U21(x0, x1))
743.81/262.84	   mark(U22(x0, x1))
743.81/262.84	   mark(U23(x0))
743.81/262.84	   mark(U31(x0, x1, x2))
743.81/262.84	   mark(U32(x0, x1, x2))
743.81/262.84	   mark(U33(x0, x1, x2))
743.81/262.84	   mark(U34(x0, x1, x2))
743.81/262.84	   mark(U35(x0, x1))
743.81/262.84	   mark(U36(x0))
743.81/262.84	   mark(U41(x0, x1))
743.81/262.84	   mark(U42(x0))
743.81/262.84	   mark(U51(x0))
743.81/262.84	   mark(U61(x0, x1))
743.81/262.84	   mark(U62(x0))
743.81/262.84	   mark(U71(x0, x1))
743.81/262.84	   mark(U72(x0, x1))
743.81/262.84	   mark(U81(x0, x1, x2))
743.81/262.84	   mark(U82(x0, x1, x2))
743.81/262.84	   mark(U83(x0, x1, x2))
743.81/262.84	   mark(U84(x0, x1, x2))
743.81/262.84	   mark(s(x0))
743.81/262.84	   mark(U91(x0, x1))
743.81/262.84	   mark(U92(x0))
743.81/262.84	   mark(0)
743.81/262.84	   U101(mark(x0), x1, x2)
743.81/262.84	   U101(x0, mark(x1), x2)
743.81/262.84	   U101(x0, x1, mark(x2))
743.81/262.84	   U101(active(x0), x1, x2)
743.81/262.84	   U101(x0, active(x1), x2)
743.81/262.84	   U101(x0, x1, active(x2))
743.81/262.84	   U102(mark(x0), x1, x2)
743.81/262.84	   U102(x0, mark(x1), x2)
743.81/262.84	   U102(x0, x1, mark(x2))
743.81/262.84	   U102(active(x0), x1, x2)
743.81/262.84	   U102(x0, active(x1), x2)
743.81/262.84	   U102(x0, x1, active(x2))
743.81/262.84	   isNatKind(mark(x0))
743.81/262.84	   isNatKind(active(x0))
743.81/262.84	   U103(mark(x0), x1, x2)
743.81/262.84	   U103(x0, mark(x1), x2)
743.81/262.84	   U103(x0, x1, mark(x2))
743.81/262.84	   U103(active(x0), x1, x2)
743.81/262.84	   U103(x0, active(x1), x2)
743.81/262.84	   U103(x0, x1, active(x2))
743.81/262.84	   isNat(mark(x0))
743.81/262.84	   isNat(active(x0))
743.81/262.84	   U104(mark(x0), x1, x2)
743.81/262.84	   U104(x0, mark(x1), x2)
743.81/262.84	   U104(x0, x1, mark(x2))
743.81/262.84	   U104(active(x0), x1, x2)
743.81/262.84	   U104(x0, active(x1), x2)
743.81/262.84	   U104(x0, x1, active(x2))
743.81/262.84	   plus(mark(x0), x1)
743.81/262.84	   plus(x0, mark(x1))
743.81/262.84	   plus(active(x0), x1)
743.81/262.84	   plus(x0, active(x1))
743.81/262.84	   x(mark(x0), x1)
743.81/262.84	   x(x0, mark(x1))
743.81/262.84	   x(active(x0), x1)
743.81/262.84	   x(x0, active(x1))
743.81/262.84	   U11(mark(x0), x1, x2)
743.81/262.84	   U11(x0, mark(x1), x2)
743.81/262.84	   U11(x0, x1, mark(x2))
743.81/262.84	   U11(active(x0), x1, x2)
743.81/262.84	   U11(x0, active(x1), x2)
743.81/262.84	   U11(x0, x1, active(x2))
743.81/262.84	   U12(mark(x0), x1, x2)
743.81/262.84	   U12(x0, mark(x1), x2)
743.81/262.84	   U12(x0, x1, mark(x2))
743.81/262.84	   U12(active(x0), x1, x2)
743.81/262.84	   U12(x0, active(x1), x2)
743.81/262.84	   U12(x0, x1, active(x2))
743.81/262.84	   U13(mark(x0), x1, x2)
743.81/262.84	   U13(x0, mark(x1), x2)
743.81/262.84	   U13(x0, x1, mark(x2))
743.81/262.84	   U13(active(x0), x1, x2)
743.81/262.84	   U13(x0, active(x1), x2)
743.81/262.84	   U13(x0, x1, active(x2))
743.81/262.84	   U14(mark(x0), x1, x2)
743.81/262.84	   U14(x0, mark(x1), x2)
743.81/262.84	   U14(x0, x1, mark(x2))
743.81/262.84	   U14(active(x0), x1, x2)
743.81/262.84	   U14(x0, active(x1), x2)
743.81/262.84	   U14(x0, x1, active(x2))
743.81/262.84	   U15(mark(x0), x1)
743.81/262.84	   U15(x0, mark(x1))
743.81/262.84	   U15(active(x0), x1)
743.81/262.84	   U15(x0, active(x1))
743.81/262.84	   U16(mark(x0))
743.81/262.84	   U16(active(x0))
743.81/262.84	   U21(mark(x0), x1)
743.81/262.84	   U21(x0, mark(x1))
743.81/262.84	   U21(active(x0), x1)
743.81/262.84	   U21(x0, active(x1))
743.81/262.84	   U22(mark(x0), x1)
743.81/262.84	   U22(x0, mark(x1))
743.81/262.84	   U22(active(x0), x1)
743.81/262.84	   U22(x0, active(x1))
743.81/262.84	   U23(mark(x0))
743.81/262.84	   U23(active(x0))
743.81/262.84	   U31(mark(x0), x1, x2)
743.81/262.84	   U31(x0, mark(x1), x2)
743.81/262.84	   U31(x0, x1, mark(x2))
743.81/262.84	   U31(active(x0), x1, x2)
743.81/262.84	   U31(x0, active(x1), x2)
743.81/262.84	   U31(x0, x1, active(x2))
743.81/262.84	   U32(mark(x0), x1, x2)
743.81/262.84	   U32(x0, mark(x1), x2)
743.81/262.84	   U32(x0, x1, mark(x2))
743.81/262.84	   U32(active(x0), x1, x2)
743.81/262.84	   U32(x0, active(x1), x2)
743.81/262.84	   U32(x0, x1, active(x2))
743.81/262.84	   U33(mark(x0), x1, x2)
743.81/262.84	   U33(x0, mark(x1), x2)
743.81/262.84	   U33(x0, x1, mark(x2))
743.81/262.84	   U33(active(x0), x1, x2)
743.81/262.84	   U33(x0, active(x1), x2)
743.81/262.84	   U33(x0, x1, active(x2))
743.81/262.84	   U34(mark(x0), x1, x2)
743.81/262.84	   U34(x0, mark(x1), x2)
743.81/262.84	   U34(x0, x1, mark(x2))
743.81/262.84	   U34(active(x0), x1, x2)
743.81/262.84	   U34(x0, active(x1), x2)
743.81/262.84	   U34(x0, x1, active(x2))
743.81/262.84	   U35(mark(x0), x1)
743.81/262.84	   U35(x0, mark(x1))
743.81/262.84	   U35(active(x0), x1)
743.81/262.84	   U35(x0, active(x1))
743.81/262.84	   U36(mark(x0))
743.81/262.84	   U36(active(x0))
743.81/262.84	   U41(mark(x0), x1)
743.81/262.84	   U41(x0, mark(x1))
743.81/262.84	   U41(active(x0), x1)
743.81/262.84	   U41(x0, active(x1))
743.81/262.84	   U42(mark(x0))
743.81/262.84	   U42(active(x0))
743.81/262.84	   U51(mark(x0))
743.81/262.84	   U51(active(x0))
743.81/262.84	   U61(mark(x0), x1)
743.81/262.84	   U61(x0, mark(x1))
743.81/262.84	   U61(active(x0), x1)
743.81/262.84	   U61(x0, active(x1))
743.81/262.84	   U62(mark(x0))
743.81/262.84	   U62(active(x0))
743.81/262.84	   U71(mark(x0), x1)
743.81/262.84	   U71(x0, mark(x1))
743.81/262.84	   U71(active(x0), x1)
743.81/262.84	   U71(x0, active(x1))
743.81/262.84	   U72(mark(x0), x1)
743.81/262.84	   U72(x0, mark(x1))
743.81/262.84	   U72(active(x0), x1)
743.81/262.84	   U72(x0, active(x1))
743.98/262.85	   U81(mark(x0), x1, x2)
743.98/262.85	   U81(x0, mark(x1), x2)
743.98/262.85	   U81(x0, x1, mark(x2))
743.98/262.85	   U81(active(x0), x1, x2)
743.98/262.85	   U81(x0, active(x1), x2)
743.98/262.85	   U81(x0, x1, active(x2))
743.98/262.85	   U82(mark(x0), x1, x2)
743.98/262.85	   U82(x0, mark(x1), x2)
743.98/262.85	   U82(x0, x1, mark(x2))
743.98/262.85	   U82(active(x0), x1, x2)
743.98/262.85	   U82(x0, active(x1), x2)
743.98/262.85	   U82(x0, x1, active(x2))
743.98/262.85	   U83(mark(x0), x1, x2)
743.98/262.85	   U83(x0, mark(x1), x2)
743.98/262.85	   U83(x0, x1, mark(x2))
743.98/262.85	   U83(active(x0), x1, x2)
743.98/262.85	   U83(x0, active(x1), x2)
743.98/262.85	   U83(x0, x1, active(x2))
743.98/262.85	   U84(mark(x0), x1, x2)
743.98/262.85	   U84(x0, mark(x1), x2)
743.98/262.85	   U84(x0, x1, mark(x2))
743.98/262.85	   U84(active(x0), x1, x2)
743.98/262.85	   U84(x0, active(x1), x2)
743.98/262.85	   U84(x0, x1, active(x2))
743.98/262.85	   s(mark(x0))
743.98/262.85	   s(active(x0))
743.98/262.85	   U91(mark(x0), x1)
743.98/262.85	   U91(x0, mark(x1))
743.98/262.85	   U91(active(x0), x1)
743.98/262.85	   U91(x0, active(x1))
743.98/262.85	   U92(mark(x0))
743.98/262.85	   U92(active(x0))
743.98/262.85	
743.98/262.85	We have to consider all minimal (P,Q,R)-chains.
743.98/262.85	----------------------------------------
743.98/262.85	
743.98/262.85	(104) UsableRulesProof (EQUIVALENT)
743.98/262.85	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.
743.98/262.85	----------------------------------------
743.98/262.85	
743.98/262.85	(105)
743.98/262.85	Obligation:
743.98/262.85	Q DP problem:
743.98/262.85	The TRS P consists of the following rules:
743.98/262.85	
743.98/262.85	   U36^1(active(X)) -> U36^1(X)
743.98/262.85	   U36^1(mark(X)) -> U36^1(X)
743.98/262.85	
743.98/262.85	R is empty.
743.98/262.85	The set Q consists of the following terms:
743.98/262.85	
743.98/262.85	   active(U101(tt, x0, x1))
743.98/262.85	   active(U102(tt, x0, x1))
743.98/262.85	   active(U103(tt, x0, x1))
743.98/262.85	   active(U104(tt, x0, x1))
743.98/262.85	   active(U11(tt, x0, x1))
743.98/262.85	   active(U12(tt, x0, x1))
743.98/262.85	   active(U13(tt, x0, x1))
743.98/262.85	   active(U14(tt, x0, x1))
743.98/262.85	   active(U15(tt, x0))
743.98/262.85	   active(U16(tt))
743.98/262.85	   active(U21(tt, x0))
743.98/262.85	   active(U22(tt, x0))
743.98/262.85	   active(U23(tt))
743.98/262.85	   active(U31(tt, x0, x1))
743.98/262.85	   active(U32(tt, x0, x1))
743.98/262.85	   active(U33(tt, x0, x1))
743.98/262.85	   active(U34(tt, x0, x1))
743.98/262.85	   active(U35(tt, x0))
743.98/262.85	   active(U36(tt))
743.98/262.85	   active(U41(tt, x0))
743.98/262.85	   active(U42(tt))
743.98/262.85	   active(U51(tt))
743.98/262.85	   active(U61(tt, x0))
743.98/262.85	   active(U62(tt))
743.98/262.85	   active(U71(tt, x0))
743.98/262.85	   active(U72(tt, x0))
743.98/262.85	   active(U81(tt, x0, x1))
743.98/262.85	   active(U82(tt, x0, x1))
743.98/262.85	   active(U83(tt, x0, x1))
743.98/262.85	   active(U84(tt, x0, x1))
743.98/262.85	   active(U91(tt, x0))
743.98/262.85	   active(U92(tt))
743.98/262.85	   active(isNat(0))
743.98/262.85	   active(isNat(plus(x0, x1)))
743.98/262.85	   active(isNat(s(x0)))
743.98/262.85	   active(isNat(x(x0, x1)))
743.98/262.85	   active(isNatKind(0))
743.98/262.85	   active(isNatKind(plus(x0, x1)))
743.98/262.85	   active(isNatKind(s(x0)))
743.98/262.85	   active(isNatKind(x(x0, x1)))
743.98/262.85	   active(plus(x0, 0))
743.98/262.85	   active(plus(x0, s(x1)))
743.98/262.85	   active(x(x0, 0))
743.98/262.85	   active(x(x0, s(x1)))
743.98/262.85	   mark(U101(x0, x1, x2))
743.98/262.85	   mark(tt)
743.98/262.85	   mark(U102(x0, x1, x2))
743.98/262.85	   mark(isNatKind(x0))
743.98/262.85	   mark(U103(x0, x1, x2))
743.98/262.85	   mark(isNat(x0))
743.98/262.85	   mark(U104(x0, x1, x2))
743.98/262.85	   mark(plus(x0, x1))
743.98/262.85	   mark(x(x0, x1))
743.98/262.85	   mark(U11(x0, x1, x2))
743.98/262.85	   mark(U12(x0, x1, x2))
743.98/262.85	   mark(U13(x0, x1, x2))
743.98/262.85	   mark(U14(x0, x1, x2))
743.98/262.85	   mark(U15(x0, x1))
743.98/262.85	   mark(U16(x0))
743.98/262.85	   mark(U21(x0, x1))
743.98/262.85	   mark(U22(x0, x1))
743.98/262.85	   mark(U23(x0))
743.98/262.85	   mark(U31(x0, x1, x2))
743.98/262.85	   mark(U32(x0, x1, x2))
743.98/262.85	   mark(U33(x0, x1, x2))
743.98/262.85	   mark(U34(x0, x1, x2))
743.98/262.85	   mark(U35(x0, x1))
743.98/262.85	   mark(U36(x0))
743.98/262.85	   mark(U41(x0, x1))
743.98/262.85	   mark(U42(x0))
743.98/262.85	   mark(U51(x0))
743.98/262.85	   mark(U61(x0, x1))
743.98/262.85	   mark(U62(x0))
743.98/262.85	   mark(U71(x0, x1))
743.98/262.85	   mark(U72(x0, x1))
743.98/262.85	   mark(U81(x0, x1, x2))
743.98/262.85	   mark(U82(x0, x1, x2))
743.98/262.85	   mark(U83(x0, x1, x2))
743.98/262.85	   mark(U84(x0, x1, x2))
743.98/262.85	   mark(s(x0))
743.98/262.85	   mark(U91(x0, x1))
743.98/262.85	   mark(U92(x0))
743.98/262.85	   mark(0)
743.98/262.85	   U101(mark(x0), x1, x2)
743.98/262.85	   U101(x0, mark(x1), x2)
743.98/262.85	   U101(x0, x1, mark(x2))
743.98/262.85	   U101(active(x0), x1, x2)
743.98/262.85	   U101(x0, active(x1), x2)
743.98/262.85	   U101(x0, x1, active(x2))
743.98/262.85	   U102(mark(x0), x1, x2)
743.98/262.85	   U102(x0, mark(x1), x2)
743.98/262.85	   U102(x0, x1, mark(x2))
743.98/262.85	   U102(active(x0), x1, x2)
743.98/262.85	   U102(x0, active(x1), x2)
743.98/262.85	   U102(x0, x1, active(x2))
743.98/262.85	   isNatKind(mark(x0))
743.98/262.85	   isNatKind(active(x0))
743.98/262.85	   U103(mark(x0), x1, x2)
743.98/262.85	   U103(x0, mark(x1), x2)
743.98/262.85	   U103(x0, x1, mark(x2))
743.98/262.85	   U103(active(x0), x1, x2)
743.98/262.85	   U103(x0, active(x1), x2)
743.98/262.85	   U103(x0, x1, active(x2))
743.98/262.85	   isNat(mark(x0))
743.98/262.85	   isNat(active(x0))
743.98/262.85	   U104(mark(x0), x1, x2)
743.98/262.85	   U104(x0, mark(x1), x2)
743.98/262.85	   U104(x0, x1, mark(x2))
743.98/262.85	   U104(active(x0), x1, x2)
743.98/262.85	   U104(x0, active(x1), x2)
743.98/262.85	   U104(x0, x1, active(x2))
743.98/262.85	   plus(mark(x0), x1)
743.98/262.85	   plus(x0, mark(x1))
743.98/262.85	   plus(active(x0), x1)
743.98/262.85	   plus(x0, active(x1))
743.98/262.85	   x(mark(x0), x1)
743.98/262.85	   x(x0, mark(x1))
743.98/262.85	   x(active(x0), x1)
743.98/262.85	   x(x0, active(x1))
743.98/262.85	   U11(mark(x0), x1, x2)
743.98/262.85	   U11(x0, mark(x1), x2)
743.98/262.85	   U11(x0, x1, mark(x2))
743.98/262.85	   U11(active(x0), x1, x2)
743.98/262.85	   U11(x0, active(x1), x2)
743.98/262.85	   U11(x0, x1, active(x2))
743.98/262.85	   U12(mark(x0), x1, x2)
743.98/262.85	   U12(x0, mark(x1), x2)
743.98/262.85	   U12(x0, x1, mark(x2))
743.98/262.85	   U12(active(x0), x1, x2)
743.98/262.85	   U12(x0, active(x1), x2)
743.98/262.85	   U12(x0, x1, active(x2))
743.98/262.85	   U13(mark(x0), x1, x2)
743.98/262.85	   U13(x0, mark(x1), x2)
743.98/262.85	   U13(x0, x1, mark(x2))
743.98/262.85	   U13(active(x0), x1, x2)
743.98/262.85	   U13(x0, active(x1), x2)
743.98/262.85	   U13(x0, x1, active(x2))
743.98/262.85	   U14(mark(x0), x1, x2)
743.98/262.85	   U14(x0, mark(x1), x2)
743.98/262.85	   U14(x0, x1, mark(x2))
743.98/262.85	   U14(active(x0), x1, x2)
743.98/262.85	   U14(x0, active(x1), x2)
743.98/262.85	   U14(x0, x1, active(x2))
743.98/262.85	   U15(mark(x0), x1)
743.98/262.85	   U15(x0, mark(x1))
743.98/262.85	   U15(active(x0), x1)
743.98/262.85	   U15(x0, active(x1))
743.98/262.85	   U16(mark(x0))
743.98/262.85	   U16(active(x0))
743.98/262.85	   U21(mark(x0), x1)
743.98/262.85	   U21(x0, mark(x1))
743.98/262.85	   U21(active(x0), x1)
743.98/262.85	   U21(x0, active(x1))
743.98/262.85	   U22(mark(x0), x1)
743.98/262.85	   U22(x0, mark(x1))
743.98/262.85	   U22(active(x0), x1)
743.98/262.85	   U22(x0, active(x1))
743.98/262.85	   U23(mark(x0))
743.98/262.85	   U23(active(x0))
744.01/262.85	   U31(mark(x0), x1, x2)
744.01/262.85	   U31(x0, mark(x1), x2)
744.01/262.85	   U31(x0, x1, mark(x2))
744.01/262.85	   U31(active(x0), x1, x2)
744.01/262.85	   U31(x0, active(x1), x2)
744.01/262.85	   U31(x0, x1, active(x2))
744.01/262.85	   U32(mark(x0), x1, x2)
744.01/262.85	   U32(x0, mark(x1), x2)
744.01/262.85	   U32(x0, x1, mark(x2))
744.01/262.85	   U32(active(x0), x1, x2)
744.01/262.85	   U32(x0, active(x1), x2)
744.01/262.85	   U32(x0, x1, active(x2))
744.01/262.85	   U33(mark(x0), x1, x2)
744.01/262.85	   U33(x0, mark(x1), x2)
744.01/262.85	   U33(x0, x1, mark(x2))
744.01/262.85	   U33(active(x0), x1, x2)
744.01/262.85	   U33(x0, active(x1), x2)
744.01/262.85	   U33(x0, x1, active(x2))
744.01/262.85	   U34(mark(x0), x1, x2)
744.01/262.85	   U34(x0, mark(x1), x2)
744.01/262.85	   U34(x0, x1, mark(x2))
744.01/262.85	   U34(active(x0), x1, x2)
744.01/262.85	   U34(x0, active(x1), x2)
744.01/262.85	   U34(x0, x1, active(x2))
744.01/262.85	   U35(mark(x0), x1)
744.01/262.85	   U35(x0, mark(x1))
744.01/262.85	   U35(active(x0), x1)
744.01/262.85	   U35(x0, active(x1))
744.01/262.85	   U36(mark(x0))
744.01/262.85	   U36(active(x0))
744.01/262.85	   U41(mark(x0), x1)
744.01/262.85	   U41(x0, mark(x1))
744.01/262.85	   U41(active(x0), x1)
744.01/262.85	   U41(x0, active(x1))
744.01/262.85	   U42(mark(x0))
744.01/262.85	   U42(active(x0))
744.01/262.85	   U51(mark(x0))
744.01/262.85	   U51(active(x0))
744.01/262.85	   U61(mark(x0), x1)
744.01/262.85	   U61(x0, mark(x1))
744.01/262.85	   U61(active(x0), x1)
744.01/262.85	   U61(x0, active(x1))
744.01/262.85	   U62(mark(x0))
744.01/262.85	   U62(active(x0))
744.01/262.85	   U71(mark(x0), x1)
744.01/262.85	   U71(x0, mark(x1))
744.01/262.85	   U71(active(x0), x1)
744.01/262.85	   U71(x0, active(x1))
744.01/262.85	   U72(mark(x0), x1)
744.01/262.85	   U72(x0, mark(x1))
744.01/262.85	   U72(active(x0), x1)
744.01/262.85	   U72(x0, active(x1))
744.01/262.85	   U81(mark(x0), x1, x2)
744.01/262.85	   U81(x0, mark(x1), x2)
744.01/262.85	   U81(x0, x1, mark(x2))
744.01/262.85	   U81(active(x0), x1, x2)
744.01/262.85	   U81(x0, active(x1), x2)
744.01/262.85	   U81(x0, x1, active(x2))
744.01/262.85	   U82(mark(x0), x1, x2)
744.01/262.85	   U82(x0, mark(x1), x2)
744.01/262.85	   U82(x0, x1, mark(x2))
744.01/262.85	   U82(active(x0), x1, x2)
744.01/262.85	   U82(x0, active(x1), x2)
744.01/262.85	   U82(x0, x1, active(x2))
744.01/262.85	   U83(mark(x0), x1, x2)
744.01/262.85	   U83(x0, mark(x1), x2)
744.01/262.85	   U83(x0, x1, mark(x2))
744.01/262.85	   U83(active(x0), x1, x2)
744.01/262.85	   U83(x0, active(x1), x2)
744.01/262.85	   U83(x0, x1, active(x2))
744.01/262.85	   U84(mark(x0), x1, x2)
744.01/262.85	   U84(x0, mark(x1), x2)
744.01/262.85	   U84(x0, x1, mark(x2))
744.01/262.85	   U84(active(x0), x1, x2)
744.01/262.85	   U84(x0, active(x1), x2)
744.01/262.85	   U84(x0, x1, active(x2))
744.01/262.85	   s(mark(x0))
744.01/262.85	   s(active(x0))
744.01/262.85	   U91(mark(x0), x1)
744.01/262.85	   U91(x0, mark(x1))
744.01/262.85	   U91(active(x0), x1)
744.01/262.85	   U91(x0, active(x1))
744.01/262.85	   U92(mark(x0))
744.01/262.85	   U92(active(x0))
744.01/262.85	
744.01/262.85	We have to consider all minimal (P,Q,R)-chains.
744.01/262.85	----------------------------------------
744.01/262.85	
744.01/262.85	(106) QReductionProof (EQUIVALENT)
744.01/262.85	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.85	
744.01/262.85	   U101(mark(x0), x1, x2)
744.01/262.85	   U101(x0, mark(x1), x2)
744.01/262.85	   U101(x0, x1, mark(x2))
744.01/262.85	   U101(active(x0), x1, x2)
744.01/262.85	   U101(x0, active(x1), x2)
744.01/262.85	   U101(x0, x1, active(x2))
744.01/262.85	   U102(mark(x0), x1, x2)
744.01/262.85	   U102(x0, mark(x1), x2)
744.01/262.85	   U102(x0, x1, mark(x2))
744.01/262.85	   U102(active(x0), x1, x2)
744.01/262.85	   U102(x0, active(x1), x2)
744.01/262.85	   U102(x0, x1, active(x2))
744.01/262.85	   isNatKind(mark(x0))
744.01/262.85	   isNatKind(active(x0))
744.01/262.85	   U103(mark(x0), x1, x2)
744.01/262.85	   U103(x0, mark(x1), x2)
744.01/262.85	   U103(x0, x1, mark(x2))
744.01/262.85	   U103(active(x0), x1, x2)
744.01/262.85	   U103(x0, active(x1), x2)
744.01/262.85	   U103(x0, x1, active(x2))
744.01/262.85	   isNat(mark(x0))
744.01/262.85	   isNat(active(x0))
744.01/262.85	   U104(mark(x0), x1, x2)
744.01/262.85	   U104(x0, mark(x1), x2)
744.01/262.85	   U104(x0, x1, mark(x2))
744.01/262.85	   U104(active(x0), x1, x2)
744.01/262.85	   U104(x0, active(x1), x2)
744.01/262.85	   U104(x0, x1, active(x2))
744.01/262.85	   plus(mark(x0), x1)
744.01/262.85	   plus(x0, mark(x1))
744.01/262.85	   plus(active(x0), x1)
744.01/262.85	   plus(x0, active(x1))
744.01/262.85	   x(mark(x0), x1)
744.01/262.85	   x(x0, mark(x1))
744.01/262.85	   x(active(x0), x1)
744.01/262.85	   x(x0, active(x1))
744.01/262.85	   U11(mark(x0), x1, x2)
744.01/262.85	   U11(x0, mark(x1), x2)
744.01/262.85	   U11(x0, x1, mark(x2))
744.01/262.85	   U11(active(x0), x1, x2)
744.01/262.85	   U11(x0, active(x1), x2)
744.01/262.85	   U11(x0, x1, active(x2))
744.01/262.85	   U12(mark(x0), x1, x2)
744.01/262.85	   U12(x0, mark(x1), x2)
744.01/262.85	   U12(x0, x1, mark(x2))
744.01/262.85	   U12(active(x0), x1, x2)
744.01/262.85	   U12(x0, active(x1), x2)
744.01/262.85	   U12(x0, x1, active(x2))
744.01/262.85	   U13(mark(x0), x1, x2)
744.01/262.85	   U13(x0, mark(x1), x2)
744.01/262.85	   U13(x0, x1, mark(x2))
744.01/262.85	   U13(active(x0), x1, x2)
744.01/262.85	   U13(x0, active(x1), x2)
744.01/262.85	   U13(x0, x1, active(x2))
744.01/262.85	   U14(mark(x0), x1, x2)
744.01/262.85	   U14(x0, mark(x1), x2)
744.01/262.85	   U14(x0, x1, mark(x2))
744.01/262.85	   U14(active(x0), x1, x2)
744.01/262.85	   U14(x0, active(x1), x2)
744.01/262.85	   U14(x0, x1, active(x2))
744.01/262.85	   U15(mark(x0), x1)
744.01/262.85	   U15(x0, mark(x1))
744.01/262.85	   U15(active(x0), x1)
744.01/262.85	   U15(x0, active(x1))
744.01/262.85	   U16(mark(x0))
744.01/262.85	   U16(active(x0))
744.01/262.85	   U21(mark(x0), x1)
744.01/262.85	   U21(x0, mark(x1))
744.01/262.85	   U21(active(x0), x1)
744.01/262.85	   U21(x0, active(x1))
744.01/262.85	   U22(mark(x0), x1)
744.01/262.85	   U22(x0, mark(x1))
744.01/262.85	   U22(active(x0), x1)
744.01/262.85	   U22(x0, active(x1))
744.01/262.85	   U23(mark(x0))
744.01/262.85	   U23(active(x0))
744.01/262.85	   U31(mark(x0), x1, x2)
744.01/262.85	   U31(x0, mark(x1), x2)
744.01/262.85	   U31(x0, x1, mark(x2))
744.01/262.85	   U31(active(x0), x1, x2)
744.01/262.85	   U31(x0, active(x1), x2)
744.01/262.85	   U31(x0, x1, active(x2))
744.01/262.85	   U32(mark(x0), x1, x2)
744.01/262.85	   U32(x0, mark(x1), x2)
744.01/262.85	   U32(x0, x1, mark(x2))
744.01/262.85	   U32(active(x0), x1, x2)
744.01/262.85	   U32(x0, active(x1), x2)
744.01/262.85	   U32(x0, x1, active(x2))
744.01/262.85	   U33(mark(x0), x1, x2)
744.01/262.85	   U33(x0, mark(x1), x2)
744.01/262.85	   U33(x0, x1, mark(x2))
744.01/262.85	   U33(active(x0), x1, x2)
744.01/262.85	   U33(x0, active(x1), x2)
744.01/262.85	   U33(x0, x1, active(x2))
744.01/262.85	   U34(mark(x0), x1, x2)
744.01/262.85	   U34(x0, mark(x1), x2)
744.01/262.85	   U34(x0, x1, mark(x2))
744.01/262.85	   U34(active(x0), x1, x2)
744.01/262.85	   U34(x0, active(x1), x2)
744.01/262.85	   U34(x0, x1, active(x2))
744.01/262.85	   U35(mark(x0), x1)
744.01/262.85	   U35(x0, mark(x1))
744.01/262.85	   U35(active(x0), x1)
744.01/262.85	   U35(x0, active(x1))
744.01/262.85	   U36(mark(x0))
744.01/262.85	   U36(active(x0))
744.01/262.85	   U41(mark(x0), x1)
744.01/262.85	   U41(x0, mark(x1))
744.01/262.85	   U41(active(x0), x1)
744.01/262.85	   U41(x0, active(x1))
744.01/262.85	   U42(mark(x0))
744.01/262.85	   U42(active(x0))
744.01/262.85	   U51(mark(x0))
744.01/262.85	   U51(active(x0))
744.01/262.85	   U61(mark(x0), x1)
744.01/262.85	   U61(x0, mark(x1))
744.01/262.85	   U61(active(x0), x1)
744.01/262.85	   U61(x0, active(x1))
744.01/262.85	   U62(mark(x0))
744.01/262.85	   U62(active(x0))
744.01/262.85	   U71(mark(x0), x1)
744.01/262.85	   U71(x0, mark(x1))
744.01/262.85	   U71(active(x0), x1)
744.01/262.85	   U71(x0, active(x1))
744.01/262.85	   U72(mark(x0), x1)
744.01/262.85	   U72(x0, mark(x1))
744.01/262.85	   U72(active(x0), x1)
744.01/262.85	   U72(x0, active(x1))
744.01/262.85	   U81(mark(x0), x1, x2)
744.01/262.85	   U81(x0, mark(x1), x2)
744.01/262.85	   U81(x0, x1, mark(x2))
744.01/262.85	   U81(active(x0), x1, x2)
744.01/262.85	   U81(x0, active(x1), x2)
744.01/262.85	   U81(x0, x1, active(x2))
744.01/262.85	   U82(mark(x0), x1, x2)
744.01/262.85	   U82(x0, mark(x1), x2)
744.01/262.85	   U82(x0, x1, mark(x2))
744.01/262.85	   U82(active(x0), x1, x2)
744.01/262.85	   U82(x0, active(x1), x2)
744.01/262.85	   U82(x0, x1, active(x2))
744.01/262.85	   U83(mark(x0), x1, x2)
744.01/262.85	   U83(x0, mark(x1), x2)
744.01/262.85	   U83(x0, x1, mark(x2))
744.01/262.85	   U83(active(x0), x1, x2)
744.01/262.85	   U83(x0, active(x1), x2)
744.01/262.85	   U83(x0, x1, active(x2))
744.01/262.85	   U84(mark(x0), x1, x2)
744.01/262.85	   U84(x0, mark(x1), x2)
744.01/262.85	   U84(x0, x1, mark(x2))
744.01/262.85	   U84(active(x0), x1, x2)
744.01/262.85	   U84(x0, active(x1), x2)
744.01/262.85	   U84(x0, x1, active(x2))
744.01/262.85	   s(mark(x0))
744.01/262.85	   s(active(x0))
744.01/262.85	   U91(mark(x0), x1)
744.01/262.85	   U91(x0, mark(x1))
744.01/262.85	   U91(active(x0), x1)
744.01/262.85	   U91(x0, active(x1))
744.01/262.85	   U92(mark(x0))
744.01/262.85	   U92(active(x0))
744.01/262.85	
744.01/262.85	
744.01/262.85	----------------------------------------
744.01/262.85	
744.01/262.85	(107)
744.01/262.85	Obligation:
744.01/262.85	Q DP problem:
744.01/262.85	The TRS P consists of the following rules:
744.01/262.85	
744.01/262.85	   U36^1(active(X)) -> U36^1(X)
744.01/262.85	   U36^1(mark(X)) -> U36^1(X)
744.01/262.85	
744.01/262.85	R is empty.
744.01/262.85	The set Q consists of the following terms:
744.01/262.85	
744.01/262.85	   active(U101(tt, x0, x1))
744.01/262.85	   active(U102(tt, x0, x1))
744.01/262.85	   active(U103(tt, x0, x1))
744.01/262.85	   active(U104(tt, x0, x1))
744.01/262.85	   active(U11(tt, x0, x1))
744.01/262.85	   active(U12(tt, x0, x1))
744.01/262.85	   active(U13(tt, x0, x1))
744.01/262.85	   active(U14(tt, x0, x1))
744.01/262.85	   active(U15(tt, x0))
744.01/262.85	   active(U16(tt))
744.01/262.85	   active(U21(tt, x0))
744.01/262.85	   active(U22(tt, x0))
744.01/262.85	   active(U23(tt))
744.01/262.85	   active(U31(tt, x0, x1))
744.01/262.85	   active(U32(tt, x0, x1))
744.01/262.85	   active(U33(tt, x0, x1))
744.01/262.85	   active(U34(tt, x0, x1))
744.01/262.85	   active(U35(tt, x0))
744.01/262.85	   active(U36(tt))
744.01/262.85	   active(U41(tt, x0))
744.01/262.85	   active(U42(tt))
744.01/262.85	   active(U51(tt))
744.01/262.85	   active(U61(tt, x0))
744.01/262.85	   active(U62(tt))
744.01/262.85	   active(U71(tt, x0))
744.01/262.85	   active(U72(tt, x0))
744.01/262.85	   active(U81(tt, x0, x1))
744.01/262.85	   active(U82(tt, x0, x1))
744.01/262.85	   active(U83(tt, x0, x1))
744.01/262.85	   active(U84(tt, x0, x1))
744.01/262.85	   active(U91(tt, x0))
744.01/262.85	   active(U92(tt))
744.01/262.85	   active(isNat(0))
744.01/262.85	   active(isNat(plus(x0, x1)))
744.01/262.85	   active(isNat(s(x0)))
744.01/262.85	   active(isNat(x(x0, x1)))
744.01/262.85	   active(isNatKind(0))
744.01/262.85	   active(isNatKind(plus(x0, x1)))
744.01/262.85	   active(isNatKind(s(x0)))
744.01/262.85	   active(isNatKind(x(x0, x1)))
744.01/262.85	   active(plus(x0, 0))
744.01/262.85	   active(plus(x0, s(x1)))
744.01/262.85	   active(x(x0, 0))
744.01/262.85	   active(x(x0, s(x1)))
744.01/262.85	   mark(U101(x0, x1, x2))
744.01/262.85	   mark(tt)
744.01/262.85	   mark(U102(x0, x1, x2))
744.01/262.85	   mark(isNatKind(x0))
744.01/262.85	   mark(U103(x0, x1, x2))
744.01/262.85	   mark(isNat(x0))
744.01/262.85	   mark(U104(x0, x1, x2))
744.01/262.85	   mark(plus(x0, x1))
744.01/262.85	   mark(x(x0, x1))
744.01/262.85	   mark(U11(x0, x1, x2))
744.01/262.85	   mark(U12(x0, x1, x2))
744.01/262.85	   mark(U13(x0, x1, x2))
744.01/262.85	   mark(U14(x0, x1, x2))
744.01/262.85	   mark(U15(x0, x1))
744.01/262.85	   mark(U16(x0))
744.01/262.85	   mark(U21(x0, x1))
744.01/262.85	   mark(U22(x0, x1))
744.01/262.85	   mark(U23(x0))
744.01/262.85	   mark(U31(x0, x1, x2))
744.01/262.85	   mark(U32(x0, x1, x2))
744.01/262.85	   mark(U33(x0, x1, x2))
744.01/262.85	   mark(U34(x0, x1, x2))
744.01/262.85	   mark(U35(x0, x1))
744.01/262.85	   mark(U36(x0))
744.01/262.85	   mark(U41(x0, x1))
744.01/262.85	   mark(U42(x0))
744.01/262.85	   mark(U51(x0))
744.01/262.85	   mark(U61(x0, x1))
744.01/262.85	   mark(U62(x0))
744.01/262.85	   mark(U71(x0, x1))
744.01/262.85	   mark(U72(x0, x1))
744.01/262.85	   mark(U81(x0, x1, x2))
744.01/262.85	   mark(U82(x0, x1, x2))
744.01/262.85	   mark(U83(x0, x1, x2))
744.01/262.85	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(108) QDPSizeChangeProof (EQUIVALENT)
744.01/262.86	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. 
744.01/262.86	
744.01/262.86	From the DPs we obtained the following set of size-change graphs:
744.01/262.86	*U36^1(active(X)) -> U36^1(X)
744.01/262.86	The graph contains the following edges 1 > 1
744.01/262.86	
744.01/262.86	
744.01/262.86	*U36^1(mark(X)) -> U36^1(X)
744.01/262.86	The graph contains the following edges 1 > 1
744.01/262.86	
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(109)
744.01/262.86	YES
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(110)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U35^1(X1, mark(X2)) -> U35^1(X1, X2)
744.01/262.86	   U35^1(mark(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(active(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(X1, active(X2)) -> U35^1(X1, X2)
744.01/262.86	
744.01/262.86	The TRS R consists of the following rules:
744.01/262.86	
744.01/262.86	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.86	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.86	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.86	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.86	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.86	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.86	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.86	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.86	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.86	   active(U16(tt)) -> mark(tt)
744.01/262.86	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.86	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.86	   active(U23(tt)) -> mark(tt)
744.01/262.86	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.86	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.86	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.86	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.86	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.86	   active(U36(tt)) -> mark(tt)
744.01/262.86	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.86	   active(U42(tt)) -> mark(tt)
744.01/262.86	   active(U51(tt)) -> mark(tt)
744.01/262.86	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.86	   active(U62(tt)) -> mark(tt)
744.01/262.86	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.86	   active(U72(tt, N)) -> mark(N)
744.01/262.86	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.86	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.86	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.86	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.86	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.86	   active(U92(tt)) -> mark(0)
744.01/262.86	   active(isNat(0)) -> mark(tt)
744.01/262.86	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.86	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.86	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.86	   active(isNatKind(0)) -> mark(tt)
744.01/262.86	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.86	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.86	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.86	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.86	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.86	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.86	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.86	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.86	   mark(tt) -> active(tt)
744.01/262.86	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.86	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.86	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.86	   mark(isNat(X)) -> active(isNat(X))
744.01/262.86	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.86	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.86	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.86	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.86	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.86	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.86	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.86	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.86	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.86	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.86	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.86	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.86	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.86	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.86	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.86	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.86	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.86	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.86	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.86	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.86	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.86	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.86	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.86	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.86	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.86	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.86	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.86	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.86	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.86	   mark(s(X)) -> active(s(mark(X)))
744.01/262.86	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.86	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.86	   mark(0) -> active(0)
744.01/262.86	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.86	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.86	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.86	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.86	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.86	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.86	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.86	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.86	   isNat(mark(X)) -> isNat(X)
744.01/262.86	   isNat(active(X)) -> isNat(X)
744.01/262.86	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.86	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.86	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.86	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.86	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.86	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.86	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.86	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.86	   x(active(X1), X2) -> x(X1, X2)
744.01/262.86	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.86	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.86	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.86	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.86	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.86	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.86	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.86	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.86	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.86	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.86	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.86	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.86	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.86	   U16(mark(X)) -> U16(X)
744.01/262.86	   U16(active(X)) -> U16(X)
744.01/262.86	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.86	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.86	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.86	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.86	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.86	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.86	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.86	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.86	   U23(mark(X)) -> U23(X)
744.01/262.86	   U23(active(X)) -> U23(X)
744.01/262.86	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.86	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.86	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.86	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.86	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.86	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.86	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.86	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.86	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.86	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.86	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.86	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.86	   U36(mark(X)) -> U36(X)
744.01/262.86	   U36(active(X)) -> U36(X)
744.01/262.86	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.86	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.86	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.86	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.86	   U42(mark(X)) -> U42(X)
744.01/262.86	   U42(active(X)) -> U42(X)
744.01/262.86	   U51(mark(X)) -> U51(X)
744.01/262.86	   U51(active(X)) -> U51(X)
744.01/262.86	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.86	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.86	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.86	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.86	   U62(mark(X)) -> U62(X)
744.01/262.86	   U62(active(X)) -> U62(X)
744.01/262.86	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.86	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.86	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.86	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.86	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.86	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.86	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.86	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.86	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.86	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.86	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.86	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.86	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.86	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.86	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.86	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.86	   s(mark(X)) -> s(X)
744.01/262.86	   s(active(X)) -> s(X)
744.01/262.86	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.86	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.86	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.86	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.86	   U92(mark(X)) -> U92(X)
744.01/262.86	   U92(active(X)) -> U92(X)
744.01/262.86	
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.86	   active(U14(tt, x0, x1))
744.01/262.86	   active(U15(tt, x0))
744.01/262.86	   active(U16(tt))
744.01/262.86	   active(U21(tt, x0))
744.01/262.86	   active(U22(tt, x0))
744.01/262.86	   active(U23(tt))
744.01/262.86	   active(U31(tt, x0, x1))
744.01/262.86	   active(U32(tt, x0, x1))
744.01/262.86	   active(U33(tt, x0, x1))
744.01/262.86	   active(U34(tt, x0, x1))
744.01/262.86	   active(U35(tt, x0))
744.01/262.86	   active(U36(tt))
744.01/262.86	   active(U41(tt, x0))
744.01/262.86	   active(U42(tt))
744.01/262.86	   active(U51(tt))
744.01/262.86	   active(U61(tt, x0))
744.01/262.86	   active(U62(tt))
744.01/262.86	   active(U71(tt, x0))
744.01/262.86	   active(U72(tt, x0))
744.01/262.86	   active(U81(tt, x0, x1))
744.01/262.86	   active(U82(tt, x0, x1))
744.01/262.86	   active(U83(tt, x0, x1))
744.01/262.86	   active(U84(tt, x0, x1))
744.01/262.86	   active(U91(tt, x0))
744.01/262.86	   active(U92(tt))
744.01/262.86	   active(isNat(0))
744.01/262.86	   active(isNat(plus(x0, x1)))
744.01/262.86	   active(isNat(s(x0)))
744.01/262.86	   active(isNat(x(x0, x1)))
744.01/262.86	   active(isNatKind(0))
744.01/262.86	   active(isNatKind(plus(x0, x1)))
744.01/262.86	   active(isNatKind(s(x0)))
744.01/262.86	   active(isNatKind(x(x0, x1)))
744.01/262.86	   active(plus(x0, 0))
744.01/262.86	   active(plus(x0, s(x1)))
744.01/262.86	   active(x(x0, 0))
744.01/262.86	   active(x(x0, s(x1)))
744.01/262.86	   mark(U101(x0, x1, x2))
744.01/262.86	   mark(tt)
744.01/262.86	   mark(U102(x0, x1, x2))
744.01/262.86	   mark(isNatKind(x0))
744.01/262.86	   mark(U103(x0, x1, x2))
744.01/262.86	   mark(isNat(x0))
744.01/262.86	   mark(U104(x0, x1, x2))
744.01/262.86	   mark(plus(x0, x1))
744.01/262.86	   mark(x(x0, x1))
744.01/262.86	   mark(U11(x0, x1, x2))
744.01/262.86	   mark(U12(x0, x1, x2))
744.01/262.86	   mark(U13(x0, x1, x2))
744.01/262.86	   mark(U14(x0, x1, x2))
744.01/262.86	   mark(U15(x0, x1))
744.01/262.86	   mark(U16(x0))
744.01/262.86	   mark(U21(x0, x1))
744.01/262.86	   mark(U22(x0, x1))
744.01/262.86	   mark(U23(x0))
744.01/262.86	   mark(U31(x0, x1, x2))
744.01/262.86	   mark(U32(x0, x1, x2))
744.01/262.86	   mark(U33(x0, x1, x2))
744.01/262.86	   mark(U34(x0, x1, x2))
744.01/262.86	   mark(U35(x0, x1))
744.01/262.86	   mark(U36(x0))
744.01/262.86	   mark(U41(x0, x1))
744.01/262.86	   mark(U42(x0))
744.01/262.86	   mark(U51(x0))
744.01/262.86	   mark(U61(x0, x1))
744.01/262.86	   mark(U62(x0))
744.01/262.86	   mark(U71(x0, x1))
744.01/262.86	   mark(U72(x0, x1))
744.01/262.86	   mark(U81(x0, x1, x2))
744.01/262.86	   mark(U82(x0, x1, x2))
744.01/262.86	   mark(U83(x0, x1, x2))
744.01/262.86	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(111) UsableRulesProof (EQUIVALENT)
744.01/262.86	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.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(112)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U35^1(X1, mark(X2)) -> U35^1(X1, X2)
744.01/262.86	   U35^1(mark(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(active(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(X1, active(X2)) -> U35^1(X1, X2)
744.01/262.86	
744.01/262.86	R is empty.
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.86	   active(U14(tt, x0, x1))
744.01/262.86	   active(U15(tt, x0))
744.01/262.86	   active(U16(tt))
744.01/262.86	   active(U21(tt, x0))
744.01/262.86	   active(U22(tt, x0))
744.01/262.86	   active(U23(tt))
744.01/262.86	   active(U31(tt, x0, x1))
744.01/262.86	   active(U32(tt, x0, x1))
744.01/262.86	   active(U33(tt, x0, x1))
744.01/262.86	   active(U34(tt, x0, x1))
744.01/262.86	   active(U35(tt, x0))
744.01/262.86	   active(U36(tt))
744.01/262.86	   active(U41(tt, x0))
744.01/262.86	   active(U42(tt))
744.01/262.86	   active(U51(tt))
744.01/262.86	   active(U61(tt, x0))
744.01/262.86	   active(U62(tt))
744.01/262.86	   active(U71(tt, x0))
744.01/262.86	   active(U72(tt, x0))
744.01/262.86	   active(U81(tt, x0, x1))
744.01/262.86	   active(U82(tt, x0, x1))
744.01/262.86	   active(U83(tt, x0, x1))
744.01/262.86	   active(U84(tt, x0, x1))
744.01/262.86	   active(U91(tt, x0))
744.01/262.86	   active(U92(tt))
744.01/262.86	   active(isNat(0))
744.01/262.86	   active(isNat(plus(x0, x1)))
744.01/262.86	   active(isNat(s(x0)))
744.01/262.86	   active(isNat(x(x0, x1)))
744.01/262.86	   active(isNatKind(0))
744.01/262.86	   active(isNatKind(plus(x0, x1)))
744.01/262.86	   active(isNatKind(s(x0)))
744.01/262.86	   active(isNatKind(x(x0, x1)))
744.01/262.86	   active(plus(x0, 0))
744.01/262.86	   active(plus(x0, s(x1)))
744.01/262.86	   active(x(x0, 0))
744.01/262.86	   active(x(x0, s(x1)))
744.01/262.86	   mark(U101(x0, x1, x2))
744.01/262.86	   mark(tt)
744.01/262.86	   mark(U102(x0, x1, x2))
744.01/262.86	   mark(isNatKind(x0))
744.01/262.86	   mark(U103(x0, x1, x2))
744.01/262.86	   mark(isNat(x0))
744.01/262.86	   mark(U104(x0, x1, x2))
744.01/262.86	   mark(plus(x0, x1))
744.01/262.86	   mark(x(x0, x1))
744.01/262.86	   mark(U11(x0, x1, x2))
744.01/262.86	   mark(U12(x0, x1, x2))
744.01/262.86	   mark(U13(x0, x1, x2))
744.01/262.86	   mark(U14(x0, x1, x2))
744.01/262.86	   mark(U15(x0, x1))
744.01/262.86	   mark(U16(x0))
744.01/262.86	   mark(U21(x0, x1))
744.01/262.86	   mark(U22(x0, x1))
744.01/262.86	   mark(U23(x0))
744.01/262.86	   mark(U31(x0, x1, x2))
744.01/262.86	   mark(U32(x0, x1, x2))
744.01/262.86	   mark(U33(x0, x1, x2))
744.01/262.86	   mark(U34(x0, x1, x2))
744.01/262.86	   mark(U35(x0, x1))
744.01/262.86	   mark(U36(x0))
744.01/262.86	   mark(U41(x0, x1))
744.01/262.86	   mark(U42(x0))
744.01/262.86	   mark(U51(x0))
744.01/262.86	   mark(U61(x0, x1))
744.01/262.86	   mark(U62(x0))
744.01/262.86	   mark(U71(x0, x1))
744.01/262.86	   mark(U72(x0, x1))
744.01/262.86	   mark(U81(x0, x1, x2))
744.01/262.86	   mark(U82(x0, x1, x2))
744.01/262.86	   mark(U83(x0, x1, x2))
744.01/262.86	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(113) QReductionProof (EQUIVALENT)
744.01/262.86	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.86	
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(114)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U35^1(X1, mark(X2)) -> U35^1(X1, X2)
744.01/262.86	   U35^1(mark(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(active(X1), X2) -> U35^1(X1, X2)
744.01/262.86	   U35^1(X1, active(X2)) -> U35^1(X1, X2)
744.01/262.86	
744.01/262.86	R is empty.
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.86	   active(U14(tt, x0, x1))
744.01/262.86	   active(U15(tt, x0))
744.01/262.86	   active(U16(tt))
744.01/262.86	   active(U21(tt, x0))
744.01/262.86	   active(U22(tt, x0))
744.01/262.86	   active(U23(tt))
744.01/262.86	   active(U31(tt, x0, x1))
744.01/262.86	   active(U32(tt, x0, x1))
744.01/262.86	   active(U33(tt, x0, x1))
744.01/262.86	   active(U34(tt, x0, x1))
744.01/262.86	   active(U35(tt, x0))
744.01/262.86	   active(U36(tt))
744.01/262.86	   active(U41(tt, x0))
744.01/262.86	   active(U42(tt))
744.01/262.86	   active(U51(tt))
744.01/262.86	   active(U61(tt, x0))
744.01/262.86	   active(U62(tt))
744.01/262.86	   active(U71(tt, x0))
744.01/262.86	   active(U72(tt, x0))
744.01/262.86	   active(U81(tt, x0, x1))
744.01/262.86	   active(U82(tt, x0, x1))
744.01/262.86	   active(U83(tt, x0, x1))
744.01/262.86	   active(U84(tt, x0, x1))
744.01/262.86	   active(U91(tt, x0))
744.01/262.86	   active(U92(tt))
744.01/262.86	   active(isNat(0))
744.01/262.86	   active(isNat(plus(x0, x1)))
744.01/262.86	   active(isNat(s(x0)))
744.01/262.86	   active(isNat(x(x0, x1)))
744.01/262.86	   active(isNatKind(0))
744.01/262.86	   active(isNatKind(plus(x0, x1)))
744.01/262.86	   active(isNatKind(s(x0)))
744.01/262.86	   active(isNatKind(x(x0, x1)))
744.01/262.86	   active(plus(x0, 0))
744.01/262.86	   active(plus(x0, s(x1)))
744.01/262.86	   active(x(x0, 0))
744.01/262.86	   active(x(x0, s(x1)))
744.01/262.86	   mark(U101(x0, x1, x2))
744.01/262.86	   mark(tt)
744.01/262.86	   mark(U102(x0, x1, x2))
744.01/262.86	   mark(isNatKind(x0))
744.01/262.86	   mark(U103(x0, x1, x2))
744.01/262.86	   mark(isNat(x0))
744.01/262.86	   mark(U104(x0, x1, x2))
744.01/262.86	   mark(plus(x0, x1))
744.01/262.86	   mark(x(x0, x1))
744.01/262.86	   mark(U11(x0, x1, x2))
744.01/262.86	   mark(U12(x0, x1, x2))
744.01/262.86	   mark(U13(x0, x1, x2))
744.01/262.86	   mark(U14(x0, x1, x2))
744.01/262.86	   mark(U15(x0, x1))
744.01/262.86	   mark(U16(x0))
744.01/262.86	   mark(U21(x0, x1))
744.01/262.86	   mark(U22(x0, x1))
744.01/262.86	   mark(U23(x0))
744.01/262.86	   mark(U31(x0, x1, x2))
744.01/262.86	   mark(U32(x0, x1, x2))
744.01/262.86	   mark(U33(x0, x1, x2))
744.01/262.86	   mark(U34(x0, x1, x2))
744.01/262.86	   mark(U35(x0, x1))
744.01/262.86	   mark(U36(x0))
744.01/262.86	   mark(U41(x0, x1))
744.01/262.86	   mark(U42(x0))
744.01/262.86	   mark(U51(x0))
744.01/262.86	   mark(U61(x0, x1))
744.01/262.86	   mark(U62(x0))
744.01/262.86	   mark(U71(x0, x1))
744.01/262.86	   mark(U72(x0, x1))
744.01/262.86	   mark(U81(x0, x1, x2))
744.01/262.86	   mark(U82(x0, x1, x2))
744.01/262.86	   mark(U83(x0, x1, x2))
744.01/262.86	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(115) QDPSizeChangeProof (EQUIVALENT)
744.01/262.86	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. 
744.01/262.86	
744.01/262.86	From the DPs we obtained the following set of size-change graphs:
744.01/262.86	*U35^1(X1, mark(X2)) -> U35^1(X1, X2)
744.01/262.86	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.86	
744.01/262.86	
744.01/262.86	*U35^1(mark(X1), X2) -> U35^1(X1, X2)
744.01/262.86	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.86	
744.01/262.86	
744.01/262.86	*U35^1(active(X1), X2) -> U35^1(X1, X2)
744.01/262.86	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.86	
744.01/262.86	
744.01/262.86	*U35^1(X1, active(X2)) -> U35^1(X1, X2)
744.01/262.86	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.86	
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(116)
744.01/262.86	YES
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(117)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U34^1(X1, mark(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(mark(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, mark(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(active(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, active(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, active(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	
744.01/262.86	The TRS R consists of the following rules:
744.01/262.86	
744.01/262.86	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.86	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.86	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.86	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.86	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.86	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.86	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.86	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.86	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.86	   active(U16(tt)) -> mark(tt)
744.01/262.86	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.86	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.86	   active(U23(tt)) -> mark(tt)
744.01/262.86	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.86	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.86	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.86	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.86	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.86	   active(U36(tt)) -> mark(tt)
744.01/262.86	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.86	   active(U42(tt)) -> mark(tt)
744.01/262.86	   active(U51(tt)) -> mark(tt)
744.01/262.86	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.86	   active(U62(tt)) -> mark(tt)
744.01/262.86	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.86	   active(U72(tt, N)) -> mark(N)
744.01/262.86	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.86	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.86	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.86	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.86	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.86	   active(U92(tt)) -> mark(0)
744.01/262.86	   active(isNat(0)) -> mark(tt)
744.01/262.86	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.86	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.86	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.86	   active(isNatKind(0)) -> mark(tt)
744.01/262.86	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.86	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.86	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.86	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.86	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.86	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.86	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.86	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.86	   mark(tt) -> active(tt)
744.01/262.86	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.86	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.86	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.86	   mark(isNat(X)) -> active(isNat(X))
744.01/262.86	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.86	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.86	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.86	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.86	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.86	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.86	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.86	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.86	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.86	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.86	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.86	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.86	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.86	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.86	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.86	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.86	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.86	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.86	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.86	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.86	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.86	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.86	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.86	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.86	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.86	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.86	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.86	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.86	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.86	   mark(s(X)) -> active(s(mark(X)))
744.01/262.86	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.86	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.86	   mark(0) -> active(0)
744.01/262.86	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.86	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.86	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.86	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.86	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.86	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.86	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.86	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.86	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.86	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.86	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.86	   isNat(mark(X)) -> isNat(X)
744.01/262.86	   isNat(active(X)) -> isNat(X)
744.01/262.86	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.86	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.86	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.86	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.86	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.86	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.86	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.86	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.86	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.86	   x(active(X1), X2) -> x(X1, X2)
744.01/262.86	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.86	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.86	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.86	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.86	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.86	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.86	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.86	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.86	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.86	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.86	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.86	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.86	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.86	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.86	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.86	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.86	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.86	   U16(mark(X)) -> U16(X)
744.01/262.86	   U16(active(X)) -> U16(X)
744.01/262.86	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.86	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.86	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.86	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.86	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.86	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.86	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.86	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.86	   U23(mark(X)) -> U23(X)
744.01/262.86	   U23(active(X)) -> U23(X)
744.01/262.86	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.86	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.86	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.86	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.86	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.86	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.86	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.86	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.86	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.86	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.86	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.86	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.86	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.86	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.86	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.86	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.86	   U36(mark(X)) -> U36(X)
744.01/262.86	   U36(active(X)) -> U36(X)
744.01/262.86	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.86	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.86	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.86	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.86	   U42(mark(X)) -> U42(X)
744.01/262.86	   U42(active(X)) -> U42(X)
744.01/262.86	   U51(mark(X)) -> U51(X)
744.01/262.86	   U51(active(X)) -> U51(X)
744.01/262.86	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.86	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.86	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.86	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.86	   U62(mark(X)) -> U62(X)
744.01/262.86	   U62(active(X)) -> U62(X)
744.01/262.86	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.86	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.86	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.86	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.86	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.86	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.86	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.86	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.86	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.86	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.86	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.86	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.86	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.86	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.86	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.86	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.86	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.86	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.86	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.86	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.86	   s(mark(X)) -> s(X)
744.01/262.86	   s(active(X)) -> s(X)
744.01/262.86	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.86	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.86	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.86	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.86	   U92(mark(X)) -> U92(X)
744.01/262.86	   U92(active(X)) -> U92(X)
744.01/262.86	
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.86	   active(U14(tt, x0, x1))
744.01/262.86	   active(U15(tt, x0))
744.01/262.86	   active(U16(tt))
744.01/262.86	   active(U21(tt, x0))
744.01/262.86	   active(U22(tt, x0))
744.01/262.86	   active(U23(tt))
744.01/262.86	   active(U31(tt, x0, x1))
744.01/262.86	   active(U32(tt, x0, x1))
744.01/262.86	   active(U33(tt, x0, x1))
744.01/262.86	   active(U34(tt, x0, x1))
744.01/262.86	   active(U35(tt, x0))
744.01/262.86	   active(U36(tt))
744.01/262.86	   active(U41(tt, x0))
744.01/262.86	   active(U42(tt))
744.01/262.86	   active(U51(tt))
744.01/262.86	   active(U61(tt, x0))
744.01/262.86	   active(U62(tt))
744.01/262.86	   active(U71(tt, x0))
744.01/262.86	   active(U72(tt, x0))
744.01/262.86	   active(U81(tt, x0, x1))
744.01/262.86	   active(U82(tt, x0, x1))
744.01/262.86	   active(U83(tt, x0, x1))
744.01/262.86	   active(U84(tt, x0, x1))
744.01/262.86	   active(U91(tt, x0))
744.01/262.86	   active(U92(tt))
744.01/262.86	   active(isNat(0))
744.01/262.86	   active(isNat(plus(x0, x1)))
744.01/262.86	   active(isNat(s(x0)))
744.01/262.86	   active(isNat(x(x0, x1)))
744.01/262.86	   active(isNatKind(0))
744.01/262.86	   active(isNatKind(plus(x0, x1)))
744.01/262.86	   active(isNatKind(s(x0)))
744.01/262.86	   active(isNatKind(x(x0, x1)))
744.01/262.86	   active(plus(x0, 0))
744.01/262.86	   active(plus(x0, s(x1)))
744.01/262.86	   active(x(x0, 0))
744.01/262.86	   active(x(x0, s(x1)))
744.01/262.86	   mark(U101(x0, x1, x2))
744.01/262.86	   mark(tt)
744.01/262.86	   mark(U102(x0, x1, x2))
744.01/262.86	   mark(isNatKind(x0))
744.01/262.86	   mark(U103(x0, x1, x2))
744.01/262.86	   mark(isNat(x0))
744.01/262.86	   mark(U104(x0, x1, x2))
744.01/262.86	   mark(plus(x0, x1))
744.01/262.86	   mark(x(x0, x1))
744.01/262.86	   mark(U11(x0, x1, x2))
744.01/262.86	   mark(U12(x0, x1, x2))
744.01/262.86	   mark(U13(x0, x1, x2))
744.01/262.86	   mark(U14(x0, x1, x2))
744.01/262.86	   mark(U15(x0, x1))
744.01/262.86	   mark(U16(x0))
744.01/262.86	   mark(U21(x0, x1))
744.01/262.86	   mark(U22(x0, x1))
744.01/262.86	   mark(U23(x0))
744.01/262.86	   mark(U31(x0, x1, x2))
744.01/262.86	   mark(U32(x0, x1, x2))
744.01/262.86	   mark(U33(x0, x1, x2))
744.01/262.86	   mark(U34(x0, x1, x2))
744.01/262.86	   mark(U35(x0, x1))
744.01/262.86	   mark(U36(x0))
744.01/262.86	   mark(U41(x0, x1))
744.01/262.86	   mark(U42(x0))
744.01/262.86	   mark(U51(x0))
744.01/262.86	   mark(U61(x0, x1))
744.01/262.86	   mark(U62(x0))
744.01/262.86	   mark(U71(x0, x1))
744.01/262.86	   mark(U72(x0, x1))
744.01/262.86	   mark(U81(x0, x1, x2))
744.01/262.86	   mark(U82(x0, x1, x2))
744.01/262.86	   mark(U83(x0, x1, x2))
744.01/262.86	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(118) UsableRulesProof (EQUIVALENT)
744.01/262.86	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.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(119)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U34^1(X1, mark(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(mark(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, mark(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(active(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, active(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, active(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	
744.01/262.86	R is empty.
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.86	   active(U14(tt, x0, x1))
744.01/262.86	   active(U15(tt, x0))
744.01/262.86	   active(U16(tt))
744.01/262.86	   active(U21(tt, x0))
744.01/262.86	   active(U22(tt, x0))
744.01/262.86	   active(U23(tt))
744.01/262.86	   active(U31(tt, x0, x1))
744.01/262.86	   active(U32(tt, x0, x1))
744.01/262.86	   active(U33(tt, x0, x1))
744.01/262.86	   active(U34(tt, x0, x1))
744.01/262.86	   active(U35(tt, x0))
744.01/262.86	   active(U36(tt))
744.01/262.86	   active(U41(tt, x0))
744.01/262.86	   active(U42(tt))
744.01/262.86	   active(U51(tt))
744.01/262.86	   active(U61(tt, x0))
744.01/262.86	   active(U62(tt))
744.01/262.86	   active(U71(tt, x0))
744.01/262.86	   active(U72(tt, x0))
744.01/262.86	   active(U81(tt, x0, x1))
744.01/262.86	   active(U82(tt, x0, x1))
744.01/262.86	   active(U83(tt, x0, x1))
744.01/262.86	   active(U84(tt, x0, x1))
744.01/262.86	   active(U91(tt, x0))
744.01/262.86	   active(U92(tt))
744.01/262.86	   active(isNat(0))
744.01/262.86	   active(isNat(plus(x0, x1)))
744.01/262.86	   active(isNat(s(x0)))
744.01/262.86	   active(isNat(x(x0, x1)))
744.01/262.86	   active(isNatKind(0))
744.01/262.86	   active(isNatKind(plus(x0, x1)))
744.01/262.86	   active(isNatKind(s(x0)))
744.01/262.86	   active(isNatKind(x(x0, x1)))
744.01/262.86	   active(plus(x0, 0))
744.01/262.86	   active(plus(x0, s(x1)))
744.01/262.86	   active(x(x0, 0))
744.01/262.86	   active(x(x0, s(x1)))
744.01/262.86	   mark(U101(x0, x1, x2))
744.01/262.86	   mark(tt)
744.01/262.86	   mark(U102(x0, x1, x2))
744.01/262.86	   mark(isNatKind(x0))
744.01/262.86	   mark(U103(x0, x1, x2))
744.01/262.86	   mark(isNat(x0))
744.01/262.86	   mark(U104(x0, x1, x2))
744.01/262.86	   mark(plus(x0, x1))
744.01/262.86	   mark(x(x0, x1))
744.01/262.86	   mark(U11(x0, x1, x2))
744.01/262.86	   mark(U12(x0, x1, x2))
744.01/262.86	   mark(U13(x0, x1, x2))
744.01/262.86	   mark(U14(x0, x1, x2))
744.01/262.86	   mark(U15(x0, x1))
744.01/262.86	   mark(U16(x0))
744.01/262.86	   mark(U21(x0, x1))
744.01/262.86	   mark(U22(x0, x1))
744.01/262.86	   mark(U23(x0))
744.01/262.86	   mark(U31(x0, x1, x2))
744.01/262.86	   mark(U32(x0, x1, x2))
744.01/262.86	   mark(U33(x0, x1, x2))
744.01/262.86	   mark(U34(x0, x1, x2))
744.01/262.86	   mark(U35(x0, x1))
744.01/262.86	   mark(U36(x0))
744.01/262.86	   mark(U41(x0, x1))
744.01/262.86	   mark(U42(x0))
744.01/262.86	   mark(U51(x0))
744.01/262.86	   mark(U61(x0, x1))
744.01/262.86	   mark(U62(x0))
744.01/262.86	   mark(U71(x0, x1))
744.01/262.86	   mark(U72(x0, x1))
744.01/262.86	   mark(U81(x0, x1, x2))
744.01/262.86	   mark(U82(x0, x1, x2))
744.01/262.86	   mark(U83(x0, x1, x2))
744.01/262.86	   mark(U84(x0, x1, x2))
744.01/262.86	   mark(s(x0))
744.01/262.86	   mark(U91(x0, x1))
744.01/262.86	   mark(U92(x0))
744.01/262.86	   mark(0)
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	We have to consider all minimal (P,Q,R)-chains.
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(120) QReductionProof (EQUIVALENT)
744.01/262.86	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.86	
744.01/262.86	   U101(mark(x0), x1, x2)
744.01/262.86	   U101(x0, mark(x1), x2)
744.01/262.86	   U101(x0, x1, mark(x2))
744.01/262.86	   U101(active(x0), x1, x2)
744.01/262.86	   U101(x0, active(x1), x2)
744.01/262.86	   U101(x0, x1, active(x2))
744.01/262.86	   U102(mark(x0), x1, x2)
744.01/262.86	   U102(x0, mark(x1), x2)
744.01/262.86	   U102(x0, x1, mark(x2))
744.01/262.86	   U102(active(x0), x1, x2)
744.01/262.86	   U102(x0, active(x1), x2)
744.01/262.86	   U102(x0, x1, active(x2))
744.01/262.86	   isNatKind(mark(x0))
744.01/262.86	   isNatKind(active(x0))
744.01/262.86	   U103(mark(x0), x1, x2)
744.01/262.86	   U103(x0, mark(x1), x2)
744.01/262.86	   U103(x0, x1, mark(x2))
744.01/262.86	   U103(active(x0), x1, x2)
744.01/262.86	   U103(x0, active(x1), x2)
744.01/262.86	   U103(x0, x1, active(x2))
744.01/262.86	   isNat(mark(x0))
744.01/262.86	   isNat(active(x0))
744.01/262.86	   U104(mark(x0), x1, x2)
744.01/262.86	   U104(x0, mark(x1), x2)
744.01/262.86	   U104(x0, x1, mark(x2))
744.01/262.86	   U104(active(x0), x1, x2)
744.01/262.86	   U104(x0, active(x1), x2)
744.01/262.86	   U104(x0, x1, active(x2))
744.01/262.86	   plus(mark(x0), x1)
744.01/262.86	   plus(x0, mark(x1))
744.01/262.86	   plus(active(x0), x1)
744.01/262.86	   plus(x0, active(x1))
744.01/262.86	   x(mark(x0), x1)
744.01/262.86	   x(x0, mark(x1))
744.01/262.86	   x(active(x0), x1)
744.01/262.86	   x(x0, active(x1))
744.01/262.86	   U11(mark(x0), x1, x2)
744.01/262.86	   U11(x0, mark(x1), x2)
744.01/262.86	   U11(x0, x1, mark(x2))
744.01/262.86	   U11(active(x0), x1, x2)
744.01/262.86	   U11(x0, active(x1), x2)
744.01/262.86	   U11(x0, x1, active(x2))
744.01/262.86	   U12(mark(x0), x1, x2)
744.01/262.86	   U12(x0, mark(x1), x2)
744.01/262.86	   U12(x0, x1, mark(x2))
744.01/262.86	   U12(active(x0), x1, x2)
744.01/262.86	   U12(x0, active(x1), x2)
744.01/262.86	   U12(x0, x1, active(x2))
744.01/262.86	   U13(mark(x0), x1, x2)
744.01/262.86	   U13(x0, mark(x1), x2)
744.01/262.86	   U13(x0, x1, mark(x2))
744.01/262.86	   U13(active(x0), x1, x2)
744.01/262.86	   U13(x0, active(x1), x2)
744.01/262.86	   U13(x0, x1, active(x2))
744.01/262.86	   U14(mark(x0), x1, x2)
744.01/262.86	   U14(x0, mark(x1), x2)
744.01/262.86	   U14(x0, x1, mark(x2))
744.01/262.86	   U14(active(x0), x1, x2)
744.01/262.86	   U14(x0, active(x1), x2)
744.01/262.86	   U14(x0, x1, active(x2))
744.01/262.86	   U15(mark(x0), x1)
744.01/262.86	   U15(x0, mark(x1))
744.01/262.86	   U15(active(x0), x1)
744.01/262.86	   U15(x0, active(x1))
744.01/262.86	   U16(mark(x0))
744.01/262.86	   U16(active(x0))
744.01/262.86	   U21(mark(x0), x1)
744.01/262.86	   U21(x0, mark(x1))
744.01/262.86	   U21(active(x0), x1)
744.01/262.86	   U21(x0, active(x1))
744.01/262.86	   U22(mark(x0), x1)
744.01/262.86	   U22(x0, mark(x1))
744.01/262.86	   U22(active(x0), x1)
744.01/262.86	   U22(x0, active(x1))
744.01/262.86	   U23(mark(x0))
744.01/262.86	   U23(active(x0))
744.01/262.86	   U31(mark(x0), x1, x2)
744.01/262.86	   U31(x0, mark(x1), x2)
744.01/262.86	   U31(x0, x1, mark(x2))
744.01/262.86	   U31(active(x0), x1, x2)
744.01/262.86	   U31(x0, active(x1), x2)
744.01/262.86	   U31(x0, x1, active(x2))
744.01/262.86	   U32(mark(x0), x1, x2)
744.01/262.86	   U32(x0, mark(x1), x2)
744.01/262.86	   U32(x0, x1, mark(x2))
744.01/262.86	   U32(active(x0), x1, x2)
744.01/262.86	   U32(x0, active(x1), x2)
744.01/262.86	   U32(x0, x1, active(x2))
744.01/262.86	   U33(mark(x0), x1, x2)
744.01/262.86	   U33(x0, mark(x1), x2)
744.01/262.86	   U33(x0, x1, mark(x2))
744.01/262.86	   U33(active(x0), x1, x2)
744.01/262.86	   U33(x0, active(x1), x2)
744.01/262.86	   U33(x0, x1, active(x2))
744.01/262.86	   U34(mark(x0), x1, x2)
744.01/262.86	   U34(x0, mark(x1), x2)
744.01/262.86	   U34(x0, x1, mark(x2))
744.01/262.86	   U34(active(x0), x1, x2)
744.01/262.86	   U34(x0, active(x1), x2)
744.01/262.86	   U34(x0, x1, active(x2))
744.01/262.86	   U35(mark(x0), x1)
744.01/262.86	   U35(x0, mark(x1))
744.01/262.86	   U35(active(x0), x1)
744.01/262.86	   U35(x0, active(x1))
744.01/262.86	   U36(mark(x0))
744.01/262.86	   U36(active(x0))
744.01/262.86	   U41(mark(x0), x1)
744.01/262.86	   U41(x0, mark(x1))
744.01/262.86	   U41(active(x0), x1)
744.01/262.86	   U41(x0, active(x1))
744.01/262.86	   U42(mark(x0))
744.01/262.86	   U42(active(x0))
744.01/262.86	   U51(mark(x0))
744.01/262.86	   U51(active(x0))
744.01/262.86	   U61(mark(x0), x1)
744.01/262.86	   U61(x0, mark(x1))
744.01/262.86	   U61(active(x0), x1)
744.01/262.86	   U61(x0, active(x1))
744.01/262.86	   U62(mark(x0))
744.01/262.86	   U62(active(x0))
744.01/262.86	   U71(mark(x0), x1)
744.01/262.86	   U71(x0, mark(x1))
744.01/262.86	   U71(active(x0), x1)
744.01/262.86	   U71(x0, active(x1))
744.01/262.86	   U72(mark(x0), x1)
744.01/262.86	   U72(x0, mark(x1))
744.01/262.86	   U72(active(x0), x1)
744.01/262.86	   U72(x0, active(x1))
744.01/262.86	   U81(mark(x0), x1, x2)
744.01/262.86	   U81(x0, mark(x1), x2)
744.01/262.86	   U81(x0, x1, mark(x2))
744.01/262.86	   U81(active(x0), x1, x2)
744.01/262.86	   U81(x0, active(x1), x2)
744.01/262.86	   U81(x0, x1, active(x2))
744.01/262.86	   U82(mark(x0), x1, x2)
744.01/262.86	   U82(x0, mark(x1), x2)
744.01/262.86	   U82(x0, x1, mark(x2))
744.01/262.86	   U82(active(x0), x1, x2)
744.01/262.86	   U82(x0, active(x1), x2)
744.01/262.86	   U82(x0, x1, active(x2))
744.01/262.86	   U83(mark(x0), x1, x2)
744.01/262.86	   U83(x0, mark(x1), x2)
744.01/262.86	   U83(x0, x1, mark(x2))
744.01/262.86	   U83(active(x0), x1, x2)
744.01/262.86	   U83(x0, active(x1), x2)
744.01/262.86	   U83(x0, x1, active(x2))
744.01/262.86	   U84(mark(x0), x1, x2)
744.01/262.86	   U84(x0, mark(x1), x2)
744.01/262.86	   U84(x0, x1, mark(x2))
744.01/262.86	   U84(active(x0), x1, x2)
744.01/262.86	   U84(x0, active(x1), x2)
744.01/262.86	   U84(x0, x1, active(x2))
744.01/262.86	   s(mark(x0))
744.01/262.86	   s(active(x0))
744.01/262.86	   U91(mark(x0), x1)
744.01/262.86	   U91(x0, mark(x1))
744.01/262.86	   U91(active(x0), x1)
744.01/262.86	   U91(x0, active(x1))
744.01/262.86	   U92(mark(x0))
744.01/262.86	   U92(active(x0))
744.01/262.86	
744.01/262.86	
744.01/262.86	----------------------------------------
744.01/262.86	
744.01/262.86	(121)
744.01/262.86	Obligation:
744.01/262.86	Q DP problem:
744.01/262.86	The TRS P consists of the following rules:
744.01/262.86	
744.01/262.86	   U34^1(X1, mark(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(mark(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, mark(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(active(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, active(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.86	   U34^1(X1, X2, active(X3)) -> U34^1(X1, X2, X3)
744.01/262.86	
744.01/262.86	R is empty.
744.01/262.86	The set Q consists of the following terms:
744.01/262.86	
744.01/262.86	   active(U101(tt, x0, x1))
744.01/262.86	   active(U102(tt, x0, x1))
744.01/262.86	   active(U103(tt, x0, x1))
744.01/262.86	   active(U104(tt, x0, x1))
744.01/262.86	   active(U11(tt, x0, x1))
744.01/262.86	   active(U12(tt, x0, x1))
744.01/262.86	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(122) QDPSizeChangeProof (EQUIVALENT)
744.01/262.87	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. 
744.01/262.87	
744.01/262.87	From the DPs we obtained the following set of size-change graphs:
744.01/262.87	*U34^1(X1, mark(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U34^1(mark(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U34^1(X1, X2, mark(X3)) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U34^1(active(X1), X2, X3) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U34^1(X1, active(X2), X3) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U34^1(X1, X2, active(X3)) -> U34^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.87	
744.01/262.87	
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(123)
744.01/262.87	YES
744.01/262.87	
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(124)
744.01/262.87	Obligation:
744.01/262.87	Q DP problem:
744.01/262.87	The TRS P consists of the following rules:
744.01/262.87	
744.01/262.87	   U33^1(X1, mark(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(mark(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, mark(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(active(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, active(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, active(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	
744.01/262.87	The TRS R consists of the following rules:
744.01/262.87	
744.01/262.87	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.87	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.87	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.87	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.87	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.87	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.87	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.87	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.87	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.87	   active(U16(tt)) -> mark(tt)
744.01/262.87	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.87	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.87	   active(U23(tt)) -> mark(tt)
744.01/262.87	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.87	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.87	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.87	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.87	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.87	   active(U36(tt)) -> mark(tt)
744.01/262.87	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.87	   active(U42(tt)) -> mark(tt)
744.01/262.87	   active(U51(tt)) -> mark(tt)
744.01/262.87	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.87	   active(U62(tt)) -> mark(tt)
744.01/262.87	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.87	   active(U72(tt, N)) -> mark(N)
744.01/262.87	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.87	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.87	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.87	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.87	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.87	   active(U92(tt)) -> mark(0)
744.01/262.87	   active(isNat(0)) -> mark(tt)
744.01/262.87	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.87	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.87	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.87	   active(isNatKind(0)) -> mark(tt)
744.01/262.87	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.87	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.87	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.87	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.87	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.87	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.87	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.87	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.87	   mark(tt) -> active(tt)
744.01/262.87	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.87	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.87	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.87	   mark(isNat(X)) -> active(isNat(X))
744.01/262.87	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.87	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.87	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.87	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.87	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.87	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.87	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.87	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.87	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.87	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.87	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.87	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.87	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.87	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.87	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.87	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.87	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.87	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.87	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.87	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.87	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.87	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.87	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.87	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.87	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.87	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.87	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.87	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.87	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.87	   mark(s(X)) -> active(s(mark(X)))
744.01/262.87	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.87	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.87	   mark(0) -> active(0)
744.01/262.87	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.87	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.87	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.87	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.87	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.87	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.87	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.87	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.87	   isNat(mark(X)) -> isNat(X)
744.01/262.87	   isNat(active(X)) -> isNat(X)
744.01/262.87	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.87	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.87	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.87	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.87	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.87	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.87	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.87	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.87	   x(active(X1), X2) -> x(X1, X2)
744.01/262.87	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.87	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.87	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.87	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.87	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.87	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.87	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.87	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.87	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.87	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.87	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.87	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.87	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.87	   U16(mark(X)) -> U16(X)
744.01/262.87	   U16(active(X)) -> U16(X)
744.01/262.87	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.87	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.87	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.87	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.87	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.87	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.87	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.87	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.87	   U23(mark(X)) -> U23(X)
744.01/262.87	   U23(active(X)) -> U23(X)
744.01/262.87	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.87	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.87	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.87	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.87	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.87	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.87	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.87	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.87	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.87	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.87	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.87	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.87	   U36(mark(X)) -> U36(X)
744.01/262.87	   U36(active(X)) -> U36(X)
744.01/262.87	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.87	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.87	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.87	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.87	   U42(mark(X)) -> U42(X)
744.01/262.87	   U42(active(X)) -> U42(X)
744.01/262.87	   U51(mark(X)) -> U51(X)
744.01/262.87	   U51(active(X)) -> U51(X)
744.01/262.87	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.87	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.87	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.87	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.87	   U62(mark(X)) -> U62(X)
744.01/262.87	   U62(active(X)) -> U62(X)
744.01/262.87	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.87	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.87	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.87	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.87	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.87	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.87	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.87	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.87	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.87	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.87	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.87	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.87	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.87	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.87	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.87	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.87	   s(mark(X)) -> s(X)
744.01/262.87	   s(active(X)) -> s(X)
744.01/262.87	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.87	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.87	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.87	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.87	   U92(mark(X)) -> U92(X)
744.01/262.87	   U92(active(X)) -> U92(X)
744.01/262.87	
744.01/262.87	The set Q consists of the following terms:
744.01/262.87	
744.01/262.87	   active(U101(tt, x0, x1))
744.01/262.87	   active(U102(tt, x0, x1))
744.01/262.87	   active(U103(tt, x0, x1))
744.01/262.87	   active(U104(tt, x0, x1))
744.01/262.87	   active(U11(tt, x0, x1))
744.01/262.87	   active(U12(tt, x0, x1))
744.01/262.87	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.87	   U16(active(x0))
744.01/262.87	   U21(mark(x0), x1)
744.01/262.87	   U21(x0, mark(x1))
744.01/262.87	   U21(active(x0), x1)
744.01/262.87	   U21(x0, active(x1))
744.01/262.87	   U22(mark(x0), x1)
744.01/262.87	   U22(x0, mark(x1))
744.01/262.87	   U22(active(x0), x1)
744.01/262.87	   U22(x0, active(x1))
744.01/262.87	   U23(mark(x0))
744.01/262.87	   U23(active(x0))
744.01/262.87	   U31(mark(x0), x1, x2)
744.01/262.87	   U31(x0, mark(x1), x2)
744.01/262.87	   U31(x0, x1, mark(x2))
744.01/262.87	   U31(active(x0), x1, x2)
744.01/262.87	   U31(x0, active(x1), x2)
744.01/262.87	   U31(x0, x1, active(x2))
744.01/262.87	   U32(mark(x0), x1, x2)
744.01/262.87	   U32(x0, mark(x1), x2)
744.01/262.87	   U32(x0, x1, mark(x2))
744.01/262.87	   U32(active(x0), x1, x2)
744.01/262.87	   U32(x0, active(x1), x2)
744.01/262.87	   U32(x0, x1, active(x2))
744.01/262.87	   U33(mark(x0), x1, x2)
744.01/262.87	   U33(x0, mark(x1), x2)
744.01/262.87	   U33(x0, x1, mark(x2))
744.01/262.87	   U33(active(x0), x1, x2)
744.01/262.87	   U33(x0, active(x1), x2)
744.01/262.87	   U33(x0, x1, active(x2))
744.01/262.87	   U34(mark(x0), x1, x2)
744.01/262.87	   U34(x0, mark(x1), x2)
744.01/262.87	   U34(x0, x1, mark(x2))
744.01/262.87	   U34(active(x0), x1, x2)
744.01/262.87	   U34(x0, active(x1), x2)
744.01/262.87	   U34(x0, x1, active(x2))
744.01/262.87	   U35(mark(x0), x1)
744.01/262.87	   U35(x0, mark(x1))
744.01/262.87	   U35(active(x0), x1)
744.01/262.87	   U35(x0, active(x1))
744.01/262.87	   U36(mark(x0))
744.01/262.87	   U36(active(x0))
744.01/262.87	   U41(mark(x0), x1)
744.01/262.87	   U41(x0, mark(x1))
744.01/262.87	   U41(active(x0), x1)
744.01/262.87	   U41(x0, active(x1))
744.01/262.87	   U42(mark(x0))
744.01/262.87	   U42(active(x0))
744.01/262.87	   U51(mark(x0))
744.01/262.87	   U51(active(x0))
744.01/262.87	   U61(mark(x0), x1)
744.01/262.87	   U61(x0, mark(x1))
744.01/262.87	   U61(active(x0), x1)
744.01/262.87	   U61(x0, active(x1))
744.01/262.87	   U62(mark(x0))
744.01/262.87	   U62(active(x0))
744.01/262.87	   U71(mark(x0), x1)
744.01/262.87	   U71(x0, mark(x1))
744.01/262.87	   U71(active(x0), x1)
744.01/262.87	   U71(x0, active(x1))
744.01/262.87	   U72(mark(x0), x1)
744.01/262.87	   U72(x0, mark(x1))
744.01/262.87	   U72(active(x0), x1)
744.01/262.87	   U72(x0, active(x1))
744.01/262.87	   U81(mark(x0), x1, x2)
744.01/262.87	   U81(x0, mark(x1), x2)
744.01/262.87	   U81(x0, x1, mark(x2))
744.01/262.87	   U81(active(x0), x1, x2)
744.01/262.87	   U81(x0, active(x1), x2)
744.01/262.87	   U81(x0, x1, active(x2))
744.01/262.87	   U82(mark(x0), x1, x2)
744.01/262.87	   U82(x0, mark(x1), x2)
744.01/262.87	   U82(x0, x1, mark(x2))
744.01/262.87	   U82(active(x0), x1, x2)
744.01/262.87	   U82(x0, active(x1), x2)
744.01/262.87	   U82(x0, x1, active(x2))
744.01/262.87	   U83(mark(x0), x1, x2)
744.01/262.87	   U83(x0, mark(x1), x2)
744.01/262.87	   U83(x0, x1, mark(x2))
744.01/262.87	   U83(active(x0), x1, x2)
744.01/262.87	   U83(x0, active(x1), x2)
744.01/262.87	   U83(x0, x1, active(x2))
744.01/262.87	   U84(mark(x0), x1, x2)
744.01/262.87	   U84(x0, mark(x1), x2)
744.01/262.87	   U84(x0, x1, mark(x2))
744.01/262.87	   U84(active(x0), x1, x2)
744.01/262.87	   U84(x0, active(x1), x2)
744.01/262.87	   U84(x0, x1, active(x2))
744.01/262.87	   s(mark(x0))
744.01/262.87	   s(active(x0))
744.01/262.87	   U91(mark(x0), x1)
744.01/262.87	   U91(x0, mark(x1))
744.01/262.87	   U91(active(x0), x1)
744.01/262.87	   U91(x0, active(x1))
744.01/262.87	   U92(mark(x0))
744.01/262.87	   U92(active(x0))
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(125) UsableRulesProof (EQUIVALENT)
744.01/262.87	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.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(126)
744.01/262.87	Obligation:
744.01/262.87	Q DP problem:
744.01/262.87	The TRS P consists of the following rules:
744.01/262.87	
744.01/262.87	   U33^1(X1, mark(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(mark(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, mark(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(active(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, active(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, active(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	
744.01/262.87	R is empty.
744.01/262.87	The set Q consists of the following terms:
744.01/262.87	
744.01/262.87	   active(U101(tt, x0, x1))
744.01/262.87	   active(U102(tt, x0, x1))
744.01/262.87	   active(U103(tt, x0, x1))
744.01/262.87	   active(U104(tt, x0, x1))
744.01/262.87	   active(U11(tt, x0, x1))
744.01/262.87	   active(U12(tt, x0, x1))
744.01/262.87	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.87	   U16(active(x0))
744.01/262.87	   U21(mark(x0), x1)
744.01/262.87	   U21(x0, mark(x1))
744.01/262.87	   U21(active(x0), x1)
744.01/262.87	   U21(x0, active(x1))
744.01/262.87	   U22(mark(x0), x1)
744.01/262.87	   U22(x0, mark(x1))
744.01/262.87	   U22(active(x0), x1)
744.01/262.87	   U22(x0, active(x1))
744.01/262.87	   U23(mark(x0))
744.01/262.87	   U23(active(x0))
744.01/262.87	   U31(mark(x0), x1, x2)
744.01/262.87	   U31(x0, mark(x1), x2)
744.01/262.87	   U31(x0, x1, mark(x2))
744.01/262.87	   U31(active(x0), x1, x2)
744.01/262.87	   U31(x0, active(x1), x2)
744.01/262.87	   U31(x0, x1, active(x2))
744.01/262.87	   U32(mark(x0), x1, x2)
744.01/262.87	   U32(x0, mark(x1), x2)
744.01/262.87	   U32(x0, x1, mark(x2))
744.01/262.87	   U32(active(x0), x1, x2)
744.01/262.87	   U32(x0, active(x1), x2)
744.01/262.87	   U32(x0, x1, active(x2))
744.01/262.87	   U33(mark(x0), x1, x2)
744.01/262.87	   U33(x0, mark(x1), x2)
744.01/262.87	   U33(x0, x1, mark(x2))
744.01/262.87	   U33(active(x0), x1, x2)
744.01/262.87	   U33(x0, active(x1), x2)
744.01/262.87	   U33(x0, x1, active(x2))
744.01/262.87	   U34(mark(x0), x1, x2)
744.01/262.87	   U34(x0, mark(x1), x2)
744.01/262.87	   U34(x0, x1, mark(x2))
744.01/262.87	   U34(active(x0), x1, x2)
744.01/262.87	   U34(x0, active(x1), x2)
744.01/262.87	   U34(x0, x1, active(x2))
744.01/262.87	   U35(mark(x0), x1)
744.01/262.87	   U35(x0, mark(x1))
744.01/262.87	   U35(active(x0), x1)
744.01/262.87	   U35(x0, active(x1))
744.01/262.87	   U36(mark(x0))
744.01/262.87	   U36(active(x0))
744.01/262.87	   U41(mark(x0), x1)
744.01/262.87	   U41(x0, mark(x1))
744.01/262.87	   U41(active(x0), x1)
744.01/262.87	   U41(x0, active(x1))
744.01/262.87	   U42(mark(x0))
744.01/262.87	   U42(active(x0))
744.01/262.87	   U51(mark(x0))
744.01/262.87	   U51(active(x0))
744.01/262.87	   U61(mark(x0), x1)
744.01/262.87	   U61(x0, mark(x1))
744.01/262.87	   U61(active(x0), x1)
744.01/262.87	   U61(x0, active(x1))
744.01/262.87	   U62(mark(x0))
744.01/262.87	   U62(active(x0))
744.01/262.87	   U71(mark(x0), x1)
744.01/262.87	   U71(x0, mark(x1))
744.01/262.87	   U71(active(x0), x1)
744.01/262.87	   U71(x0, active(x1))
744.01/262.87	   U72(mark(x0), x1)
744.01/262.87	   U72(x0, mark(x1))
744.01/262.87	   U72(active(x0), x1)
744.01/262.87	   U72(x0, active(x1))
744.01/262.87	   U81(mark(x0), x1, x2)
744.01/262.87	   U81(x0, mark(x1), x2)
744.01/262.87	   U81(x0, x1, mark(x2))
744.01/262.87	   U81(active(x0), x1, x2)
744.01/262.87	   U81(x0, active(x1), x2)
744.01/262.87	   U81(x0, x1, active(x2))
744.01/262.87	   U82(mark(x0), x1, x2)
744.01/262.87	   U82(x0, mark(x1), x2)
744.01/262.87	   U82(x0, x1, mark(x2))
744.01/262.87	   U82(active(x0), x1, x2)
744.01/262.87	   U82(x0, active(x1), x2)
744.01/262.87	   U82(x0, x1, active(x2))
744.01/262.87	   U83(mark(x0), x1, x2)
744.01/262.87	   U83(x0, mark(x1), x2)
744.01/262.87	   U83(x0, x1, mark(x2))
744.01/262.87	   U83(active(x0), x1, x2)
744.01/262.87	   U83(x0, active(x1), x2)
744.01/262.87	   U83(x0, x1, active(x2))
744.01/262.87	   U84(mark(x0), x1, x2)
744.01/262.87	   U84(x0, mark(x1), x2)
744.01/262.87	   U84(x0, x1, mark(x2))
744.01/262.87	   U84(active(x0), x1, x2)
744.01/262.87	   U84(x0, active(x1), x2)
744.01/262.87	   U84(x0, x1, active(x2))
744.01/262.87	   s(mark(x0))
744.01/262.87	   s(active(x0))
744.01/262.87	   U91(mark(x0), x1)
744.01/262.87	   U91(x0, mark(x1))
744.01/262.87	   U91(active(x0), x1)
744.01/262.87	   U91(x0, active(x1))
744.01/262.87	   U92(mark(x0))
744.01/262.87	   U92(active(x0))
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(127) QReductionProof (EQUIVALENT)
744.01/262.87	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.87	
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.87	   U16(active(x0))
744.01/262.87	   U21(mark(x0), x1)
744.01/262.87	   U21(x0, mark(x1))
744.01/262.87	   U21(active(x0), x1)
744.01/262.87	   U21(x0, active(x1))
744.01/262.87	   U22(mark(x0), x1)
744.01/262.87	   U22(x0, mark(x1))
744.01/262.87	   U22(active(x0), x1)
744.01/262.87	   U22(x0, active(x1))
744.01/262.87	   U23(mark(x0))
744.01/262.87	   U23(active(x0))
744.01/262.87	   U31(mark(x0), x1, x2)
744.01/262.87	   U31(x0, mark(x1), x2)
744.01/262.87	   U31(x0, x1, mark(x2))
744.01/262.87	   U31(active(x0), x1, x2)
744.01/262.87	   U31(x0, active(x1), x2)
744.01/262.87	   U31(x0, x1, active(x2))
744.01/262.87	   U32(mark(x0), x1, x2)
744.01/262.87	   U32(x0, mark(x1), x2)
744.01/262.87	   U32(x0, x1, mark(x2))
744.01/262.87	   U32(active(x0), x1, x2)
744.01/262.87	   U32(x0, active(x1), x2)
744.01/262.87	   U32(x0, x1, active(x2))
744.01/262.87	   U33(mark(x0), x1, x2)
744.01/262.87	   U33(x0, mark(x1), x2)
744.01/262.87	   U33(x0, x1, mark(x2))
744.01/262.87	   U33(active(x0), x1, x2)
744.01/262.87	   U33(x0, active(x1), x2)
744.01/262.87	   U33(x0, x1, active(x2))
744.01/262.87	   U34(mark(x0), x1, x2)
744.01/262.87	   U34(x0, mark(x1), x2)
744.01/262.87	   U34(x0, x1, mark(x2))
744.01/262.87	   U34(active(x0), x1, x2)
744.01/262.87	   U34(x0, active(x1), x2)
744.01/262.87	   U34(x0, x1, active(x2))
744.01/262.87	   U35(mark(x0), x1)
744.01/262.87	   U35(x0, mark(x1))
744.01/262.87	   U35(active(x0), x1)
744.01/262.87	   U35(x0, active(x1))
744.01/262.87	   U36(mark(x0))
744.01/262.87	   U36(active(x0))
744.01/262.87	   U41(mark(x0), x1)
744.01/262.87	   U41(x0, mark(x1))
744.01/262.87	   U41(active(x0), x1)
744.01/262.87	   U41(x0, active(x1))
744.01/262.87	   U42(mark(x0))
744.01/262.87	   U42(active(x0))
744.01/262.87	   U51(mark(x0))
744.01/262.87	   U51(active(x0))
744.01/262.87	   U61(mark(x0), x1)
744.01/262.87	   U61(x0, mark(x1))
744.01/262.87	   U61(active(x0), x1)
744.01/262.87	   U61(x0, active(x1))
744.01/262.87	   U62(mark(x0))
744.01/262.87	   U62(active(x0))
744.01/262.87	   U71(mark(x0), x1)
744.01/262.87	   U71(x0, mark(x1))
744.01/262.87	   U71(active(x0), x1)
744.01/262.87	   U71(x0, active(x1))
744.01/262.87	   U72(mark(x0), x1)
744.01/262.87	   U72(x0, mark(x1))
744.01/262.87	   U72(active(x0), x1)
744.01/262.87	   U72(x0, active(x1))
744.01/262.87	   U81(mark(x0), x1, x2)
744.01/262.87	   U81(x0, mark(x1), x2)
744.01/262.87	   U81(x0, x1, mark(x2))
744.01/262.87	   U81(active(x0), x1, x2)
744.01/262.87	   U81(x0, active(x1), x2)
744.01/262.87	   U81(x0, x1, active(x2))
744.01/262.87	   U82(mark(x0), x1, x2)
744.01/262.87	   U82(x0, mark(x1), x2)
744.01/262.87	   U82(x0, x1, mark(x2))
744.01/262.87	   U82(active(x0), x1, x2)
744.01/262.87	   U82(x0, active(x1), x2)
744.01/262.87	   U82(x0, x1, active(x2))
744.01/262.87	   U83(mark(x0), x1, x2)
744.01/262.87	   U83(x0, mark(x1), x2)
744.01/262.87	   U83(x0, x1, mark(x2))
744.01/262.87	   U83(active(x0), x1, x2)
744.01/262.87	   U83(x0, active(x1), x2)
744.01/262.87	   U83(x0, x1, active(x2))
744.01/262.87	   U84(mark(x0), x1, x2)
744.01/262.87	   U84(x0, mark(x1), x2)
744.01/262.87	   U84(x0, x1, mark(x2))
744.01/262.87	   U84(active(x0), x1, x2)
744.01/262.87	   U84(x0, active(x1), x2)
744.01/262.87	   U84(x0, x1, active(x2))
744.01/262.87	   s(mark(x0))
744.01/262.87	   s(active(x0))
744.01/262.87	   U91(mark(x0), x1)
744.01/262.87	   U91(x0, mark(x1))
744.01/262.87	   U91(active(x0), x1)
744.01/262.87	   U91(x0, active(x1))
744.01/262.87	   U92(mark(x0))
744.01/262.87	   U92(active(x0))
744.01/262.87	
744.01/262.87	
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(128)
744.01/262.87	Obligation:
744.01/262.87	Q DP problem:
744.01/262.87	The TRS P consists of the following rules:
744.01/262.87	
744.01/262.87	   U33^1(X1, mark(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(mark(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, mark(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(active(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, active(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	   U33^1(X1, X2, active(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	
744.01/262.87	R is empty.
744.01/262.87	The set Q consists of the following terms:
744.01/262.87	
744.01/262.87	   active(U101(tt, x0, x1))
744.01/262.87	   active(U102(tt, x0, x1))
744.01/262.87	   active(U103(tt, x0, x1))
744.01/262.87	   active(U104(tt, x0, x1))
744.01/262.87	   active(U11(tt, x0, x1))
744.01/262.87	   active(U12(tt, x0, x1))
744.01/262.87	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(129) QDPSizeChangeProof (EQUIVALENT)
744.01/262.87	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. 
744.01/262.87	
744.01/262.87	From the DPs we obtained the following set of size-change graphs:
744.01/262.87	*U33^1(X1, mark(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U33^1(mark(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U33^1(X1, X2, mark(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U33^1(active(X1), X2, X3) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U33^1(X1, active(X2), X3) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.87	
744.01/262.87	
744.01/262.87	*U33^1(X1, X2, active(X3)) -> U33^1(X1, X2, X3)
744.01/262.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.87	
744.01/262.87	
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(130)
744.01/262.87	YES
744.01/262.87	
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(131)
744.01/262.87	Obligation:
744.01/262.87	Q DP problem:
744.01/262.87	The TRS P consists of the following rules:
744.01/262.87	
744.01/262.87	   U32^1(X1, mark(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(mark(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, X2, mark(X3)) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(active(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, active(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, X2, active(X3)) -> U32^1(X1, X2, X3)
744.01/262.87	
744.01/262.87	The TRS R consists of the following rules:
744.01/262.87	
744.01/262.87	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.87	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.87	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.87	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.87	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.87	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.87	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.87	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.87	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.87	   active(U16(tt)) -> mark(tt)
744.01/262.87	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.87	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.87	   active(U23(tt)) -> mark(tt)
744.01/262.87	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.87	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.87	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.87	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.87	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.87	   active(U36(tt)) -> mark(tt)
744.01/262.87	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.87	   active(U42(tt)) -> mark(tt)
744.01/262.87	   active(U51(tt)) -> mark(tt)
744.01/262.87	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.87	   active(U62(tt)) -> mark(tt)
744.01/262.87	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.87	   active(U72(tt, N)) -> mark(N)
744.01/262.87	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.87	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.87	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.87	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.87	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.87	   active(U92(tt)) -> mark(0)
744.01/262.87	   active(isNat(0)) -> mark(tt)
744.01/262.87	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.87	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.87	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.87	   active(isNatKind(0)) -> mark(tt)
744.01/262.87	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.87	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.87	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.87	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.87	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.87	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.87	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.87	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.87	   mark(tt) -> active(tt)
744.01/262.87	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.87	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.87	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.87	   mark(isNat(X)) -> active(isNat(X))
744.01/262.87	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.87	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.87	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.87	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.87	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.87	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.87	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.87	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.87	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.87	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.87	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.87	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.87	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.87	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.87	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.87	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.87	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.87	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.87	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.87	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.87	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.87	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.87	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.87	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.87	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.87	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.87	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.87	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.87	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.87	   mark(s(X)) -> active(s(mark(X)))
744.01/262.87	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.87	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.87	   mark(0) -> active(0)
744.01/262.87	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.87	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.87	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.87	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.87	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.87	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.87	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.87	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.87	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.87	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.87	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.87	   isNat(mark(X)) -> isNat(X)
744.01/262.87	   isNat(active(X)) -> isNat(X)
744.01/262.87	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.87	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.87	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.87	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.87	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.87	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.87	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.87	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.87	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.87	   x(active(X1), X2) -> x(X1, X2)
744.01/262.87	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.87	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.87	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.87	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.87	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.87	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.87	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.87	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.87	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.87	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.87	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.87	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.87	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.87	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.87	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.87	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.87	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.87	   U16(mark(X)) -> U16(X)
744.01/262.87	   U16(active(X)) -> U16(X)
744.01/262.87	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.87	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.87	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.87	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.87	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.87	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.87	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.87	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.87	   U23(mark(X)) -> U23(X)
744.01/262.87	   U23(active(X)) -> U23(X)
744.01/262.87	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.87	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.87	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.87	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.87	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.87	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.87	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.87	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.87	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.87	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.87	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.87	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.87	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.87	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.87	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.87	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.87	   U36(mark(X)) -> U36(X)
744.01/262.87	   U36(active(X)) -> U36(X)
744.01/262.87	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.87	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.87	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.87	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.87	   U42(mark(X)) -> U42(X)
744.01/262.87	   U42(active(X)) -> U42(X)
744.01/262.87	   U51(mark(X)) -> U51(X)
744.01/262.87	   U51(active(X)) -> U51(X)
744.01/262.87	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.87	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.87	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.87	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.87	   U62(mark(X)) -> U62(X)
744.01/262.87	   U62(active(X)) -> U62(X)
744.01/262.87	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.87	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.87	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.87	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.87	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.87	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.87	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.87	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.87	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.87	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.87	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.87	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.87	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.87	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.87	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.87	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.87	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.87	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.87	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.87	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.87	   s(mark(X)) -> s(X)
744.01/262.87	   s(active(X)) -> s(X)
744.01/262.87	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.87	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.87	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.87	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.87	   U92(mark(X)) -> U92(X)
744.01/262.87	   U92(active(X)) -> U92(X)
744.01/262.87	
744.01/262.87	The set Q consists of the following terms:
744.01/262.87	
744.01/262.87	   active(U101(tt, x0, x1))
744.01/262.87	   active(U102(tt, x0, x1))
744.01/262.87	   active(U103(tt, x0, x1))
744.01/262.87	   active(U104(tt, x0, x1))
744.01/262.87	   active(U11(tt, x0, x1))
744.01/262.87	   active(U12(tt, x0, x1))
744.01/262.87	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.87	   U16(active(x0))
744.01/262.87	   U21(mark(x0), x1)
744.01/262.87	   U21(x0, mark(x1))
744.01/262.87	   U21(active(x0), x1)
744.01/262.87	   U21(x0, active(x1))
744.01/262.87	   U22(mark(x0), x1)
744.01/262.87	   U22(x0, mark(x1))
744.01/262.87	   U22(active(x0), x1)
744.01/262.87	   U22(x0, active(x1))
744.01/262.87	   U23(mark(x0))
744.01/262.87	   U23(active(x0))
744.01/262.87	   U31(mark(x0), x1, x2)
744.01/262.87	   U31(x0, mark(x1), x2)
744.01/262.87	   U31(x0, x1, mark(x2))
744.01/262.87	   U31(active(x0), x1, x2)
744.01/262.87	   U31(x0, active(x1), x2)
744.01/262.87	   U31(x0, x1, active(x2))
744.01/262.87	   U32(mark(x0), x1, x2)
744.01/262.87	   U32(x0, mark(x1), x2)
744.01/262.87	   U32(x0, x1, mark(x2))
744.01/262.87	   U32(active(x0), x1, x2)
744.01/262.87	   U32(x0, active(x1), x2)
744.01/262.87	   U32(x0, x1, active(x2))
744.01/262.87	   U33(mark(x0), x1, x2)
744.01/262.87	   U33(x0, mark(x1), x2)
744.01/262.87	   U33(x0, x1, mark(x2))
744.01/262.87	   U33(active(x0), x1, x2)
744.01/262.87	   U33(x0, active(x1), x2)
744.01/262.87	   U33(x0, x1, active(x2))
744.01/262.87	   U34(mark(x0), x1, x2)
744.01/262.87	   U34(x0, mark(x1), x2)
744.01/262.87	   U34(x0, x1, mark(x2))
744.01/262.87	   U34(active(x0), x1, x2)
744.01/262.87	   U34(x0, active(x1), x2)
744.01/262.87	   U34(x0, x1, active(x2))
744.01/262.87	   U35(mark(x0), x1)
744.01/262.87	   U35(x0, mark(x1))
744.01/262.87	   U35(active(x0), x1)
744.01/262.87	   U35(x0, active(x1))
744.01/262.87	   U36(mark(x0))
744.01/262.87	   U36(active(x0))
744.01/262.87	   U41(mark(x0), x1)
744.01/262.87	   U41(x0, mark(x1))
744.01/262.87	   U41(active(x0), x1)
744.01/262.87	   U41(x0, active(x1))
744.01/262.87	   U42(mark(x0))
744.01/262.87	   U42(active(x0))
744.01/262.87	   U51(mark(x0))
744.01/262.87	   U51(active(x0))
744.01/262.87	   U61(mark(x0), x1)
744.01/262.87	   U61(x0, mark(x1))
744.01/262.87	   U61(active(x0), x1)
744.01/262.87	   U61(x0, active(x1))
744.01/262.87	   U62(mark(x0))
744.01/262.87	   U62(active(x0))
744.01/262.87	   U71(mark(x0), x1)
744.01/262.87	   U71(x0, mark(x1))
744.01/262.87	   U71(active(x0), x1)
744.01/262.87	   U71(x0, active(x1))
744.01/262.87	   U72(mark(x0), x1)
744.01/262.87	   U72(x0, mark(x1))
744.01/262.87	   U72(active(x0), x1)
744.01/262.87	   U72(x0, active(x1))
744.01/262.87	   U81(mark(x0), x1, x2)
744.01/262.87	   U81(x0, mark(x1), x2)
744.01/262.87	   U81(x0, x1, mark(x2))
744.01/262.87	   U81(active(x0), x1, x2)
744.01/262.87	   U81(x0, active(x1), x2)
744.01/262.87	   U81(x0, x1, active(x2))
744.01/262.87	   U82(mark(x0), x1, x2)
744.01/262.87	   U82(x0, mark(x1), x2)
744.01/262.87	   U82(x0, x1, mark(x2))
744.01/262.87	   U82(active(x0), x1, x2)
744.01/262.87	   U82(x0, active(x1), x2)
744.01/262.87	   U82(x0, x1, active(x2))
744.01/262.87	   U83(mark(x0), x1, x2)
744.01/262.87	   U83(x0, mark(x1), x2)
744.01/262.87	   U83(x0, x1, mark(x2))
744.01/262.87	   U83(active(x0), x1, x2)
744.01/262.87	   U83(x0, active(x1), x2)
744.01/262.87	   U83(x0, x1, active(x2))
744.01/262.87	   U84(mark(x0), x1, x2)
744.01/262.87	   U84(x0, mark(x1), x2)
744.01/262.87	   U84(x0, x1, mark(x2))
744.01/262.87	   U84(active(x0), x1, x2)
744.01/262.87	   U84(x0, active(x1), x2)
744.01/262.87	   U84(x0, x1, active(x2))
744.01/262.87	   s(mark(x0))
744.01/262.87	   s(active(x0))
744.01/262.87	   U91(mark(x0), x1)
744.01/262.87	   U91(x0, mark(x1))
744.01/262.87	   U91(active(x0), x1)
744.01/262.87	   U91(x0, active(x1))
744.01/262.87	   U92(mark(x0))
744.01/262.87	   U92(active(x0))
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(132) UsableRulesProof (EQUIVALENT)
744.01/262.87	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.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(133)
744.01/262.87	Obligation:
744.01/262.87	Q DP problem:
744.01/262.87	The TRS P consists of the following rules:
744.01/262.87	
744.01/262.87	   U32^1(X1, mark(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(mark(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, X2, mark(X3)) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(active(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, active(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.87	   U32^1(X1, X2, active(X3)) -> U32^1(X1, X2, X3)
744.01/262.87	
744.01/262.87	R is empty.
744.01/262.87	The set Q consists of the following terms:
744.01/262.87	
744.01/262.87	   active(U101(tt, x0, x1))
744.01/262.87	   active(U102(tt, x0, x1))
744.01/262.87	   active(U103(tt, x0, x1))
744.01/262.87	   active(U104(tt, x0, x1))
744.01/262.87	   active(U11(tt, x0, x1))
744.01/262.87	   active(U12(tt, x0, x1))
744.01/262.87	   active(U13(tt, x0, x1))
744.01/262.87	   active(U14(tt, x0, x1))
744.01/262.87	   active(U15(tt, x0))
744.01/262.87	   active(U16(tt))
744.01/262.87	   active(U21(tt, x0))
744.01/262.87	   active(U22(tt, x0))
744.01/262.87	   active(U23(tt))
744.01/262.87	   active(U31(tt, x0, x1))
744.01/262.87	   active(U32(tt, x0, x1))
744.01/262.87	   active(U33(tt, x0, x1))
744.01/262.87	   active(U34(tt, x0, x1))
744.01/262.87	   active(U35(tt, x0))
744.01/262.87	   active(U36(tt))
744.01/262.87	   active(U41(tt, x0))
744.01/262.87	   active(U42(tt))
744.01/262.87	   active(U51(tt))
744.01/262.87	   active(U61(tt, x0))
744.01/262.87	   active(U62(tt))
744.01/262.87	   active(U71(tt, x0))
744.01/262.87	   active(U72(tt, x0))
744.01/262.87	   active(U81(tt, x0, x1))
744.01/262.87	   active(U82(tt, x0, x1))
744.01/262.87	   active(U83(tt, x0, x1))
744.01/262.87	   active(U84(tt, x0, x1))
744.01/262.87	   active(U91(tt, x0))
744.01/262.87	   active(U92(tt))
744.01/262.87	   active(isNat(0))
744.01/262.87	   active(isNat(plus(x0, x1)))
744.01/262.87	   active(isNat(s(x0)))
744.01/262.87	   active(isNat(x(x0, x1)))
744.01/262.87	   active(isNatKind(0))
744.01/262.87	   active(isNatKind(plus(x0, x1)))
744.01/262.87	   active(isNatKind(s(x0)))
744.01/262.87	   active(isNatKind(x(x0, x1)))
744.01/262.87	   active(plus(x0, 0))
744.01/262.87	   active(plus(x0, s(x1)))
744.01/262.87	   active(x(x0, 0))
744.01/262.87	   active(x(x0, s(x1)))
744.01/262.87	   mark(U101(x0, x1, x2))
744.01/262.87	   mark(tt)
744.01/262.87	   mark(U102(x0, x1, x2))
744.01/262.87	   mark(isNatKind(x0))
744.01/262.87	   mark(U103(x0, x1, x2))
744.01/262.87	   mark(isNat(x0))
744.01/262.87	   mark(U104(x0, x1, x2))
744.01/262.87	   mark(plus(x0, x1))
744.01/262.87	   mark(x(x0, x1))
744.01/262.87	   mark(U11(x0, x1, x2))
744.01/262.87	   mark(U12(x0, x1, x2))
744.01/262.87	   mark(U13(x0, x1, x2))
744.01/262.87	   mark(U14(x0, x1, x2))
744.01/262.87	   mark(U15(x0, x1))
744.01/262.87	   mark(U16(x0))
744.01/262.87	   mark(U21(x0, x1))
744.01/262.87	   mark(U22(x0, x1))
744.01/262.87	   mark(U23(x0))
744.01/262.87	   mark(U31(x0, x1, x2))
744.01/262.87	   mark(U32(x0, x1, x2))
744.01/262.87	   mark(U33(x0, x1, x2))
744.01/262.87	   mark(U34(x0, x1, x2))
744.01/262.87	   mark(U35(x0, x1))
744.01/262.87	   mark(U36(x0))
744.01/262.87	   mark(U41(x0, x1))
744.01/262.87	   mark(U42(x0))
744.01/262.87	   mark(U51(x0))
744.01/262.87	   mark(U61(x0, x1))
744.01/262.87	   mark(U62(x0))
744.01/262.87	   mark(U71(x0, x1))
744.01/262.87	   mark(U72(x0, x1))
744.01/262.87	   mark(U81(x0, x1, x2))
744.01/262.87	   mark(U82(x0, x1, x2))
744.01/262.87	   mark(U83(x0, x1, x2))
744.01/262.87	   mark(U84(x0, x1, x2))
744.01/262.87	   mark(s(x0))
744.01/262.87	   mark(U91(x0, x1))
744.01/262.87	   mark(U92(x0))
744.01/262.87	   mark(0)
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.87	   U16(active(x0))
744.01/262.87	   U21(mark(x0), x1)
744.01/262.87	   U21(x0, mark(x1))
744.01/262.87	   U21(active(x0), x1)
744.01/262.87	   U21(x0, active(x1))
744.01/262.87	   U22(mark(x0), x1)
744.01/262.87	   U22(x0, mark(x1))
744.01/262.87	   U22(active(x0), x1)
744.01/262.87	   U22(x0, active(x1))
744.01/262.87	   U23(mark(x0))
744.01/262.87	   U23(active(x0))
744.01/262.87	   U31(mark(x0), x1, x2)
744.01/262.87	   U31(x0, mark(x1), x2)
744.01/262.87	   U31(x0, x1, mark(x2))
744.01/262.87	   U31(active(x0), x1, x2)
744.01/262.87	   U31(x0, active(x1), x2)
744.01/262.87	   U31(x0, x1, active(x2))
744.01/262.87	   U32(mark(x0), x1, x2)
744.01/262.87	   U32(x0, mark(x1), x2)
744.01/262.87	   U32(x0, x1, mark(x2))
744.01/262.87	   U32(active(x0), x1, x2)
744.01/262.87	   U32(x0, active(x1), x2)
744.01/262.87	   U32(x0, x1, active(x2))
744.01/262.87	   U33(mark(x0), x1, x2)
744.01/262.87	   U33(x0, mark(x1), x2)
744.01/262.87	   U33(x0, x1, mark(x2))
744.01/262.87	   U33(active(x0), x1, x2)
744.01/262.87	   U33(x0, active(x1), x2)
744.01/262.87	   U33(x0, x1, active(x2))
744.01/262.87	   U34(mark(x0), x1, x2)
744.01/262.87	   U34(x0, mark(x1), x2)
744.01/262.87	   U34(x0, x1, mark(x2))
744.01/262.87	   U34(active(x0), x1, x2)
744.01/262.87	   U34(x0, active(x1), x2)
744.01/262.87	   U34(x0, x1, active(x2))
744.01/262.87	   U35(mark(x0), x1)
744.01/262.87	   U35(x0, mark(x1))
744.01/262.87	   U35(active(x0), x1)
744.01/262.87	   U35(x0, active(x1))
744.01/262.87	   U36(mark(x0))
744.01/262.87	   U36(active(x0))
744.01/262.87	   U41(mark(x0), x1)
744.01/262.87	   U41(x0, mark(x1))
744.01/262.87	   U41(active(x0), x1)
744.01/262.87	   U41(x0, active(x1))
744.01/262.87	   U42(mark(x0))
744.01/262.87	   U42(active(x0))
744.01/262.87	   U51(mark(x0))
744.01/262.87	   U51(active(x0))
744.01/262.87	   U61(mark(x0), x1)
744.01/262.87	   U61(x0, mark(x1))
744.01/262.87	   U61(active(x0), x1)
744.01/262.87	   U61(x0, active(x1))
744.01/262.87	   U62(mark(x0))
744.01/262.87	   U62(active(x0))
744.01/262.87	   U71(mark(x0), x1)
744.01/262.87	   U71(x0, mark(x1))
744.01/262.87	   U71(active(x0), x1)
744.01/262.87	   U71(x0, active(x1))
744.01/262.87	   U72(mark(x0), x1)
744.01/262.87	   U72(x0, mark(x1))
744.01/262.87	   U72(active(x0), x1)
744.01/262.87	   U72(x0, active(x1))
744.01/262.87	   U81(mark(x0), x1, x2)
744.01/262.87	   U81(x0, mark(x1), x2)
744.01/262.87	   U81(x0, x1, mark(x2))
744.01/262.87	   U81(active(x0), x1, x2)
744.01/262.87	   U81(x0, active(x1), x2)
744.01/262.87	   U81(x0, x1, active(x2))
744.01/262.87	   U82(mark(x0), x1, x2)
744.01/262.87	   U82(x0, mark(x1), x2)
744.01/262.87	   U82(x0, x1, mark(x2))
744.01/262.87	   U82(active(x0), x1, x2)
744.01/262.87	   U82(x0, active(x1), x2)
744.01/262.87	   U82(x0, x1, active(x2))
744.01/262.87	   U83(mark(x0), x1, x2)
744.01/262.87	   U83(x0, mark(x1), x2)
744.01/262.87	   U83(x0, x1, mark(x2))
744.01/262.87	   U83(active(x0), x1, x2)
744.01/262.87	   U83(x0, active(x1), x2)
744.01/262.87	   U83(x0, x1, active(x2))
744.01/262.87	   U84(mark(x0), x1, x2)
744.01/262.87	   U84(x0, mark(x1), x2)
744.01/262.87	   U84(x0, x1, mark(x2))
744.01/262.87	   U84(active(x0), x1, x2)
744.01/262.87	   U84(x0, active(x1), x2)
744.01/262.87	   U84(x0, x1, active(x2))
744.01/262.87	   s(mark(x0))
744.01/262.87	   s(active(x0))
744.01/262.87	   U91(mark(x0), x1)
744.01/262.87	   U91(x0, mark(x1))
744.01/262.87	   U91(active(x0), x1)
744.01/262.87	   U91(x0, active(x1))
744.01/262.87	   U92(mark(x0))
744.01/262.87	   U92(active(x0))
744.01/262.87	
744.01/262.87	We have to consider all minimal (P,Q,R)-chains.
744.01/262.87	----------------------------------------
744.01/262.87	
744.01/262.87	(134) QReductionProof (EQUIVALENT)
744.01/262.87	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.87	
744.01/262.87	   U101(mark(x0), x1, x2)
744.01/262.87	   U101(x0, mark(x1), x2)
744.01/262.87	   U101(x0, x1, mark(x2))
744.01/262.87	   U101(active(x0), x1, x2)
744.01/262.87	   U101(x0, active(x1), x2)
744.01/262.87	   U101(x0, x1, active(x2))
744.01/262.87	   U102(mark(x0), x1, x2)
744.01/262.87	   U102(x0, mark(x1), x2)
744.01/262.87	   U102(x0, x1, mark(x2))
744.01/262.87	   U102(active(x0), x1, x2)
744.01/262.87	   U102(x0, active(x1), x2)
744.01/262.87	   U102(x0, x1, active(x2))
744.01/262.87	   isNatKind(mark(x0))
744.01/262.87	   isNatKind(active(x0))
744.01/262.87	   U103(mark(x0), x1, x2)
744.01/262.87	   U103(x0, mark(x1), x2)
744.01/262.87	   U103(x0, x1, mark(x2))
744.01/262.87	   U103(active(x0), x1, x2)
744.01/262.87	   U103(x0, active(x1), x2)
744.01/262.87	   U103(x0, x1, active(x2))
744.01/262.87	   isNat(mark(x0))
744.01/262.87	   isNat(active(x0))
744.01/262.87	   U104(mark(x0), x1, x2)
744.01/262.87	   U104(x0, mark(x1), x2)
744.01/262.87	   U104(x0, x1, mark(x2))
744.01/262.87	   U104(active(x0), x1, x2)
744.01/262.87	   U104(x0, active(x1), x2)
744.01/262.87	   U104(x0, x1, active(x2))
744.01/262.87	   plus(mark(x0), x1)
744.01/262.87	   plus(x0, mark(x1))
744.01/262.87	   plus(active(x0), x1)
744.01/262.87	   plus(x0, active(x1))
744.01/262.87	   x(mark(x0), x1)
744.01/262.87	   x(x0, mark(x1))
744.01/262.87	   x(active(x0), x1)
744.01/262.87	   x(x0, active(x1))
744.01/262.87	   U11(mark(x0), x1, x2)
744.01/262.87	   U11(x0, mark(x1), x2)
744.01/262.87	   U11(x0, x1, mark(x2))
744.01/262.87	   U11(active(x0), x1, x2)
744.01/262.87	   U11(x0, active(x1), x2)
744.01/262.87	   U11(x0, x1, active(x2))
744.01/262.87	   U12(mark(x0), x1, x2)
744.01/262.87	   U12(x0, mark(x1), x2)
744.01/262.87	   U12(x0, x1, mark(x2))
744.01/262.87	   U12(active(x0), x1, x2)
744.01/262.87	   U12(x0, active(x1), x2)
744.01/262.87	   U12(x0, x1, active(x2))
744.01/262.87	   U13(mark(x0), x1, x2)
744.01/262.87	   U13(x0, mark(x1), x2)
744.01/262.87	   U13(x0, x1, mark(x2))
744.01/262.87	   U13(active(x0), x1, x2)
744.01/262.87	   U13(x0, active(x1), x2)
744.01/262.87	   U13(x0, x1, active(x2))
744.01/262.87	   U14(mark(x0), x1, x2)
744.01/262.87	   U14(x0, mark(x1), x2)
744.01/262.87	   U14(x0, x1, mark(x2))
744.01/262.87	   U14(active(x0), x1, x2)
744.01/262.87	   U14(x0, active(x1), x2)
744.01/262.87	   U14(x0, x1, active(x2))
744.01/262.87	   U15(mark(x0), x1)
744.01/262.87	   U15(x0, mark(x1))
744.01/262.87	   U15(active(x0), x1)
744.01/262.87	   U15(x0, active(x1))
744.01/262.87	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(135)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U32^1(X1, mark(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.88	   U32^1(mark(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.88	   U32^1(X1, X2, mark(X3)) -> U32^1(X1, X2, X3)
744.01/262.88	   U32^1(active(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.88	   U32^1(X1, active(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.88	   U32^1(X1, X2, active(X3)) -> U32^1(X1, X2, X3)
744.01/262.88	
744.01/262.88	R is empty.
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(136) QDPSizeChangeProof (EQUIVALENT)
744.01/262.88	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. 
744.01/262.88	
744.01/262.88	From the DPs we obtained the following set of size-change graphs:
744.01/262.88	*U32^1(X1, mark(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U32^1(mark(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U32^1(X1, X2, mark(X3)) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U32^1(active(X1), X2, X3) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U32^1(X1, active(X2), X3) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U32^1(X1, X2, active(X3)) -> U32^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.88	
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(137)
744.01/262.88	YES
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(138)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U31^1(X1, mark(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(mark(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, mark(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(active(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, active(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, active(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	
744.01/262.88	The TRS R consists of the following rules:
744.01/262.88	
744.01/262.88	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.88	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.88	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.88	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.88	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.88	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.88	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.88	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.88	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.88	   active(U16(tt)) -> mark(tt)
744.01/262.88	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.88	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.88	   active(U23(tt)) -> mark(tt)
744.01/262.88	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.88	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.88	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.88	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.88	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.88	   active(U36(tt)) -> mark(tt)
744.01/262.88	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.88	   active(U42(tt)) -> mark(tt)
744.01/262.88	   active(U51(tt)) -> mark(tt)
744.01/262.88	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.88	   active(U62(tt)) -> mark(tt)
744.01/262.88	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.88	   active(U72(tt, N)) -> mark(N)
744.01/262.88	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.88	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.88	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.88	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.88	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.88	   active(U92(tt)) -> mark(0)
744.01/262.88	   active(isNat(0)) -> mark(tt)
744.01/262.88	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.88	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.88	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.88	   active(isNatKind(0)) -> mark(tt)
744.01/262.88	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.88	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.88	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.88	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.88	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.88	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.88	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.88	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.88	   mark(tt) -> active(tt)
744.01/262.88	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.88	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.88	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.88	   mark(isNat(X)) -> active(isNat(X))
744.01/262.88	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.88	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.88	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.88	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.88	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.88	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.88	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.88	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.88	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.88	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.88	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.88	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.88	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.88	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.88	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.88	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.88	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.88	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.88	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.88	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.88	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.88	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.88	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.88	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.88	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.88	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.88	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.88	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.88	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.88	   mark(s(X)) -> active(s(mark(X)))
744.01/262.88	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.88	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.88	   mark(0) -> active(0)
744.01/262.88	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.88	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.88	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.88	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.88	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.88	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.88	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.88	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.88	   isNat(mark(X)) -> isNat(X)
744.01/262.88	   isNat(active(X)) -> isNat(X)
744.01/262.88	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.88	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.88	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.88	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.88	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.88	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.88	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.88	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.88	   x(active(X1), X2) -> x(X1, X2)
744.01/262.88	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.88	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.88	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.88	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.88	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.88	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.88	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.88	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.88	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.88	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.88	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.88	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.88	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.88	   U16(mark(X)) -> U16(X)
744.01/262.88	   U16(active(X)) -> U16(X)
744.01/262.88	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.88	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.88	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.88	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.88	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.88	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.88	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.88	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.88	   U23(mark(X)) -> U23(X)
744.01/262.88	   U23(active(X)) -> U23(X)
744.01/262.88	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.88	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.88	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.88	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.88	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.88	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.88	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.88	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.88	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.88	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.88	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.88	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.88	   U36(mark(X)) -> U36(X)
744.01/262.88	   U36(active(X)) -> U36(X)
744.01/262.88	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.88	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.88	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.88	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.88	   U42(mark(X)) -> U42(X)
744.01/262.88	   U42(active(X)) -> U42(X)
744.01/262.88	   U51(mark(X)) -> U51(X)
744.01/262.88	   U51(active(X)) -> U51(X)
744.01/262.88	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.88	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.88	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.88	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.88	   U62(mark(X)) -> U62(X)
744.01/262.88	   U62(active(X)) -> U62(X)
744.01/262.88	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.88	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.88	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.88	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.88	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.88	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.88	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.88	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.88	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.88	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.88	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.88	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.88	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.88	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.88	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.88	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.88	   s(mark(X)) -> s(X)
744.01/262.88	   s(active(X)) -> s(X)
744.01/262.88	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.88	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.88	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.88	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.88	   U92(mark(X)) -> U92(X)
744.01/262.88	   U92(active(X)) -> U92(X)
744.01/262.88	
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.88	   U102(x0, active(x1), x2)
744.01/262.88	   U102(x0, x1, active(x2))
744.01/262.88	   isNatKind(mark(x0))
744.01/262.88	   isNatKind(active(x0))
744.01/262.88	   U103(mark(x0), x1, x2)
744.01/262.88	   U103(x0, mark(x1), x2)
744.01/262.88	   U103(x0, x1, mark(x2))
744.01/262.88	   U103(active(x0), x1, x2)
744.01/262.88	   U103(x0, active(x1), x2)
744.01/262.88	   U103(x0, x1, active(x2))
744.01/262.88	   isNat(mark(x0))
744.01/262.88	   isNat(active(x0))
744.01/262.88	   U104(mark(x0), x1, x2)
744.01/262.88	   U104(x0, mark(x1), x2)
744.01/262.88	   U104(x0, x1, mark(x2))
744.01/262.88	   U104(active(x0), x1, x2)
744.01/262.88	   U104(x0, active(x1), x2)
744.01/262.88	   U104(x0, x1, active(x2))
744.01/262.88	   plus(mark(x0), x1)
744.01/262.88	   plus(x0, mark(x1))
744.01/262.88	   plus(active(x0), x1)
744.01/262.88	   plus(x0, active(x1))
744.01/262.88	   x(mark(x0), x1)
744.01/262.88	   x(x0, mark(x1))
744.01/262.88	   x(active(x0), x1)
744.01/262.88	   x(x0, active(x1))
744.01/262.88	   U11(mark(x0), x1, x2)
744.01/262.88	   U11(x0, mark(x1), x2)
744.01/262.88	   U11(x0, x1, mark(x2))
744.01/262.88	   U11(active(x0), x1, x2)
744.01/262.88	   U11(x0, active(x1), x2)
744.01/262.88	   U11(x0, x1, active(x2))
744.01/262.88	   U12(mark(x0), x1, x2)
744.01/262.88	   U12(x0, mark(x1), x2)
744.01/262.88	   U12(x0, x1, mark(x2))
744.01/262.88	   U12(active(x0), x1, x2)
744.01/262.88	   U12(x0, active(x1), x2)
744.01/262.88	   U12(x0, x1, active(x2))
744.01/262.88	   U13(mark(x0), x1, x2)
744.01/262.88	   U13(x0, mark(x1), x2)
744.01/262.88	   U13(x0, x1, mark(x2))
744.01/262.88	   U13(active(x0), x1, x2)
744.01/262.88	   U13(x0, active(x1), x2)
744.01/262.88	   U13(x0, x1, active(x2))
744.01/262.88	   U14(mark(x0), x1, x2)
744.01/262.88	   U14(x0, mark(x1), x2)
744.01/262.88	   U14(x0, x1, mark(x2))
744.01/262.88	   U14(active(x0), x1, x2)
744.01/262.88	   U14(x0, active(x1), x2)
744.01/262.88	   U14(x0, x1, active(x2))
744.01/262.88	   U15(mark(x0), x1)
744.01/262.88	   U15(x0, mark(x1))
744.01/262.88	   U15(active(x0), x1)
744.01/262.88	   U15(x0, active(x1))
744.01/262.88	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(139) UsableRulesProof (EQUIVALENT)
744.01/262.88	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.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(140)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U31^1(X1, mark(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(mark(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, mark(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(active(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, active(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, active(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	
744.01/262.88	R is empty.
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.88	   U102(x0, active(x1), x2)
744.01/262.88	   U102(x0, x1, active(x2))
744.01/262.88	   isNatKind(mark(x0))
744.01/262.88	   isNatKind(active(x0))
744.01/262.88	   U103(mark(x0), x1, x2)
744.01/262.88	   U103(x0, mark(x1), x2)
744.01/262.88	   U103(x0, x1, mark(x2))
744.01/262.88	   U103(active(x0), x1, x2)
744.01/262.88	   U103(x0, active(x1), x2)
744.01/262.88	   U103(x0, x1, active(x2))
744.01/262.88	   isNat(mark(x0))
744.01/262.88	   isNat(active(x0))
744.01/262.88	   U104(mark(x0), x1, x2)
744.01/262.88	   U104(x0, mark(x1), x2)
744.01/262.88	   U104(x0, x1, mark(x2))
744.01/262.88	   U104(active(x0), x1, x2)
744.01/262.88	   U104(x0, active(x1), x2)
744.01/262.88	   U104(x0, x1, active(x2))
744.01/262.88	   plus(mark(x0), x1)
744.01/262.88	   plus(x0, mark(x1))
744.01/262.88	   plus(active(x0), x1)
744.01/262.88	   plus(x0, active(x1))
744.01/262.88	   x(mark(x0), x1)
744.01/262.88	   x(x0, mark(x1))
744.01/262.88	   x(active(x0), x1)
744.01/262.88	   x(x0, active(x1))
744.01/262.88	   U11(mark(x0), x1, x2)
744.01/262.88	   U11(x0, mark(x1), x2)
744.01/262.88	   U11(x0, x1, mark(x2))
744.01/262.88	   U11(active(x0), x1, x2)
744.01/262.88	   U11(x0, active(x1), x2)
744.01/262.88	   U11(x0, x1, active(x2))
744.01/262.88	   U12(mark(x0), x1, x2)
744.01/262.88	   U12(x0, mark(x1), x2)
744.01/262.88	   U12(x0, x1, mark(x2))
744.01/262.88	   U12(active(x0), x1, x2)
744.01/262.88	   U12(x0, active(x1), x2)
744.01/262.88	   U12(x0, x1, active(x2))
744.01/262.88	   U13(mark(x0), x1, x2)
744.01/262.88	   U13(x0, mark(x1), x2)
744.01/262.88	   U13(x0, x1, mark(x2))
744.01/262.88	   U13(active(x0), x1, x2)
744.01/262.88	   U13(x0, active(x1), x2)
744.01/262.88	   U13(x0, x1, active(x2))
744.01/262.88	   U14(mark(x0), x1, x2)
744.01/262.88	   U14(x0, mark(x1), x2)
744.01/262.88	   U14(x0, x1, mark(x2))
744.01/262.88	   U14(active(x0), x1, x2)
744.01/262.88	   U14(x0, active(x1), x2)
744.01/262.88	   U14(x0, x1, active(x2))
744.01/262.88	   U15(mark(x0), x1)
744.01/262.88	   U15(x0, mark(x1))
744.01/262.88	   U15(active(x0), x1)
744.01/262.88	   U15(x0, active(x1))
744.01/262.88	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(141) QReductionProof (EQUIVALENT)
744.01/262.88	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.88	
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.88	   U102(x0, active(x1), x2)
744.01/262.88	   U102(x0, x1, active(x2))
744.01/262.88	   isNatKind(mark(x0))
744.01/262.88	   isNatKind(active(x0))
744.01/262.88	   U103(mark(x0), x1, x2)
744.01/262.88	   U103(x0, mark(x1), x2)
744.01/262.88	   U103(x0, x1, mark(x2))
744.01/262.88	   U103(active(x0), x1, x2)
744.01/262.88	   U103(x0, active(x1), x2)
744.01/262.88	   U103(x0, x1, active(x2))
744.01/262.88	   isNat(mark(x0))
744.01/262.88	   isNat(active(x0))
744.01/262.88	   U104(mark(x0), x1, x2)
744.01/262.88	   U104(x0, mark(x1), x2)
744.01/262.88	   U104(x0, x1, mark(x2))
744.01/262.88	   U104(active(x0), x1, x2)
744.01/262.88	   U104(x0, active(x1), x2)
744.01/262.88	   U104(x0, x1, active(x2))
744.01/262.88	   plus(mark(x0), x1)
744.01/262.88	   plus(x0, mark(x1))
744.01/262.88	   plus(active(x0), x1)
744.01/262.88	   plus(x0, active(x1))
744.01/262.88	   x(mark(x0), x1)
744.01/262.88	   x(x0, mark(x1))
744.01/262.88	   x(active(x0), x1)
744.01/262.88	   x(x0, active(x1))
744.01/262.88	   U11(mark(x0), x1, x2)
744.01/262.88	   U11(x0, mark(x1), x2)
744.01/262.88	   U11(x0, x1, mark(x2))
744.01/262.88	   U11(active(x0), x1, x2)
744.01/262.88	   U11(x0, active(x1), x2)
744.01/262.88	   U11(x0, x1, active(x2))
744.01/262.88	   U12(mark(x0), x1, x2)
744.01/262.88	   U12(x0, mark(x1), x2)
744.01/262.88	   U12(x0, x1, mark(x2))
744.01/262.88	   U12(active(x0), x1, x2)
744.01/262.88	   U12(x0, active(x1), x2)
744.01/262.88	   U12(x0, x1, active(x2))
744.01/262.88	   U13(mark(x0), x1, x2)
744.01/262.88	   U13(x0, mark(x1), x2)
744.01/262.88	   U13(x0, x1, mark(x2))
744.01/262.88	   U13(active(x0), x1, x2)
744.01/262.88	   U13(x0, active(x1), x2)
744.01/262.88	   U13(x0, x1, active(x2))
744.01/262.88	   U14(mark(x0), x1, x2)
744.01/262.88	   U14(x0, mark(x1), x2)
744.01/262.88	   U14(x0, x1, mark(x2))
744.01/262.88	   U14(active(x0), x1, x2)
744.01/262.88	   U14(x0, active(x1), x2)
744.01/262.88	   U14(x0, x1, active(x2))
744.01/262.88	   U15(mark(x0), x1)
744.01/262.88	   U15(x0, mark(x1))
744.01/262.88	   U15(active(x0), x1)
744.01/262.88	   U15(x0, active(x1))
744.01/262.88	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(142)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U31^1(X1, mark(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(mark(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, mark(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(active(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, active(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	   U31^1(X1, X2, active(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	
744.01/262.88	R is empty.
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(143) QDPSizeChangeProof (EQUIVALENT)
744.01/262.88	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. 
744.01/262.88	
744.01/262.88	From the DPs we obtained the following set of size-change graphs:
744.01/262.88	*U31^1(X1, mark(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U31^1(mark(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U31^1(X1, X2, mark(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U31^1(active(X1), X2, X3) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U31^1(X1, active(X2), X3) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.01/262.88	
744.01/262.88	
744.01/262.88	*U31^1(X1, X2, active(X3)) -> U31^1(X1, X2, X3)
744.01/262.88	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.01/262.88	
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(144)
744.01/262.88	YES
744.01/262.88	
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(145)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U23^1(active(X)) -> U23^1(X)
744.01/262.88	   U23^1(mark(X)) -> U23^1(X)
744.01/262.88	
744.01/262.88	The TRS R consists of the following rules:
744.01/262.88	
744.01/262.88	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.88	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.88	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.88	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.88	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.88	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.88	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.88	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.88	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.88	   active(U16(tt)) -> mark(tt)
744.01/262.88	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.88	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.88	   active(U23(tt)) -> mark(tt)
744.01/262.88	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.88	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.88	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.88	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.88	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.88	   active(U36(tt)) -> mark(tt)
744.01/262.88	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.88	   active(U42(tt)) -> mark(tt)
744.01/262.88	   active(U51(tt)) -> mark(tt)
744.01/262.88	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.88	   active(U62(tt)) -> mark(tt)
744.01/262.88	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.88	   active(U72(tt, N)) -> mark(N)
744.01/262.88	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.88	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.88	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.88	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.88	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.88	   active(U92(tt)) -> mark(0)
744.01/262.88	   active(isNat(0)) -> mark(tt)
744.01/262.88	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.88	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.88	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.88	   active(isNatKind(0)) -> mark(tt)
744.01/262.88	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.88	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.88	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.88	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.88	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.88	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.88	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.88	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.88	   mark(tt) -> active(tt)
744.01/262.88	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.88	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.88	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.88	   mark(isNat(X)) -> active(isNat(X))
744.01/262.88	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.88	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.88	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.88	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.88	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.88	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.88	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.88	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.88	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.88	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.88	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.88	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.88	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.88	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.88	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.88	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.88	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.88	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.88	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.88	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.88	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.88	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.88	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.88	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.88	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.88	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.88	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.88	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.88	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.88	   mark(s(X)) -> active(s(mark(X)))
744.01/262.88	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.88	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.88	   mark(0) -> active(0)
744.01/262.88	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.88	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.88	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.88	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.88	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.88	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.88	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.88	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.88	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.88	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.88	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.88	   isNat(mark(X)) -> isNat(X)
744.01/262.88	   isNat(active(X)) -> isNat(X)
744.01/262.88	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.88	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.88	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.88	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.88	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.88	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.88	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.88	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.88	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.88	   x(active(X1), X2) -> x(X1, X2)
744.01/262.88	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.88	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.88	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.88	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.88	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.88	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.88	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.88	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.88	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.88	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.88	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.88	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.88	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.88	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.88	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.88	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.88	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.88	   U16(mark(X)) -> U16(X)
744.01/262.88	   U16(active(X)) -> U16(X)
744.01/262.88	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.88	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.88	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.88	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.88	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.88	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.88	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.88	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.88	   U23(mark(X)) -> U23(X)
744.01/262.88	   U23(active(X)) -> U23(X)
744.01/262.88	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.88	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.88	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.88	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.88	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.88	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.88	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.88	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.88	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.88	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.88	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.88	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.88	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.88	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.88	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.88	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.88	   U36(mark(X)) -> U36(X)
744.01/262.88	   U36(active(X)) -> U36(X)
744.01/262.88	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.88	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.88	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.88	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.88	   U42(mark(X)) -> U42(X)
744.01/262.88	   U42(active(X)) -> U42(X)
744.01/262.88	   U51(mark(X)) -> U51(X)
744.01/262.88	   U51(active(X)) -> U51(X)
744.01/262.88	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.88	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.88	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.88	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.88	   U62(mark(X)) -> U62(X)
744.01/262.88	   U62(active(X)) -> U62(X)
744.01/262.88	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.88	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.88	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.88	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.88	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.88	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.88	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.88	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.88	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.88	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.88	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.88	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.88	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.88	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.88	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.88	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.88	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.88	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.88	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.88	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.88	   s(mark(X)) -> s(X)
744.01/262.88	   s(active(X)) -> s(X)
744.01/262.88	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.88	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.88	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.88	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.88	   U92(mark(X)) -> U92(X)
744.01/262.88	   U92(active(X)) -> U92(X)
744.01/262.88	
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.88	   U102(x0, active(x1), x2)
744.01/262.88	   U102(x0, x1, active(x2))
744.01/262.88	   isNatKind(mark(x0))
744.01/262.88	   isNatKind(active(x0))
744.01/262.88	   U103(mark(x0), x1, x2)
744.01/262.88	   U103(x0, mark(x1), x2)
744.01/262.88	   U103(x0, x1, mark(x2))
744.01/262.88	   U103(active(x0), x1, x2)
744.01/262.88	   U103(x0, active(x1), x2)
744.01/262.88	   U103(x0, x1, active(x2))
744.01/262.88	   isNat(mark(x0))
744.01/262.88	   isNat(active(x0))
744.01/262.88	   U104(mark(x0), x1, x2)
744.01/262.88	   U104(x0, mark(x1), x2)
744.01/262.88	   U104(x0, x1, mark(x2))
744.01/262.88	   U104(active(x0), x1, x2)
744.01/262.88	   U104(x0, active(x1), x2)
744.01/262.88	   U104(x0, x1, active(x2))
744.01/262.88	   plus(mark(x0), x1)
744.01/262.88	   plus(x0, mark(x1))
744.01/262.88	   plus(active(x0), x1)
744.01/262.88	   plus(x0, active(x1))
744.01/262.88	   x(mark(x0), x1)
744.01/262.88	   x(x0, mark(x1))
744.01/262.88	   x(active(x0), x1)
744.01/262.88	   x(x0, active(x1))
744.01/262.88	   U11(mark(x0), x1, x2)
744.01/262.88	   U11(x0, mark(x1), x2)
744.01/262.88	   U11(x0, x1, mark(x2))
744.01/262.88	   U11(active(x0), x1, x2)
744.01/262.88	   U11(x0, active(x1), x2)
744.01/262.88	   U11(x0, x1, active(x2))
744.01/262.88	   U12(mark(x0), x1, x2)
744.01/262.88	   U12(x0, mark(x1), x2)
744.01/262.88	   U12(x0, x1, mark(x2))
744.01/262.88	   U12(active(x0), x1, x2)
744.01/262.88	   U12(x0, active(x1), x2)
744.01/262.88	   U12(x0, x1, active(x2))
744.01/262.88	   U13(mark(x0), x1, x2)
744.01/262.88	   U13(x0, mark(x1), x2)
744.01/262.88	   U13(x0, x1, mark(x2))
744.01/262.88	   U13(active(x0), x1, x2)
744.01/262.88	   U13(x0, active(x1), x2)
744.01/262.88	   U13(x0, x1, active(x2))
744.01/262.88	   U14(mark(x0), x1, x2)
744.01/262.88	   U14(x0, mark(x1), x2)
744.01/262.88	   U14(x0, x1, mark(x2))
744.01/262.88	   U14(active(x0), x1, x2)
744.01/262.88	   U14(x0, active(x1), x2)
744.01/262.88	   U14(x0, x1, active(x2))
744.01/262.88	   U15(mark(x0), x1)
744.01/262.88	   U15(x0, mark(x1))
744.01/262.88	   U15(active(x0), x1)
744.01/262.88	   U15(x0, active(x1))
744.01/262.88	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(146) UsableRulesProof (EQUIVALENT)
744.01/262.88	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.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(147)
744.01/262.88	Obligation:
744.01/262.88	Q DP problem:
744.01/262.88	The TRS P consists of the following rules:
744.01/262.88	
744.01/262.88	   U23^1(active(X)) -> U23^1(X)
744.01/262.88	   U23^1(mark(X)) -> U23^1(X)
744.01/262.88	
744.01/262.88	R is empty.
744.01/262.88	The set Q consists of the following terms:
744.01/262.88	
744.01/262.88	   active(U101(tt, x0, x1))
744.01/262.88	   active(U102(tt, x0, x1))
744.01/262.88	   active(U103(tt, x0, x1))
744.01/262.88	   active(U104(tt, x0, x1))
744.01/262.88	   active(U11(tt, x0, x1))
744.01/262.88	   active(U12(tt, x0, x1))
744.01/262.88	   active(U13(tt, x0, x1))
744.01/262.88	   active(U14(tt, x0, x1))
744.01/262.88	   active(U15(tt, x0))
744.01/262.88	   active(U16(tt))
744.01/262.88	   active(U21(tt, x0))
744.01/262.88	   active(U22(tt, x0))
744.01/262.88	   active(U23(tt))
744.01/262.88	   active(U31(tt, x0, x1))
744.01/262.88	   active(U32(tt, x0, x1))
744.01/262.88	   active(U33(tt, x0, x1))
744.01/262.88	   active(U34(tt, x0, x1))
744.01/262.88	   active(U35(tt, x0))
744.01/262.88	   active(U36(tt))
744.01/262.88	   active(U41(tt, x0))
744.01/262.88	   active(U42(tt))
744.01/262.88	   active(U51(tt))
744.01/262.88	   active(U61(tt, x0))
744.01/262.88	   active(U62(tt))
744.01/262.88	   active(U71(tt, x0))
744.01/262.88	   active(U72(tt, x0))
744.01/262.88	   active(U81(tt, x0, x1))
744.01/262.88	   active(U82(tt, x0, x1))
744.01/262.88	   active(U83(tt, x0, x1))
744.01/262.88	   active(U84(tt, x0, x1))
744.01/262.88	   active(U91(tt, x0))
744.01/262.88	   active(U92(tt))
744.01/262.88	   active(isNat(0))
744.01/262.88	   active(isNat(plus(x0, x1)))
744.01/262.88	   active(isNat(s(x0)))
744.01/262.88	   active(isNat(x(x0, x1)))
744.01/262.88	   active(isNatKind(0))
744.01/262.88	   active(isNatKind(plus(x0, x1)))
744.01/262.88	   active(isNatKind(s(x0)))
744.01/262.88	   active(isNatKind(x(x0, x1)))
744.01/262.88	   active(plus(x0, 0))
744.01/262.88	   active(plus(x0, s(x1)))
744.01/262.88	   active(x(x0, 0))
744.01/262.88	   active(x(x0, s(x1)))
744.01/262.88	   mark(U101(x0, x1, x2))
744.01/262.88	   mark(tt)
744.01/262.88	   mark(U102(x0, x1, x2))
744.01/262.88	   mark(isNatKind(x0))
744.01/262.88	   mark(U103(x0, x1, x2))
744.01/262.88	   mark(isNat(x0))
744.01/262.88	   mark(U104(x0, x1, x2))
744.01/262.88	   mark(plus(x0, x1))
744.01/262.88	   mark(x(x0, x1))
744.01/262.88	   mark(U11(x0, x1, x2))
744.01/262.88	   mark(U12(x0, x1, x2))
744.01/262.88	   mark(U13(x0, x1, x2))
744.01/262.88	   mark(U14(x0, x1, x2))
744.01/262.88	   mark(U15(x0, x1))
744.01/262.88	   mark(U16(x0))
744.01/262.88	   mark(U21(x0, x1))
744.01/262.88	   mark(U22(x0, x1))
744.01/262.88	   mark(U23(x0))
744.01/262.88	   mark(U31(x0, x1, x2))
744.01/262.88	   mark(U32(x0, x1, x2))
744.01/262.88	   mark(U33(x0, x1, x2))
744.01/262.88	   mark(U34(x0, x1, x2))
744.01/262.88	   mark(U35(x0, x1))
744.01/262.88	   mark(U36(x0))
744.01/262.88	   mark(U41(x0, x1))
744.01/262.88	   mark(U42(x0))
744.01/262.88	   mark(U51(x0))
744.01/262.88	   mark(U61(x0, x1))
744.01/262.88	   mark(U62(x0))
744.01/262.88	   mark(U71(x0, x1))
744.01/262.88	   mark(U72(x0, x1))
744.01/262.88	   mark(U81(x0, x1, x2))
744.01/262.88	   mark(U82(x0, x1, x2))
744.01/262.88	   mark(U83(x0, x1, x2))
744.01/262.88	   mark(U84(x0, x1, x2))
744.01/262.88	   mark(s(x0))
744.01/262.88	   mark(U91(x0, x1))
744.01/262.88	   mark(U92(x0))
744.01/262.88	   mark(0)
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.88	   U102(x0, active(x1), x2)
744.01/262.88	   U102(x0, x1, active(x2))
744.01/262.88	   isNatKind(mark(x0))
744.01/262.88	   isNatKind(active(x0))
744.01/262.88	   U103(mark(x0), x1, x2)
744.01/262.88	   U103(x0, mark(x1), x2)
744.01/262.88	   U103(x0, x1, mark(x2))
744.01/262.88	   U103(active(x0), x1, x2)
744.01/262.88	   U103(x0, active(x1), x2)
744.01/262.88	   U103(x0, x1, active(x2))
744.01/262.88	   isNat(mark(x0))
744.01/262.88	   isNat(active(x0))
744.01/262.88	   U104(mark(x0), x1, x2)
744.01/262.88	   U104(x0, mark(x1), x2)
744.01/262.88	   U104(x0, x1, mark(x2))
744.01/262.88	   U104(active(x0), x1, x2)
744.01/262.88	   U104(x0, active(x1), x2)
744.01/262.88	   U104(x0, x1, active(x2))
744.01/262.88	   plus(mark(x0), x1)
744.01/262.88	   plus(x0, mark(x1))
744.01/262.88	   plus(active(x0), x1)
744.01/262.88	   plus(x0, active(x1))
744.01/262.88	   x(mark(x0), x1)
744.01/262.88	   x(x0, mark(x1))
744.01/262.88	   x(active(x0), x1)
744.01/262.88	   x(x0, active(x1))
744.01/262.88	   U11(mark(x0), x1, x2)
744.01/262.88	   U11(x0, mark(x1), x2)
744.01/262.88	   U11(x0, x1, mark(x2))
744.01/262.88	   U11(active(x0), x1, x2)
744.01/262.88	   U11(x0, active(x1), x2)
744.01/262.88	   U11(x0, x1, active(x2))
744.01/262.88	   U12(mark(x0), x1, x2)
744.01/262.88	   U12(x0, mark(x1), x2)
744.01/262.88	   U12(x0, x1, mark(x2))
744.01/262.88	   U12(active(x0), x1, x2)
744.01/262.88	   U12(x0, active(x1), x2)
744.01/262.88	   U12(x0, x1, active(x2))
744.01/262.88	   U13(mark(x0), x1, x2)
744.01/262.88	   U13(x0, mark(x1), x2)
744.01/262.88	   U13(x0, x1, mark(x2))
744.01/262.88	   U13(active(x0), x1, x2)
744.01/262.88	   U13(x0, active(x1), x2)
744.01/262.88	   U13(x0, x1, active(x2))
744.01/262.88	   U14(mark(x0), x1, x2)
744.01/262.88	   U14(x0, mark(x1), x2)
744.01/262.88	   U14(x0, x1, mark(x2))
744.01/262.88	   U14(active(x0), x1, x2)
744.01/262.88	   U14(x0, active(x1), x2)
744.01/262.88	   U14(x0, x1, active(x2))
744.01/262.88	   U15(mark(x0), x1)
744.01/262.88	   U15(x0, mark(x1))
744.01/262.88	   U15(active(x0), x1)
744.01/262.88	   U15(x0, active(x1))
744.01/262.88	   U16(mark(x0))
744.01/262.88	   U16(active(x0))
744.01/262.88	   U21(mark(x0), x1)
744.01/262.88	   U21(x0, mark(x1))
744.01/262.88	   U21(active(x0), x1)
744.01/262.88	   U21(x0, active(x1))
744.01/262.88	   U22(mark(x0), x1)
744.01/262.88	   U22(x0, mark(x1))
744.01/262.88	   U22(active(x0), x1)
744.01/262.88	   U22(x0, active(x1))
744.01/262.88	   U23(mark(x0))
744.01/262.88	   U23(active(x0))
744.01/262.88	   U31(mark(x0), x1, x2)
744.01/262.88	   U31(x0, mark(x1), x2)
744.01/262.88	   U31(x0, x1, mark(x2))
744.01/262.88	   U31(active(x0), x1, x2)
744.01/262.88	   U31(x0, active(x1), x2)
744.01/262.88	   U31(x0, x1, active(x2))
744.01/262.88	   U32(mark(x0), x1, x2)
744.01/262.88	   U32(x0, mark(x1), x2)
744.01/262.88	   U32(x0, x1, mark(x2))
744.01/262.88	   U32(active(x0), x1, x2)
744.01/262.88	   U32(x0, active(x1), x2)
744.01/262.88	   U32(x0, x1, active(x2))
744.01/262.88	   U33(mark(x0), x1, x2)
744.01/262.88	   U33(x0, mark(x1), x2)
744.01/262.88	   U33(x0, x1, mark(x2))
744.01/262.88	   U33(active(x0), x1, x2)
744.01/262.88	   U33(x0, active(x1), x2)
744.01/262.88	   U33(x0, x1, active(x2))
744.01/262.88	   U34(mark(x0), x1, x2)
744.01/262.88	   U34(x0, mark(x1), x2)
744.01/262.88	   U34(x0, x1, mark(x2))
744.01/262.88	   U34(active(x0), x1, x2)
744.01/262.88	   U34(x0, active(x1), x2)
744.01/262.88	   U34(x0, x1, active(x2))
744.01/262.88	   U35(mark(x0), x1)
744.01/262.88	   U35(x0, mark(x1))
744.01/262.88	   U35(active(x0), x1)
744.01/262.88	   U35(x0, active(x1))
744.01/262.88	   U36(mark(x0))
744.01/262.88	   U36(active(x0))
744.01/262.88	   U41(mark(x0), x1)
744.01/262.88	   U41(x0, mark(x1))
744.01/262.88	   U41(active(x0), x1)
744.01/262.88	   U41(x0, active(x1))
744.01/262.88	   U42(mark(x0))
744.01/262.88	   U42(active(x0))
744.01/262.88	   U51(mark(x0))
744.01/262.88	   U51(active(x0))
744.01/262.88	   U61(mark(x0), x1)
744.01/262.88	   U61(x0, mark(x1))
744.01/262.88	   U61(active(x0), x1)
744.01/262.88	   U61(x0, active(x1))
744.01/262.88	   U62(mark(x0))
744.01/262.88	   U62(active(x0))
744.01/262.88	   U71(mark(x0), x1)
744.01/262.88	   U71(x0, mark(x1))
744.01/262.88	   U71(active(x0), x1)
744.01/262.88	   U71(x0, active(x1))
744.01/262.88	   U72(mark(x0), x1)
744.01/262.88	   U72(x0, mark(x1))
744.01/262.88	   U72(active(x0), x1)
744.01/262.88	   U72(x0, active(x1))
744.01/262.88	   U81(mark(x0), x1, x2)
744.01/262.88	   U81(x0, mark(x1), x2)
744.01/262.88	   U81(x0, x1, mark(x2))
744.01/262.88	   U81(active(x0), x1, x2)
744.01/262.88	   U81(x0, active(x1), x2)
744.01/262.88	   U81(x0, x1, active(x2))
744.01/262.88	   U82(mark(x0), x1, x2)
744.01/262.88	   U82(x0, mark(x1), x2)
744.01/262.88	   U82(x0, x1, mark(x2))
744.01/262.88	   U82(active(x0), x1, x2)
744.01/262.88	   U82(x0, active(x1), x2)
744.01/262.88	   U82(x0, x1, active(x2))
744.01/262.88	   U83(mark(x0), x1, x2)
744.01/262.88	   U83(x0, mark(x1), x2)
744.01/262.88	   U83(x0, x1, mark(x2))
744.01/262.88	   U83(active(x0), x1, x2)
744.01/262.88	   U83(x0, active(x1), x2)
744.01/262.88	   U83(x0, x1, active(x2))
744.01/262.88	   U84(mark(x0), x1, x2)
744.01/262.88	   U84(x0, mark(x1), x2)
744.01/262.88	   U84(x0, x1, mark(x2))
744.01/262.88	   U84(active(x0), x1, x2)
744.01/262.88	   U84(x0, active(x1), x2)
744.01/262.88	   U84(x0, x1, active(x2))
744.01/262.88	   s(mark(x0))
744.01/262.88	   s(active(x0))
744.01/262.88	   U91(mark(x0), x1)
744.01/262.88	   U91(x0, mark(x1))
744.01/262.88	   U91(active(x0), x1)
744.01/262.88	   U91(x0, active(x1))
744.01/262.88	   U92(mark(x0))
744.01/262.88	   U92(active(x0))
744.01/262.88	
744.01/262.88	We have to consider all minimal (P,Q,R)-chains.
744.01/262.88	----------------------------------------
744.01/262.88	
744.01/262.88	(148) QReductionProof (EQUIVALENT)
744.01/262.88	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.88	
744.01/262.88	   U101(mark(x0), x1, x2)
744.01/262.88	   U101(x0, mark(x1), x2)
744.01/262.88	   U101(x0, x1, mark(x2))
744.01/262.88	   U101(active(x0), x1, x2)
744.01/262.88	   U101(x0, active(x1), x2)
744.01/262.88	   U101(x0, x1, active(x2))
744.01/262.88	   U102(mark(x0), x1, x2)
744.01/262.88	   U102(x0, mark(x1), x2)
744.01/262.88	   U102(x0, x1, mark(x2))
744.01/262.88	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(149)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U23^1(active(X)) -> U23^1(X)
744.01/262.89	   U23^1(mark(X)) -> U23^1(X)
744.01/262.89	
744.01/262.89	R is empty.
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(150) QDPSizeChangeProof (EQUIVALENT)
744.01/262.89	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. 
744.01/262.89	
744.01/262.89	From the DPs we obtained the following set of size-change graphs:
744.01/262.89	*U23^1(active(X)) -> U23^1(X)
744.01/262.89	The graph contains the following edges 1 > 1
744.01/262.89	
744.01/262.89	
744.01/262.89	*U23^1(mark(X)) -> U23^1(X)
744.01/262.89	The graph contains the following edges 1 > 1
744.01/262.89	
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(151)
744.01/262.89	YES
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(152)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U22^1(X1, mark(X2)) -> U22^1(X1, X2)
744.01/262.89	   U22^1(mark(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(active(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(X1, active(X2)) -> U22^1(X1, X2)
744.01/262.89	
744.01/262.89	The TRS R consists of the following rules:
744.01/262.89	
744.01/262.89	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.89	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.89	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.89	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.89	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.89	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.89	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.89	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.89	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.89	   active(U16(tt)) -> mark(tt)
744.01/262.89	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.89	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.89	   active(U23(tt)) -> mark(tt)
744.01/262.89	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.89	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.89	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.89	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.89	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.89	   active(U36(tt)) -> mark(tt)
744.01/262.89	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.89	   active(U42(tt)) -> mark(tt)
744.01/262.89	   active(U51(tt)) -> mark(tt)
744.01/262.89	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.89	   active(U62(tt)) -> mark(tt)
744.01/262.89	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.89	   active(U72(tt, N)) -> mark(N)
744.01/262.89	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.89	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.89	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.89	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.89	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.89	   active(U92(tt)) -> mark(0)
744.01/262.89	   active(isNat(0)) -> mark(tt)
744.01/262.89	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.89	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.89	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.89	   active(isNatKind(0)) -> mark(tt)
744.01/262.89	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.89	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.89	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.89	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.89	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.89	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.89	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.89	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.89	   mark(tt) -> active(tt)
744.01/262.89	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.89	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.89	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.89	   mark(isNat(X)) -> active(isNat(X))
744.01/262.89	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.89	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.89	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.89	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.89	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.89	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.89	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.89	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.89	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.89	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.89	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.89	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.89	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.89	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.89	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.89	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.89	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.89	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.89	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.89	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.89	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.89	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.89	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.89	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.89	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.89	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.89	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.89	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.89	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.89	   mark(s(X)) -> active(s(mark(X)))
744.01/262.89	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.89	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.89	   mark(0) -> active(0)
744.01/262.89	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.89	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.89	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.89	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.89	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.89	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.89	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.89	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.89	   isNat(mark(X)) -> isNat(X)
744.01/262.89	   isNat(active(X)) -> isNat(X)
744.01/262.89	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.89	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.89	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.89	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.89	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.89	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.89	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.89	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.89	   x(active(X1), X2) -> x(X1, X2)
744.01/262.89	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.89	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.89	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.89	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.89	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.89	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.89	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.89	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.89	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.89	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.89	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.89	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.89	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.89	   U16(mark(X)) -> U16(X)
744.01/262.89	   U16(active(X)) -> U16(X)
744.01/262.89	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.89	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.89	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.89	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.89	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.89	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.89	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.89	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.89	   U23(mark(X)) -> U23(X)
744.01/262.89	   U23(active(X)) -> U23(X)
744.01/262.89	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.89	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.89	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.89	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.89	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.89	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.89	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.89	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.89	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.89	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.89	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.89	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.89	   U36(mark(X)) -> U36(X)
744.01/262.89	   U36(active(X)) -> U36(X)
744.01/262.89	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.89	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.89	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.89	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.89	   U42(mark(X)) -> U42(X)
744.01/262.89	   U42(active(X)) -> U42(X)
744.01/262.89	   U51(mark(X)) -> U51(X)
744.01/262.89	   U51(active(X)) -> U51(X)
744.01/262.89	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.89	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.89	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.89	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.89	   U62(mark(X)) -> U62(X)
744.01/262.89	   U62(active(X)) -> U62(X)
744.01/262.89	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.89	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.89	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.89	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.89	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.89	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.89	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.89	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.89	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.89	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.89	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.89	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.89	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.89	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.89	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.89	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.89	   s(mark(X)) -> s(X)
744.01/262.89	   s(active(X)) -> s(X)
744.01/262.89	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.89	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.89	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.89	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.89	   U92(mark(X)) -> U92(X)
744.01/262.89	   U92(active(X)) -> U92(X)
744.01/262.89	
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.89	   U101(x0, active(x1), x2)
744.01/262.89	   U101(x0, x1, active(x2))
744.01/262.89	   U102(mark(x0), x1, x2)
744.01/262.89	   U102(x0, mark(x1), x2)
744.01/262.89	   U102(x0, x1, mark(x2))
744.01/262.89	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(153) UsableRulesProof (EQUIVALENT)
744.01/262.89	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.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(154)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U22^1(X1, mark(X2)) -> U22^1(X1, X2)
744.01/262.89	   U22^1(mark(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(active(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(X1, active(X2)) -> U22^1(X1, X2)
744.01/262.89	
744.01/262.89	R is empty.
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.89	   U101(x0, active(x1), x2)
744.01/262.89	   U101(x0, x1, active(x2))
744.01/262.89	   U102(mark(x0), x1, x2)
744.01/262.89	   U102(x0, mark(x1), x2)
744.01/262.89	   U102(x0, x1, mark(x2))
744.01/262.89	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(155) QReductionProof (EQUIVALENT)
744.01/262.89	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.89	
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.89	   U101(x0, active(x1), x2)
744.01/262.89	   U101(x0, x1, active(x2))
744.01/262.89	   U102(mark(x0), x1, x2)
744.01/262.89	   U102(x0, mark(x1), x2)
744.01/262.89	   U102(x0, x1, mark(x2))
744.01/262.89	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(156)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U22^1(X1, mark(X2)) -> U22^1(X1, X2)
744.01/262.89	   U22^1(mark(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(active(X1), X2) -> U22^1(X1, X2)
744.01/262.89	   U22^1(X1, active(X2)) -> U22^1(X1, X2)
744.01/262.89	
744.01/262.89	R is empty.
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(157) QDPSizeChangeProof (EQUIVALENT)
744.01/262.89	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. 
744.01/262.89	
744.01/262.89	From the DPs we obtained the following set of size-change graphs:
744.01/262.89	*U22^1(X1, mark(X2)) -> U22^1(X1, X2)
744.01/262.89	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.89	
744.01/262.89	
744.01/262.89	*U22^1(mark(X1), X2) -> U22^1(X1, X2)
744.01/262.89	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.89	
744.01/262.89	
744.01/262.89	*U22^1(active(X1), X2) -> U22^1(X1, X2)
744.01/262.89	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.89	
744.01/262.89	
744.01/262.89	*U22^1(X1, active(X2)) -> U22^1(X1, X2)
744.01/262.89	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.89	
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(158)
744.01/262.89	YES
744.01/262.89	
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(159)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U21^1(X1, mark(X2)) -> U21^1(X1, X2)
744.01/262.89	   U21^1(mark(X1), X2) -> U21^1(X1, X2)
744.01/262.89	   U21^1(active(X1), X2) -> U21^1(X1, X2)
744.01/262.89	   U21^1(X1, active(X2)) -> U21^1(X1, X2)
744.01/262.89	
744.01/262.89	The TRS R consists of the following rules:
744.01/262.89	
744.01/262.89	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.89	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.89	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.89	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.89	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.89	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.89	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.89	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.89	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.89	   active(U16(tt)) -> mark(tt)
744.01/262.89	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.89	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.89	   active(U23(tt)) -> mark(tt)
744.01/262.89	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.89	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.89	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.89	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.89	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.89	   active(U36(tt)) -> mark(tt)
744.01/262.89	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.89	   active(U42(tt)) -> mark(tt)
744.01/262.89	   active(U51(tt)) -> mark(tt)
744.01/262.89	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.89	   active(U62(tt)) -> mark(tt)
744.01/262.89	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.89	   active(U72(tt, N)) -> mark(N)
744.01/262.89	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.89	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.89	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.89	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.89	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.89	   active(U92(tt)) -> mark(0)
744.01/262.89	   active(isNat(0)) -> mark(tt)
744.01/262.89	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.89	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.89	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.89	   active(isNatKind(0)) -> mark(tt)
744.01/262.89	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.89	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.89	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.89	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.89	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.89	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.89	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.89	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.89	   mark(tt) -> active(tt)
744.01/262.89	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.89	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.89	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.89	   mark(isNat(X)) -> active(isNat(X))
744.01/262.89	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.89	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.89	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.89	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.89	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.89	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.89	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.89	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.89	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.89	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.89	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.89	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.89	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.89	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.89	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.89	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.89	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.89	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.89	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.89	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.89	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.89	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.89	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.89	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.89	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.89	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.89	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.89	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.89	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.89	   mark(s(X)) -> active(s(mark(X)))
744.01/262.89	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.89	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.89	   mark(0) -> active(0)
744.01/262.89	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.89	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.89	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.89	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.89	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.89	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.89	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.89	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.89	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.89	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.89	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.89	   isNat(mark(X)) -> isNat(X)
744.01/262.89	   isNat(active(X)) -> isNat(X)
744.01/262.89	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.89	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.89	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.89	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.89	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.89	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.89	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.89	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.89	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.89	   x(active(X1), X2) -> x(X1, X2)
744.01/262.89	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.89	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.89	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.89	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.89	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.89	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.89	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.89	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.89	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.89	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.89	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.89	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.89	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.89	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.89	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.89	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.89	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.89	   U16(mark(X)) -> U16(X)
744.01/262.89	   U16(active(X)) -> U16(X)
744.01/262.89	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.89	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.89	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.89	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.89	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.89	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.89	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.89	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.89	   U23(mark(X)) -> U23(X)
744.01/262.89	   U23(active(X)) -> U23(X)
744.01/262.89	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.89	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.89	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.89	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.89	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.89	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.89	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.89	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.89	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.89	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.89	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.89	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.89	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.89	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.89	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.89	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.89	   U36(mark(X)) -> U36(X)
744.01/262.89	   U36(active(X)) -> U36(X)
744.01/262.89	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.89	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.89	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.89	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.89	   U42(mark(X)) -> U42(X)
744.01/262.89	   U42(active(X)) -> U42(X)
744.01/262.89	   U51(mark(X)) -> U51(X)
744.01/262.89	   U51(active(X)) -> U51(X)
744.01/262.89	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.89	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.89	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.89	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.89	   U62(mark(X)) -> U62(X)
744.01/262.89	   U62(active(X)) -> U62(X)
744.01/262.89	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.89	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.89	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.89	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.89	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.89	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.89	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.89	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.89	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.89	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.89	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.89	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.89	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.89	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.89	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.89	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.89	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.89	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.89	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.89	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.89	   s(mark(X)) -> s(X)
744.01/262.89	   s(active(X)) -> s(X)
744.01/262.89	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.89	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.89	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.89	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.89	   U92(mark(X)) -> U92(X)
744.01/262.89	   U92(active(X)) -> U92(X)
744.01/262.89	
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.89	   U101(x0, active(x1), x2)
744.01/262.89	   U101(x0, x1, active(x2))
744.01/262.89	   U102(mark(x0), x1, x2)
744.01/262.89	   U102(x0, mark(x1), x2)
744.01/262.89	   U102(x0, x1, mark(x2))
744.01/262.89	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(160) UsableRulesProof (EQUIVALENT)
744.01/262.89	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.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(161)
744.01/262.89	Obligation:
744.01/262.89	Q DP problem:
744.01/262.89	The TRS P consists of the following rules:
744.01/262.89	
744.01/262.89	   U21^1(X1, mark(X2)) -> U21^1(X1, X2)
744.01/262.89	   U21^1(mark(X1), X2) -> U21^1(X1, X2)
744.01/262.89	   U21^1(active(X1), X2) -> U21^1(X1, X2)
744.01/262.89	   U21^1(X1, active(X2)) -> U21^1(X1, X2)
744.01/262.89	
744.01/262.89	R is empty.
744.01/262.89	The set Q consists of the following terms:
744.01/262.89	
744.01/262.89	   active(U101(tt, x0, x1))
744.01/262.89	   active(U102(tt, x0, x1))
744.01/262.89	   active(U103(tt, x0, x1))
744.01/262.89	   active(U104(tt, x0, x1))
744.01/262.89	   active(U11(tt, x0, x1))
744.01/262.89	   active(U12(tt, x0, x1))
744.01/262.89	   active(U13(tt, x0, x1))
744.01/262.89	   active(U14(tt, x0, x1))
744.01/262.89	   active(U15(tt, x0))
744.01/262.89	   active(U16(tt))
744.01/262.89	   active(U21(tt, x0))
744.01/262.89	   active(U22(tt, x0))
744.01/262.89	   active(U23(tt))
744.01/262.89	   active(U31(tt, x0, x1))
744.01/262.89	   active(U32(tt, x0, x1))
744.01/262.89	   active(U33(tt, x0, x1))
744.01/262.89	   active(U34(tt, x0, x1))
744.01/262.89	   active(U35(tt, x0))
744.01/262.89	   active(U36(tt))
744.01/262.89	   active(U41(tt, x0))
744.01/262.89	   active(U42(tt))
744.01/262.89	   active(U51(tt))
744.01/262.89	   active(U61(tt, x0))
744.01/262.89	   active(U62(tt))
744.01/262.89	   active(U71(tt, x0))
744.01/262.89	   active(U72(tt, x0))
744.01/262.89	   active(U81(tt, x0, x1))
744.01/262.89	   active(U82(tt, x0, x1))
744.01/262.89	   active(U83(tt, x0, x1))
744.01/262.89	   active(U84(tt, x0, x1))
744.01/262.89	   active(U91(tt, x0))
744.01/262.89	   active(U92(tt))
744.01/262.89	   active(isNat(0))
744.01/262.89	   active(isNat(plus(x0, x1)))
744.01/262.89	   active(isNat(s(x0)))
744.01/262.89	   active(isNat(x(x0, x1)))
744.01/262.89	   active(isNatKind(0))
744.01/262.89	   active(isNatKind(plus(x0, x1)))
744.01/262.89	   active(isNatKind(s(x0)))
744.01/262.89	   active(isNatKind(x(x0, x1)))
744.01/262.89	   active(plus(x0, 0))
744.01/262.89	   active(plus(x0, s(x1)))
744.01/262.89	   active(x(x0, 0))
744.01/262.89	   active(x(x0, s(x1)))
744.01/262.89	   mark(U101(x0, x1, x2))
744.01/262.89	   mark(tt)
744.01/262.89	   mark(U102(x0, x1, x2))
744.01/262.89	   mark(isNatKind(x0))
744.01/262.89	   mark(U103(x0, x1, x2))
744.01/262.89	   mark(isNat(x0))
744.01/262.89	   mark(U104(x0, x1, x2))
744.01/262.89	   mark(plus(x0, x1))
744.01/262.89	   mark(x(x0, x1))
744.01/262.89	   mark(U11(x0, x1, x2))
744.01/262.89	   mark(U12(x0, x1, x2))
744.01/262.89	   mark(U13(x0, x1, x2))
744.01/262.89	   mark(U14(x0, x1, x2))
744.01/262.89	   mark(U15(x0, x1))
744.01/262.89	   mark(U16(x0))
744.01/262.89	   mark(U21(x0, x1))
744.01/262.89	   mark(U22(x0, x1))
744.01/262.89	   mark(U23(x0))
744.01/262.89	   mark(U31(x0, x1, x2))
744.01/262.89	   mark(U32(x0, x1, x2))
744.01/262.89	   mark(U33(x0, x1, x2))
744.01/262.89	   mark(U34(x0, x1, x2))
744.01/262.89	   mark(U35(x0, x1))
744.01/262.89	   mark(U36(x0))
744.01/262.89	   mark(U41(x0, x1))
744.01/262.89	   mark(U42(x0))
744.01/262.89	   mark(U51(x0))
744.01/262.89	   mark(U61(x0, x1))
744.01/262.89	   mark(U62(x0))
744.01/262.89	   mark(U71(x0, x1))
744.01/262.89	   mark(U72(x0, x1))
744.01/262.89	   mark(U81(x0, x1, x2))
744.01/262.89	   mark(U82(x0, x1, x2))
744.01/262.89	   mark(U83(x0, x1, x2))
744.01/262.89	   mark(U84(x0, x1, x2))
744.01/262.89	   mark(s(x0))
744.01/262.89	   mark(U91(x0, x1))
744.01/262.89	   mark(U92(x0))
744.01/262.89	   mark(0)
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.89	   U101(x0, active(x1), x2)
744.01/262.89	   U101(x0, x1, active(x2))
744.01/262.89	   U102(mark(x0), x1, x2)
744.01/262.89	   U102(x0, mark(x1), x2)
744.01/262.89	   U102(x0, x1, mark(x2))
744.01/262.89	   U102(active(x0), x1, x2)
744.01/262.89	   U102(x0, active(x1), x2)
744.01/262.89	   U102(x0, x1, active(x2))
744.01/262.89	   isNatKind(mark(x0))
744.01/262.89	   isNatKind(active(x0))
744.01/262.89	   U103(mark(x0), x1, x2)
744.01/262.89	   U103(x0, mark(x1), x2)
744.01/262.89	   U103(x0, x1, mark(x2))
744.01/262.89	   U103(active(x0), x1, x2)
744.01/262.89	   U103(x0, active(x1), x2)
744.01/262.89	   U103(x0, x1, active(x2))
744.01/262.89	   isNat(mark(x0))
744.01/262.89	   isNat(active(x0))
744.01/262.89	   U104(mark(x0), x1, x2)
744.01/262.89	   U104(x0, mark(x1), x2)
744.01/262.89	   U104(x0, x1, mark(x2))
744.01/262.89	   U104(active(x0), x1, x2)
744.01/262.89	   U104(x0, active(x1), x2)
744.01/262.89	   U104(x0, x1, active(x2))
744.01/262.89	   plus(mark(x0), x1)
744.01/262.89	   plus(x0, mark(x1))
744.01/262.89	   plus(active(x0), x1)
744.01/262.89	   plus(x0, active(x1))
744.01/262.89	   x(mark(x0), x1)
744.01/262.89	   x(x0, mark(x1))
744.01/262.89	   x(active(x0), x1)
744.01/262.89	   x(x0, active(x1))
744.01/262.89	   U11(mark(x0), x1, x2)
744.01/262.89	   U11(x0, mark(x1), x2)
744.01/262.89	   U11(x0, x1, mark(x2))
744.01/262.89	   U11(active(x0), x1, x2)
744.01/262.89	   U11(x0, active(x1), x2)
744.01/262.89	   U11(x0, x1, active(x2))
744.01/262.89	   U12(mark(x0), x1, x2)
744.01/262.89	   U12(x0, mark(x1), x2)
744.01/262.89	   U12(x0, x1, mark(x2))
744.01/262.89	   U12(active(x0), x1, x2)
744.01/262.89	   U12(x0, active(x1), x2)
744.01/262.89	   U12(x0, x1, active(x2))
744.01/262.89	   U13(mark(x0), x1, x2)
744.01/262.89	   U13(x0, mark(x1), x2)
744.01/262.89	   U13(x0, x1, mark(x2))
744.01/262.89	   U13(active(x0), x1, x2)
744.01/262.89	   U13(x0, active(x1), x2)
744.01/262.89	   U13(x0, x1, active(x2))
744.01/262.89	   U14(mark(x0), x1, x2)
744.01/262.89	   U14(x0, mark(x1), x2)
744.01/262.89	   U14(x0, x1, mark(x2))
744.01/262.89	   U14(active(x0), x1, x2)
744.01/262.89	   U14(x0, active(x1), x2)
744.01/262.89	   U14(x0, x1, active(x2))
744.01/262.89	   U15(mark(x0), x1)
744.01/262.89	   U15(x0, mark(x1))
744.01/262.89	   U15(active(x0), x1)
744.01/262.89	   U15(x0, active(x1))
744.01/262.89	   U16(mark(x0))
744.01/262.89	   U16(active(x0))
744.01/262.89	   U21(mark(x0), x1)
744.01/262.89	   U21(x0, mark(x1))
744.01/262.89	   U21(active(x0), x1)
744.01/262.89	   U21(x0, active(x1))
744.01/262.89	   U22(mark(x0), x1)
744.01/262.89	   U22(x0, mark(x1))
744.01/262.89	   U22(active(x0), x1)
744.01/262.89	   U22(x0, active(x1))
744.01/262.89	   U23(mark(x0))
744.01/262.89	   U23(active(x0))
744.01/262.89	   U31(mark(x0), x1, x2)
744.01/262.89	   U31(x0, mark(x1), x2)
744.01/262.89	   U31(x0, x1, mark(x2))
744.01/262.89	   U31(active(x0), x1, x2)
744.01/262.89	   U31(x0, active(x1), x2)
744.01/262.89	   U31(x0, x1, active(x2))
744.01/262.89	   U32(mark(x0), x1, x2)
744.01/262.89	   U32(x0, mark(x1), x2)
744.01/262.89	   U32(x0, x1, mark(x2))
744.01/262.89	   U32(active(x0), x1, x2)
744.01/262.89	   U32(x0, active(x1), x2)
744.01/262.89	   U32(x0, x1, active(x2))
744.01/262.89	   U33(mark(x0), x1, x2)
744.01/262.89	   U33(x0, mark(x1), x2)
744.01/262.89	   U33(x0, x1, mark(x2))
744.01/262.89	   U33(active(x0), x1, x2)
744.01/262.89	   U33(x0, active(x1), x2)
744.01/262.89	   U33(x0, x1, active(x2))
744.01/262.89	   U34(mark(x0), x1, x2)
744.01/262.89	   U34(x0, mark(x1), x2)
744.01/262.89	   U34(x0, x1, mark(x2))
744.01/262.89	   U34(active(x0), x1, x2)
744.01/262.89	   U34(x0, active(x1), x2)
744.01/262.89	   U34(x0, x1, active(x2))
744.01/262.89	   U35(mark(x0), x1)
744.01/262.89	   U35(x0, mark(x1))
744.01/262.89	   U35(active(x0), x1)
744.01/262.89	   U35(x0, active(x1))
744.01/262.89	   U36(mark(x0))
744.01/262.89	   U36(active(x0))
744.01/262.89	   U41(mark(x0), x1)
744.01/262.89	   U41(x0, mark(x1))
744.01/262.89	   U41(active(x0), x1)
744.01/262.89	   U41(x0, active(x1))
744.01/262.89	   U42(mark(x0))
744.01/262.89	   U42(active(x0))
744.01/262.89	   U51(mark(x0))
744.01/262.89	   U51(active(x0))
744.01/262.89	   U61(mark(x0), x1)
744.01/262.89	   U61(x0, mark(x1))
744.01/262.89	   U61(active(x0), x1)
744.01/262.89	   U61(x0, active(x1))
744.01/262.89	   U62(mark(x0))
744.01/262.89	   U62(active(x0))
744.01/262.89	   U71(mark(x0), x1)
744.01/262.89	   U71(x0, mark(x1))
744.01/262.89	   U71(active(x0), x1)
744.01/262.89	   U71(x0, active(x1))
744.01/262.89	   U72(mark(x0), x1)
744.01/262.89	   U72(x0, mark(x1))
744.01/262.89	   U72(active(x0), x1)
744.01/262.89	   U72(x0, active(x1))
744.01/262.89	   U81(mark(x0), x1, x2)
744.01/262.89	   U81(x0, mark(x1), x2)
744.01/262.89	   U81(x0, x1, mark(x2))
744.01/262.89	   U81(active(x0), x1, x2)
744.01/262.89	   U81(x0, active(x1), x2)
744.01/262.89	   U81(x0, x1, active(x2))
744.01/262.89	   U82(mark(x0), x1, x2)
744.01/262.89	   U82(x0, mark(x1), x2)
744.01/262.89	   U82(x0, x1, mark(x2))
744.01/262.89	   U82(active(x0), x1, x2)
744.01/262.89	   U82(x0, active(x1), x2)
744.01/262.89	   U82(x0, x1, active(x2))
744.01/262.89	   U83(mark(x0), x1, x2)
744.01/262.89	   U83(x0, mark(x1), x2)
744.01/262.89	   U83(x0, x1, mark(x2))
744.01/262.89	   U83(active(x0), x1, x2)
744.01/262.89	   U83(x0, active(x1), x2)
744.01/262.89	   U83(x0, x1, active(x2))
744.01/262.89	   U84(mark(x0), x1, x2)
744.01/262.89	   U84(x0, mark(x1), x2)
744.01/262.89	   U84(x0, x1, mark(x2))
744.01/262.89	   U84(active(x0), x1, x2)
744.01/262.89	   U84(x0, active(x1), x2)
744.01/262.89	   U84(x0, x1, active(x2))
744.01/262.89	   s(mark(x0))
744.01/262.89	   s(active(x0))
744.01/262.89	   U91(mark(x0), x1)
744.01/262.89	   U91(x0, mark(x1))
744.01/262.89	   U91(active(x0), x1)
744.01/262.89	   U91(x0, active(x1))
744.01/262.89	   U92(mark(x0))
744.01/262.89	   U92(active(x0))
744.01/262.89	
744.01/262.89	We have to consider all minimal (P,Q,R)-chains.
744.01/262.89	----------------------------------------
744.01/262.89	
744.01/262.89	(162) QReductionProof (EQUIVALENT)
744.01/262.89	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.89	
744.01/262.89	   U101(mark(x0), x1, x2)
744.01/262.89	   U101(x0, mark(x1), x2)
744.01/262.89	   U101(x0, x1, mark(x2))
744.01/262.89	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.90	   U81(x0, x1, active(x2))
744.01/262.90	   U82(mark(x0), x1, x2)
744.01/262.90	   U82(x0, mark(x1), x2)
744.01/262.90	   U82(x0, x1, mark(x2))
744.01/262.90	   U82(active(x0), x1, x2)
744.01/262.90	   U82(x0, active(x1), x2)
744.01/262.90	   U82(x0, x1, active(x2))
744.01/262.90	   U83(mark(x0), x1, x2)
744.01/262.90	   U83(x0, mark(x1), x2)
744.01/262.90	   U83(x0, x1, mark(x2))
744.01/262.90	   U83(active(x0), x1, x2)
744.01/262.90	   U83(x0, active(x1), x2)
744.01/262.90	   U83(x0, x1, active(x2))
744.01/262.90	   U84(mark(x0), x1, x2)
744.01/262.90	   U84(x0, mark(x1), x2)
744.01/262.90	   U84(x0, x1, mark(x2))
744.01/262.90	   U84(active(x0), x1, x2)
744.01/262.90	   U84(x0, active(x1), x2)
744.01/262.90	   U84(x0, x1, active(x2))
744.01/262.90	   s(mark(x0))
744.01/262.90	   s(active(x0))
744.01/262.90	   U91(mark(x0), x1)
744.01/262.90	   U91(x0, mark(x1))
744.01/262.90	   U91(active(x0), x1)
744.01/262.90	   U91(x0, active(x1))
744.01/262.90	   U92(mark(x0))
744.01/262.90	   U92(active(x0))
744.01/262.90	
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(163)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U21^1(X1, mark(X2)) -> U21^1(X1, X2)
744.01/262.90	   U21^1(mark(X1), X2) -> U21^1(X1, X2)
744.01/262.90	   U21^1(active(X1), X2) -> U21^1(X1, X2)
744.01/262.90	   U21^1(X1, active(X2)) -> U21^1(X1, X2)
744.01/262.90	
744.01/262.90	R is empty.
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	
744.01/262.90	We have to consider all minimal (P,Q,R)-chains.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(164) QDPSizeChangeProof (EQUIVALENT)
744.01/262.90	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. 
744.01/262.90	
744.01/262.90	From the DPs we obtained the following set of size-change graphs:
744.01/262.90	*U21^1(X1, mark(X2)) -> U21^1(X1, X2)
744.01/262.90	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.90	
744.01/262.90	
744.01/262.90	*U21^1(mark(X1), X2) -> U21^1(X1, X2)
744.01/262.90	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.90	
744.01/262.90	
744.01/262.90	*U21^1(active(X1), X2) -> U21^1(X1, X2)
744.01/262.90	The graph contains the following edges 1 > 1, 2 >= 2
744.01/262.90	
744.01/262.90	
744.01/262.90	*U21^1(X1, active(X2)) -> U21^1(X1, X2)
744.01/262.90	The graph contains the following edges 1 >= 1, 2 > 2
744.01/262.90	
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(165)
744.01/262.90	YES
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(166)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U16^1(active(X)) -> U16^1(X)
744.01/262.90	   U16^1(mark(X)) -> U16^1(X)
744.01/262.90	
744.01/262.90	The TRS R consists of the following rules:
744.01/262.90	
744.01/262.90	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.90	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.90	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.90	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.90	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.90	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.90	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.90	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.90	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.90	   active(U16(tt)) -> mark(tt)
744.01/262.90	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.90	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.90	   active(U23(tt)) -> mark(tt)
744.01/262.90	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.90	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.90	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.90	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.90	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.90	   active(U36(tt)) -> mark(tt)
744.01/262.90	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.90	   active(U42(tt)) -> mark(tt)
744.01/262.90	   active(U51(tt)) -> mark(tt)
744.01/262.90	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.90	   active(U62(tt)) -> mark(tt)
744.01/262.90	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.90	   active(U72(tt, N)) -> mark(N)
744.01/262.90	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.90	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.90	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.90	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.90	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.90	   active(U92(tt)) -> mark(0)
744.01/262.90	   active(isNat(0)) -> mark(tt)
744.01/262.90	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.90	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.90	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.90	   active(isNatKind(0)) -> mark(tt)
744.01/262.90	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.90	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.90	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.90	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.90	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.90	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.90	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.90	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.90	   mark(tt) -> active(tt)
744.01/262.90	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.90	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.90	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.90	   mark(isNat(X)) -> active(isNat(X))
744.01/262.90	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.90	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.90	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.90	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.90	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.90	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.90	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.90	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.90	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.90	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.90	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.90	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.90	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.90	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.90	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.90	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.90	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.90	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.90	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.90	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.90	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.90	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.90	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.90	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.90	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.90	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.90	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.90	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.90	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.90	   mark(s(X)) -> active(s(mark(X)))
744.01/262.90	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.90	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.90	   mark(0) -> active(0)
744.01/262.90	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.90	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.90	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.90	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.90	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.90	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.90	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.90	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.90	   isNat(mark(X)) -> isNat(X)
744.01/262.90	   isNat(active(X)) -> isNat(X)
744.01/262.90	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.90	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.90	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.90	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.90	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.90	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.90	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.90	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.90	   x(active(X1), X2) -> x(X1, X2)
744.01/262.90	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.90	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.90	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.90	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.90	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.90	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.90	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.90	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.90	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.90	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.90	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.90	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.90	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.90	   U16(mark(X)) -> U16(X)
744.01/262.90	   U16(active(X)) -> U16(X)
744.01/262.90	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.90	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.90	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.90	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.90	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.90	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.90	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.90	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.90	   U23(mark(X)) -> U23(X)
744.01/262.90	   U23(active(X)) -> U23(X)
744.01/262.90	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.90	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.90	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.90	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.90	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.90	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.90	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.90	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.90	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.90	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.90	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.90	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.90	   U36(mark(X)) -> U36(X)
744.01/262.90	   U36(active(X)) -> U36(X)
744.01/262.90	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.90	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.90	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.90	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.90	   U42(mark(X)) -> U42(X)
744.01/262.90	   U42(active(X)) -> U42(X)
744.01/262.90	   U51(mark(X)) -> U51(X)
744.01/262.90	   U51(active(X)) -> U51(X)
744.01/262.90	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.90	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.90	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.90	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.90	   U62(mark(X)) -> U62(X)
744.01/262.90	   U62(active(X)) -> U62(X)
744.01/262.90	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.90	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.90	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.90	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.90	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.90	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.90	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.90	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.90	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.90	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.90	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.90	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.90	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.90	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.90	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.90	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.90	   s(mark(X)) -> s(X)
744.01/262.90	   s(active(X)) -> s(X)
744.01/262.90	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.90	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.90	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.90	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.90	   U92(mark(X)) -> U92(X)
744.01/262.90	   U92(active(X)) -> U92(X)
744.01/262.90	
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	   U101(mark(x0), x1, x2)
744.01/262.90	   U101(x0, mark(x1), x2)
744.01/262.90	   U101(x0, x1, mark(x2))
744.01/262.90	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.90	   U81(x0, x1, active(x2))
744.01/262.90	   U82(mark(x0), x1, x2)
744.01/262.90	   U82(x0, mark(x1), x2)
744.01/262.90	   U82(x0, x1, mark(x2))
744.01/262.90	   U82(active(x0), x1, x2)
744.01/262.90	   U82(x0, active(x1), x2)
744.01/262.90	   U82(x0, x1, active(x2))
744.01/262.90	   U83(mark(x0), x1, x2)
744.01/262.90	   U83(x0, mark(x1), x2)
744.01/262.90	   U83(x0, x1, mark(x2))
744.01/262.90	   U83(active(x0), x1, x2)
744.01/262.90	   U83(x0, active(x1), x2)
744.01/262.90	   U83(x0, x1, active(x2))
744.01/262.90	   U84(mark(x0), x1, x2)
744.01/262.90	   U84(x0, mark(x1), x2)
744.01/262.90	   U84(x0, x1, mark(x2))
744.01/262.90	   U84(active(x0), x1, x2)
744.01/262.90	   U84(x0, active(x1), x2)
744.01/262.90	   U84(x0, x1, active(x2))
744.01/262.90	   s(mark(x0))
744.01/262.90	   s(active(x0))
744.01/262.90	   U91(mark(x0), x1)
744.01/262.90	   U91(x0, mark(x1))
744.01/262.90	   U91(active(x0), x1)
744.01/262.90	   U91(x0, active(x1))
744.01/262.90	   U92(mark(x0))
744.01/262.90	   U92(active(x0))
744.01/262.90	
744.01/262.90	We have to consider all minimal (P,Q,R)-chains.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(167) UsableRulesProof (EQUIVALENT)
744.01/262.90	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.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(168)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U16^1(active(X)) -> U16^1(X)
744.01/262.90	   U16^1(mark(X)) -> U16^1(X)
744.01/262.90	
744.01/262.90	R is empty.
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	   U101(mark(x0), x1, x2)
744.01/262.90	   U101(x0, mark(x1), x2)
744.01/262.90	   U101(x0, x1, mark(x2))
744.01/262.90	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.90	   U81(x0, x1, active(x2))
744.01/262.90	   U82(mark(x0), x1, x2)
744.01/262.90	   U82(x0, mark(x1), x2)
744.01/262.90	   U82(x0, x1, mark(x2))
744.01/262.90	   U82(active(x0), x1, x2)
744.01/262.90	   U82(x0, active(x1), x2)
744.01/262.90	   U82(x0, x1, active(x2))
744.01/262.90	   U83(mark(x0), x1, x2)
744.01/262.90	   U83(x0, mark(x1), x2)
744.01/262.90	   U83(x0, x1, mark(x2))
744.01/262.90	   U83(active(x0), x1, x2)
744.01/262.90	   U83(x0, active(x1), x2)
744.01/262.90	   U83(x0, x1, active(x2))
744.01/262.90	   U84(mark(x0), x1, x2)
744.01/262.90	   U84(x0, mark(x1), x2)
744.01/262.90	   U84(x0, x1, mark(x2))
744.01/262.90	   U84(active(x0), x1, x2)
744.01/262.90	   U84(x0, active(x1), x2)
744.01/262.90	   U84(x0, x1, active(x2))
744.01/262.90	   s(mark(x0))
744.01/262.90	   s(active(x0))
744.01/262.90	   U91(mark(x0), x1)
744.01/262.90	   U91(x0, mark(x1))
744.01/262.90	   U91(active(x0), x1)
744.01/262.90	   U91(x0, active(x1))
744.01/262.90	   U92(mark(x0))
744.01/262.90	   U92(active(x0))
744.01/262.90	
744.01/262.90	We have to consider all minimal (P,Q,R)-chains.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(169) QReductionProof (EQUIVALENT)
744.01/262.90	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.90	
744.01/262.90	   U101(mark(x0), x1, x2)
744.01/262.90	   U101(x0, mark(x1), x2)
744.01/262.90	   U101(x0, x1, mark(x2))
744.01/262.90	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.90	   U81(x0, x1, active(x2))
744.01/262.90	   U82(mark(x0), x1, x2)
744.01/262.90	   U82(x0, mark(x1), x2)
744.01/262.90	   U82(x0, x1, mark(x2))
744.01/262.90	   U82(active(x0), x1, x2)
744.01/262.90	   U82(x0, active(x1), x2)
744.01/262.90	   U82(x0, x1, active(x2))
744.01/262.90	   U83(mark(x0), x1, x2)
744.01/262.90	   U83(x0, mark(x1), x2)
744.01/262.90	   U83(x0, x1, mark(x2))
744.01/262.90	   U83(active(x0), x1, x2)
744.01/262.90	   U83(x0, active(x1), x2)
744.01/262.90	   U83(x0, x1, active(x2))
744.01/262.90	   U84(mark(x0), x1, x2)
744.01/262.90	   U84(x0, mark(x1), x2)
744.01/262.90	   U84(x0, x1, mark(x2))
744.01/262.90	   U84(active(x0), x1, x2)
744.01/262.90	   U84(x0, active(x1), x2)
744.01/262.90	   U84(x0, x1, active(x2))
744.01/262.90	   s(mark(x0))
744.01/262.90	   s(active(x0))
744.01/262.90	   U91(mark(x0), x1)
744.01/262.90	   U91(x0, mark(x1))
744.01/262.90	   U91(active(x0), x1)
744.01/262.90	   U91(x0, active(x1))
744.01/262.90	   U92(mark(x0))
744.01/262.90	   U92(active(x0))
744.01/262.90	
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(170)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U16^1(active(X)) -> U16^1(X)
744.01/262.90	   U16^1(mark(X)) -> U16^1(X)
744.01/262.90	
744.01/262.90	R is empty.
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	
744.01/262.90	We have to consider all minimal (P,Q,R)-chains.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(171) QDPSizeChangeProof (EQUIVALENT)
744.01/262.90	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. 
744.01/262.90	
744.01/262.90	From the DPs we obtained the following set of size-change graphs:
744.01/262.90	*U16^1(active(X)) -> U16^1(X)
744.01/262.90	The graph contains the following edges 1 > 1
744.01/262.90	
744.01/262.90	
744.01/262.90	*U16^1(mark(X)) -> U16^1(X)
744.01/262.90	The graph contains the following edges 1 > 1
744.01/262.90	
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(172)
744.01/262.90	YES
744.01/262.90	
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(173)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U15^1(X1, mark(X2)) -> U15^1(X1, X2)
744.01/262.90	   U15^1(mark(X1), X2) -> U15^1(X1, X2)
744.01/262.90	   U15^1(active(X1), X2) -> U15^1(X1, X2)
744.01/262.90	   U15^1(X1, active(X2)) -> U15^1(X1, X2)
744.01/262.90	
744.01/262.90	The TRS R consists of the following rules:
744.01/262.90	
744.01/262.90	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.01/262.90	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.01/262.90	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.01/262.90	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.01/262.90	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.01/262.90	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.01/262.90	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.01/262.90	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.01/262.90	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.01/262.90	   active(U16(tt)) -> mark(tt)
744.01/262.90	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.01/262.90	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.01/262.90	   active(U23(tt)) -> mark(tt)
744.01/262.90	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.01/262.90	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.01/262.90	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.01/262.90	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.01/262.90	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.01/262.90	   active(U36(tt)) -> mark(tt)
744.01/262.90	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.01/262.90	   active(U42(tt)) -> mark(tt)
744.01/262.90	   active(U51(tt)) -> mark(tt)
744.01/262.90	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.01/262.90	   active(U62(tt)) -> mark(tt)
744.01/262.90	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.01/262.90	   active(U72(tt, N)) -> mark(N)
744.01/262.90	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.01/262.90	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.01/262.90	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.01/262.90	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.01/262.90	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.01/262.90	   active(U92(tt)) -> mark(0)
744.01/262.90	   active(isNat(0)) -> mark(tt)
744.01/262.90	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.01/262.90	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.01/262.90	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.01/262.90	   active(isNatKind(0)) -> mark(tt)
744.01/262.90	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.01/262.90	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.01/262.90	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.01/262.90	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.01/262.90	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.01/262.90	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.01/262.90	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.01/262.90	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.01/262.90	   mark(tt) -> active(tt)
744.01/262.90	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.01/262.90	   mark(isNatKind(X)) -> active(isNatKind(X))
744.01/262.90	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.01/262.90	   mark(isNat(X)) -> active(isNat(X))
744.01/262.90	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.01/262.90	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.01/262.90	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.01/262.90	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.01/262.90	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.01/262.90	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.01/262.90	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.01/262.90	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.01/262.90	   mark(U16(X)) -> active(U16(mark(X)))
744.01/262.90	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.01/262.90	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.01/262.90	   mark(U23(X)) -> active(U23(mark(X)))
744.01/262.90	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.01/262.90	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.01/262.90	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.01/262.90	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.01/262.90	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.01/262.90	   mark(U36(X)) -> active(U36(mark(X)))
744.01/262.90	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.01/262.90	   mark(U42(X)) -> active(U42(mark(X)))
744.01/262.90	   mark(U51(X)) -> active(U51(mark(X)))
744.01/262.90	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.01/262.90	   mark(U62(X)) -> active(U62(mark(X)))
744.01/262.90	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.01/262.90	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.01/262.90	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.01/262.90	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.01/262.90	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.01/262.90	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.01/262.90	   mark(s(X)) -> active(s(mark(X)))
744.01/262.90	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.01/262.90	   mark(U92(X)) -> active(U92(mark(X)))
744.01/262.90	   mark(0) -> active(0)
744.01/262.90	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.01/262.90	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.01/262.90	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.01/262.90	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.01/262.90	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.01/262.90	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.01/262.90	   isNatKind(mark(X)) -> isNatKind(X)
744.01/262.90	   isNatKind(active(X)) -> isNatKind(X)
744.01/262.90	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.01/262.90	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.01/262.90	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.01/262.90	   isNat(mark(X)) -> isNat(X)
744.01/262.90	   isNat(active(X)) -> isNat(X)
744.01/262.90	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.01/262.90	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.01/262.90	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.01/262.90	   plus(mark(X1), X2) -> plus(X1, X2)
744.01/262.90	   plus(X1, mark(X2)) -> plus(X1, X2)
744.01/262.90	   plus(active(X1), X2) -> plus(X1, X2)
744.01/262.90	   plus(X1, active(X2)) -> plus(X1, X2)
744.01/262.90	   x(mark(X1), X2) -> x(X1, X2)
744.01/262.90	   x(X1, mark(X2)) -> x(X1, X2)
744.01/262.90	   x(active(X1), X2) -> x(X1, X2)
744.01/262.90	   x(X1, active(X2)) -> x(X1, X2)
744.01/262.90	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.01/262.90	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.01/262.90	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.01/262.90	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.01/262.90	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.01/262.90	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.01/262.90	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.01/262.90	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.01/262.90	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.01/262.90	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.01/262.90	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.01/262.90	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.01/262.90	   U15(mark(X1), X2) -> U15(X1, X2)
744.01/262.90	   U15(X1, mark(X2)) -> U15(X1, X2)
744.01/262.90	   U15(active(X1), X2) -> U15(X1, X2)
744.01/262.90	   U15(X1, active(X2)) -> U15(X1, X2)
744.01/262.90	   U16(mark(X)) -> U16(X)
744.01/262.90	   U16(active(X)) -> U16(X)
744.01/262.90	   U21(mark(X1), X2) -> U21(X1, X2)
744.01/262.90	   U21(X1, mark(X2)) -> U21(X1, X2)
744.01/262.90	   U21(active(X1), X2) -> U21(X1, X2)
744.01/262.90	   U21(X1, active(X2)) -> U21(X1, X2)
744.01/262.90	   U22(mark(X1), X2) -> U22(X1, X2)
744.01/262.90	   U22(X1, mark(X2)) -> U22(X1, X2)
744.01/262.90	   U22(active(X1), X2) -> U22(X1, X2)
744.01/262.90	   U22(X1, active(X2)) -> U22(X1, X2)
744.01/262.90	   U23(mark(X)) -> U23(X)
744.01/262.90	   U23(active(X)) -> U23(X)
744.01/262.90	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.01/262.90	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.01/262.90	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.01/262.90	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.01/262.90	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.01/262.90	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.01/262.90	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.01/262.90	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.01/262.90	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.01/262.90	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.01/262.90	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.01/262.90	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.01/262.90	   U35(mark(X1), X2) -> U35(X1, X2)
744.01/262.90	   U35(X1, mark(X2)) -> U35(X1, X2)
744.01/262.90	   U35(active(X1), X2) -> U35(X1, X2)
744.01/262.90	   U35(X1, active(X2)) -> U35(X1, X2)
744.01/262.90	   U36(mark(X)) -> U36(X)
744.01/262.90	   U36(active(X)) -> U36(X)
744.01/262.90	   U41(mark(X1), X2) -> U41(X1, X2)
744.01/262.90	   U41(X1, mark(X2)) -> U41(X1, X2)
744.01/262.90	   U41(active(X1), X2) -> U41(X1, X2)
744.01/262.90	   U41(X1, active(X2)) -> U41(X1, X2)
744.01/262.90	   U42(mark(X)) -> U42(X)
744.01/262.90	   U42(active(X)) -> U42(X)
744.01/262.90	   U51(mark(X)) -> U51(X)
744.01/262.90	   U51(active(X)) -> U51(X)
744.01/262.90	   U61(mark(X1), X2) -> U61(X1, X2)
744.01/262.90	   U61(X1, mark(X2)) -> U61(X1, X2)
744.01/262.90	   U61(active(X1), X2) -> U61(X1, X2)
744.01/262.90	   U61(X1, active(X2)) -> U61(X1, X2)
744.01/262.90	   U62(mark(X)) -> U62(X)
744.01/262.90	   U62(active(X)) -> U62(X)
744.01/262.90	   U71(mark(X1), X2) -> U71(X1, X2)
744.01/262.90	   U71(X1, mark(X2)) -> U71(X1, X2)
744.01/262.90	   U71(active(X1), X2) -> U71(X1, X2)
744.01/262.90	   U71(X1, active(X2)) -> U71(X1, X2)
744.01/262.90	   U72(mark(X1), X2) -> U72(X1, X2)
744.01/262.90	   U72(X1, mark(X2)) -> U72(X1, X2)
744.01/262.90	   U72(active(X1), X2) -> U72(X1, X2)
744.01/262.90	   U72(X1, active(X2)) -> U72(X1, X2)
744.01/262.90	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.01/262.90	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.01/262.90	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.01/262.90	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.01/262.90	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.01/262.90	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.01/262.90	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.01/262.90	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.01/262.90	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.01/262.90	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.01/262.90	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.01/262.90	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.01/262.90	   s(mark(X)) -> s(X)
744.01/262.90	   s(active(X)) -> s(X)
744.01/262.90	   U91(mark(X1), X2) -> U91(X1, X2)
744.01/262.90	   U91(X1, mark(X2)) -> U91(X1, X2)
744.01/262.90	   U91(active(X1), X2) -> U91(X1, X2)
744.01/262.90	   U91(X1, active(X2)) -> U91(X1, X2)
744.01/262.90	   U92(mark(X)) -> U92(X)
744.01/262.90	   U92(active(X)) -> U92(X)
744.01/262.90	
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	   U101(mark(x0), x1, x2)
744.01/262.90	   U101(x0, mark(x1), x2)
744.01/262.90	   U101(x0, x1, mark(x2))
744.01/262.90	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.90	   U81(x0, x1, active(x2))
744.01/262.90	   U82(mark(x0), x1, x2)
744.01/262.90	   U82(x0, mark(x1), x2)
744.01/262.90	   U82(x0, x1, mark(x2))
744.01/262.90	   U82(active(x0), x1, x2)
744.01/262.90	   U82(x0, active(x1), x2)
744.01/262.90	   U82(x0, x1, active(x2))
744.01/262.90	   U83(mark(x0), x1, x2)
744.01/262.90	   U83(x0, mark(x1), x2)
744.01/262.90	   U83(x0, x1, mark(x2))
744.01/262.90	   U83(active(x0), x1, x2)
744.01/262.90	   U83(x0, active(x1), x2)
744.01/262.90	   U83(x0, x1, active(x2))
744.01/262.90	   U84(mark(x0), x1, x2)
744.01/262.90	   U84(x0, mark(x1), x2)
744.01/262.90	   U84(x0, x1, mark(x2))
744.01/262.90	   U84(active(x0), x1, x2)
744.01/262.90	   U84(x0, active(x1), x2)
744.01/262.90	   U84(x0, x1, active(x2))
744.01/262.90	   s(mark(x0))
744.01/262.90	   s(active(x0))
744.01/262.90	   U91(mark(x0), x1)
744.01/262.90	   U91(x0, mark(x1))
744.01/262.90	   U91(active(x0), x1)
744.01/262.90	   U91(x0, active(x1))
744.01/262.90	   U92(mark(x0))
744.01/262.90	   U92(active(x0))
744.01/262.90	
744.01/262.90	We have to consider all minimal (P,Q,R)-chains.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(174) UsableRulesProof (EQUIVALENT)
744.01/262.90	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.
744.01/262.90	----------------------------------------
744.01/262.90	
744.01/262.90	(175)
744.01/262.90	Obligation:
744.01/262.90	Q DP problem:
744.01/262.90	The TRS P consists of the following rules:
744.01/262.90	
744.01/262.90	   U15^1(X1, mark(X2)) -> U15^1(X1, X2)
744.01/262.90	   U15^1(mark(X1), X2) -> U15^1(X1, X2)
744.01/262.90	   U15^1(active(X1), X2) -> U15^1(X1, X2)
744.01/262.90	   U15^1(X1, active(X2)) -> U15^1(X1, X2)
744.01/262.90	
744.01/262.90	R is empty.
744.01/262.90	The set Q consists of the following terms:
744.01/262.90	
744.01/262.90	   active(U101(tt, x0, x1))
744.01/262.90	   active(U102(tt, x0, x1))
744.01/262.90	   active(U103(tt, x0, x1))
744.01/262.90	   active(U104(tt, x0, x1))
744.01/262.90	   active(U11(tt, x0, x1))
744.01/262.90	   active(U12(tt, x0, x1))
744.01/262.90	   active(U13(tt, x0, x1))
744.01/262.90	   active(U14(tt, x0, x1))
744.01/262.90	   active(U15(tt, x0))
744.01/262.90	   active(U16(tt))
744.01/262.90	   active(U21(tt, x0))
744.01/262.90	   active(U22(tt, x0))
744.01/262.90	   active(U23(tt))
744.01/262.90	   active(U31(tt, x0, x1))
744.01/262.90	   active(U32(tt, x0, x1))
744.01/262.90	   active(U33(tt, x0, x1))
744.01/262.90	   active(U34(tt, x0, x1))
744.01/262.90	   active(U35(tt, x0))
744.01/262.90	   active(U36(tt))
744.01/262.90	   active(U41(tt, x0))
744.01/262.90	   active(U42(tt))
744.01/262.90	   active(U51(tt))
744.01/262.90	   active(U61(tt, x0))
744.01/262.90	   active(U62(tt))
744.01/262.90	   active(U71(tt, x0))
744.01/262.90	   active(U72(tt, x0))
744.01/262.90	   active(U81(tt, x0, x1))
744.01/262.90	   active(U82(tt, x0, x1))
744.01/262.90	   active(U83(tt, x0, x1))
744.01/262.90	   active(U84(tt, x0, x1))
744.01/262.90	   active(U91(tt, x0))
744.01/262.90	   active(U92(tt))
744.01/262.90	   active(isNat(0))
744.01/262.90	   active(isNat(plus(x0, x1)))
744.01/262.90	   active(isNat(s(x0)))
744.01/262.90	   active(isNat(x(x0, x1)))
744.01/262.90	   active(isNatKind(0))
744.01/262.90	   active(isNatKind(plus(x0, x1)))
744.01/262.90	   active(isNatKind(s(x0)))
744.01/262.90	   active(isNatKind(x(x0, x1)))
744.01/262.90	   active(plus(x0, 0))
744.01/262.90	   active(plus(x0, s(x1)))
744.01/262.90	   active(x(x0, 0))
744.01/262.90	   active(x(x0, s(x1)))
744.01/262.90	   mark(U101(x0, x1, x2))
744.01/262.90	   mark(tt)
744.01/262.90	   mark(U102(x0, x1, x2))
744.01/262.90	   mark(isNatKind(x0))
744.01/262.90	   mark(U103(x0, x1, x2))
744.01/262.90	   mark(isNat(x0))
744.01/262.90	   mark(U104(x0, x1, x2))
744.01/262.90	   mark(plus(x0, x1))
744.01/262.90	   mark(x(x0, x1))
744.01/262.90	   mark(U11(x0, x1, x2))
744.01/262.90	   mark(U12(x0, x1, x2))
744.01/262.90	   mark(U13(x0, x1, x2))
744.01/262.90	   mark(U14(x0, x1, x2))
744.01/262.90	   mark(U15(x0, x1))
744.01/262.90	   mark(U16(x0))
744.01/262.90	   mark(U21(x0, x1))
744.01/262.90	   mark(U22(x0, x1))
744.01/262.90	   mark(U23(x0))
744.01/262.90	   mark(U31(x0, x1, x2))
744.01/262.90	   mark(U32(x0, x1, x2))
744.01/262.90	   mark(U33(x0, x1, x2))
744.01/262.90	   mark(U34(x0, x1, x2))
744.01/262.90	   mark(U35(x0, x1))
744.01/262.90	   mark(U36(x0))
744.01/262.90	   mark(U41(x0, x1))
744.01/262.90	   mark(U42(x0))
744.01/262.90	   mark(U51(x0))
744.01/262.90	   mark(U61(x0, x1))
744.01/262.90	   mark(U62(x0))
744.01/262.90	   mark(U71(x0, x1))
744.01/262.90	   mark(U72(x0, x1))
744.01/262.90	   mark(U81(x0, x1, x2))
744.01/262.90	   mark(U82(x0, x1, x2))
744.01/262.90	   mark(U83(x0, x1, x2))
744.01/262.90	   mark(U84(x0, x1, x2))
744.01/262.90	   mark(s(x0))
744.01/262.90	   mark(U91(x0, x1))
744.01/262.90	   mark(U92(x0))
744.01/262.90	   mark(0)
744.01/262.90	   U101(mark(x0), x1, x2)
744.01/262.90	   U101(x0, mark(x1), x2)
744.01/262.90	   U101(x0, x1, mark(x2))
744.01/262.90	   U101(active(x0), x1, x2)
744.01/262.90	   U101(x0, active(x1), x2)
744.01/262.90	   U101(x0, x1, active(x2))
744.01/262.90	   U102(mark(x0), x1, x2)
744.01/262.90	   U102(x0, mark(x1), x2)
744.01/262.90	   U102(x0, x1, mark(x2))
744.01/262.90	   U102(active(x0), x1, x2)
744.01/262.90	   U102(x0, active(x1), x2)
744.01/262.90	   U102(x0, x1, active(x2))
744.01/262.90	   isNatKind(mark(x0))
744.01/262.90	   isNatKind(active(x0))
744.01/262.90	   U103(mark(x0), x1, x2)
744.01/262.90	   U103(x0, mark(x1), x2)
744.01/262.90	   U103(x0, x1, mark(x2))
744.01/262.90	   U103(active(x0), x1, x2)
744.01/262.90	   U103(x0, active(x1), x2)
744.01/262.90	   U103(x0, x1, active(x2))
744.01/262.90	   isNat(mark(x0))
744.01/262.90	   isNat(active(x0))
744.01/262.90	   U104(mark(x0), x1, x2)
744.01/262.90	   U104(x0, mark(x1), x2)
744.01/262.90	   U104(x0, x1, mark(x2))
744.01/262.90	   U104(active(x0), x1, x2)
744.01/262.90	   U104(x0, active(x1), x2)
744.01/262.90	   U104(x0, x1, active(x2))
744.01/262.90	   plus(mark(x0), x1)
744.01/262.90	   plus(x0, mark(x1))
744.01/262.90	   plus(active(x0), x1)
744.01/262.90	   plus(x0, active(x1))
744.01/262.90	   x(mark(x0), x1)
744.01/262.90	   x(x0, mark(x1))
744.01/262.90	   x(active(x0), x1)
744.01/262.90	   x(x0, active(x1))
744.01/262.90	   U11(mark(x0), x1, x2)
744.01/262.90	   U11(x0, mark(x1), x2)
744.01/262.90	   U11(x0, x1, mark(x2))
744.01/262.90	   U11(active(x0), x1, x2)
744.01/262.90	   U11(x0, active(x1), x2)
744.01/262.90	   U11(x0, x1, active(x2))
744.01/262.90	   U12(mark(x0), x1, x2)
744.01/262.90	   U12(x0, mark(x1), x2)
744.01/262.90	   U12(x0, x1, mark(x2))
744.01/262.90	   U12(active(x0), x1, x2)
744.01/262.90	   U12(x0, active(x1), x2)
744.01/262.90	   U12(x0, x1, active(x2))
744.01/262.90	   U13(mark(x0), x1, x2)
744.01/262.90	   U13(x0, mark(x1), x2)
744.01/262.90	   U13(x0, x1, mark(x2))
744.01/262.90	   U13(active(x0), x1, x2)
744.01/262.90	   U13(x0, active(x1), x2)
744.01/262.90	   U13(x0, x1, active(x2))
744.01/262.90	   U14(mark(x0), x1, x2)
744.01/262.90	   U14(x0, mark(x1), x2)
744.01/262.90	   U14(x0, x1, mark(x2))
744.01/262.90	   U14(active(x0), x1, x2)
744.01/262.90	   U14(x0, active(x1), x2)
744.01/262.90	   U14(x0, x1, active(x2))
744.01/262.90	   U15(mark(x0), x1)
744.01/262.90	   U15(x0, mark(x1))
744.01/262.90	   U15(active(x0), x1)
744.01/262.90	   U15(x0, active(x1))
744.01/262.90	   U16(mark(x0))
744.01/262.90	   U16(active(x0))
744.01/262.90	   U21(mark(x0), x1)
744.01/262.90	   U21(x0, mark(x1))
744.01/262.90	   U21(active(x0), x1)
744.01/262.90	   U21(x0, active(x1))
744.01/262.90	   U22(mark(x0), x1)
744.01/262.90	   U22(x0, mark(x1))
744.01/262.90	   U22(active(x0), x1)
744.01/262.90	   U22(x0, active(x1))
744.01/262.90	   U23(mark(x0))
744.01/262.90	   U23(active(x0))
744.01/262.90	   U31(mark(x0), x1, x2)
744.01/262.90	   U31(x0, mark(x1), x2)
744.01/262.90	   U31(x0, x1, mark(x2))
744.01/262.90	   U31(active(x0), x1, x2)
744.01/262.90	   U31(x0, active(x1), x2)
744.01/262.90	   U31(x0, x1, active(x2))
744.01/262.90	   U32(mark(x0), x1, x2)
744.01/262.90	   U32(x0, mark(x1), x2)
744.01/262.90	   U32(x0, x1, mark(x2))
744.01/262.90	   U32(active(x0), x1, x2)
744.01/262.90	   U32(x0, active(x1), x2)
744.01/262.90	   U32(x0, x1, active(x2))
744.01/262.90	   U33(mark(x0), x1, x2)
744.01/262.90	   U33(x0, mark(x1), x2)
744.01/262.90	   U33(x0, x1, mark(x2))
744.01/262.90	   U33(active(x0), x1, x2)
744.01/262.90	   U33(x0, active(x1), x2)
744.01/262.90	   U33(x0, x1, active(x2))
744.01/262.90	   U34(mark(x0), x1, x2)
744.01/262.90	   U34(x0, mark(x1), x2)
744.01/262.90	   U34(x0, x1, mark(x2))
744.01/262.90	   U34(active(x0), x1, x2)
744.01/262.90	   U34(x0, active(x1), x2)
744.01/262.90	   U34(x0, x1, active(x2))
744.01/262.90	   U35(mark(x0), x1)
744.01/262.90	   U35(x0, mark(x1))
744.01/262.90	   U35(active(x0), x1)
744.01/262.90	   U35(x0, active(x1))
744.01/262.90	   U36(mark(x0))
744.01/262.90	   U36(active(x0))
744.01/262.90	   U41(mark(x0), x1)
744.01/262.90	   U41(x0, mark(x1))
744.01/262.90	   U41(active(x0), x1)
744.01/262.90	   U41(x0, active(x1))
744.01/262.90	   U42(mark(x0))
744.01/262.90	   U42(active(x0))
744.01/262.90	   U51(mark(x0))
744.01/262.90	   U51(active(x0))
744.01/262.90	   U61(mark(x0), x1)
744.01/262.90	   U61(x0, mark(x1))
744.01/262.90	   U61(active(x0), x1)
744.01/262.90	   U61(x0, active(x1))
744.01/262.90	   U62(mark(x0))
744.01/262.90	   U62(active(x0))
744.01/262.90	   U71(mark(x0), x1)
744.01/262.90	   U71(x0, mark(x1))
744.01/262.90	   U71(active(x0), x1)
744.01/262.90	   U71(x0, active(x1))
744.01/262.90	   U72(mark(x0), x1)
744.01/262.90	   U72(x0, mark(x1))
744.01/262.90	   U72(active(x0), x1)
744.01/262.90	   U72(x0, active(x1))
744.01/262.90	   U81(mark(x0), x1, x2)
744.01/262.90	   U81(x0, mark(x1), x2)
744.01/262.90	   U81(x0, x1, mark(x2))
744.01/262.90	   U81(active(x0), x1, x2)
744.01/262.90	   U81(x0, active(x1), x2)
744.01/262.91	   U81(x0, x1, active(x2))
744.01/262.91	   U82(mark(x0), x1, x2)
744.01/262.91	   U82(x0, mark(x1), x2)
744.01/262.91	   U82(x0, x1, mark(x2))
744.01/262.91	   U82(active(x0), x1, x2)
744.01/262.91	   U82(x0, active(x1), x2)
744.01/262.91	   U82(x0, x1, active(x2))
744.01/262.91	   U83(mark(x0), x1, x2)
744.01/262.91	   U83(x0, mark(x1), x2)
744.01/262.91	   U83(x0, x1, mark(x2))
744.01/262.91	   U83(active(x0), x1, x2)
744.01/262.91	   U83(x0, active(x1), x2)
744.01/262.91	   U83(x0, x1, active(x2))
744.01/262.91	   U84(mark(x0), x1, x2)
744.01/262.91	   U84(x0, mark(x1), x2)
744.01/262.91	   U84(x0, x1, mark(x2))
744.01/262.91	   U84(active(x0), x1, x2)
744.01/262.91	   U84(x0, active(x1), x2)
744.01/262.91	   U84(x0, x1, active(x2))
744.01/262.91	   s(mark(x0))
744.01/262.91	   s(active(x0))
744.01/262.91	   U91(mark(x0), x1)
744.01/262.91	   U91(x0, mark(x1))
744.01/262.91	   U91(active(x0), x1)
744.01/262.91	   U91(x0, active(x1))
744.01/262.91	   U92(mark(x0))
744.01/262.91	   U92(active(x0))
744.01/262.91	
744.01/262.91	We have to consider all minimal (P,Q,R)-chains.
744.01/262.91	----------------------------------------
744.01/262.91	
744.01/262.91	(176) QReductionProof (EQUIVALENT)
744.01/262.91	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.01/262.91	
744.01/262.91	   U101(mark(x0), x1, x2)
744.01/262.91	   U101(x0, mark(x1), x2)
744.01/262.91	   U101(x0, x1, mark(x2))
744.01/262.91	   U101(active(x0), x1, x2)
744.01/262.91	   U101(x0, active(x1), x2)
744.01/262.91	   U101(x0, x1, active(x2))
744.01/262.91	   U102(mark(x0), x1, x2)
744.01/262.91	   U102(x0, mark(x1), x2)
744.01/262.91	   U102(x0, x1, mark(x2))
744.01/262.91	   U102(active(x0), x1, x2)
744.01/262.91	   U102(x0, active(x1), x2)
744.01/262.91	   U102(x0, x1, active(x2))
744.01/262.91	   isNatKind(mark(x0))
744.01/262.91	   isNatKind(active(x0))
744.01/262.91	   U103(mark(x0), x1, x2)
744.01/262.91	   U103(x0, mark(x1), x2)
744.01/262.91	   U103(x0, x1, mark(x2))
744.01/262.91	   U103(active(x0), x1, x2)
744.01/262.91	   U103(x0, active(x1), x2)
744.01/262.91	   U103(x0, x1, active(x2))
744.01/262.91	   isNat(mark(x0))
744.01/262.91	   isNat(active(x0))
744.01/262.91	   U104(mark(x0), x1, x2)
744.01/262.91	   U104(x0, mark(x1), x2)
744.01/262.91	   U104(x0, x1, mark(x2))
744.01/262.91	   U104(active(x0), x1, x2)
744.01/262.91	   U104(x0, active(x1), x2)
744.01/262.91	   U104(x0, x1, active(x2))
744.01/262.91	   plus(mark(x0), x1)
744.01/262.91	   plus(x0, mark(x1))
744.01/262.91	   plus(active(x0), x1)
744.01/262.91	   plus(x0, active(x1))
744.01/262.91	   x(mark(x0), x1)
744.01/262.91	   x(x0, mark(x1))
744.01/262.91	   x(active(x0), x1)
744.01/262.91	   x(x0, active(x1))
744.01/262.91	   U11(mark(x0), x1, x2)
744.01/262.91	   U11(x0, mark(x1), x2)
744.01/262.91	   U11(x0, x1, mark(x2))
744.01/262.91	   U11(active(x0), x1, x2)
744.01/262.91	   U11(x0, active(x1), x2)
744.01/262.91	   U11(x0, x1, active(x2))
744.01/262.91	   U12(mark(x0), x1, x2)
744.01/262.91	   U12(x0, mark(x1), x2)
744.01/262.91	   U12(x0, x1, mark(x2))
744.01/262.91	   U12(active(x0), x1, x2)
744.01/262.91	   U12(x0, active(x1), x2)
744.01/262.91	   U12(x0, x1, active(x2))
744.01/262.91	   U13(mark(x0), x1, x2)
744.01/262.91	   U13(x0, mark(x1), x2)
744.01/262.91	   U13(x0, x1, mark(x2))
744.01/262.91	   U13(active(x0), x1, x2)
744.01/262.91	   U13(x0, active(x1), x2)
744.01/262.91	   U13(x0, x1, active(x2))
744.01/262.91	   U14(mark(x0), x1, x2)
744.01/262.91	   U14(x0, mark(x1), x2)
744.01/262.91	   U14(x0, x1, mark(x2))
744.01/262.91	   U14(active(x0), x1, x2)
744.01/262.91	   U14(x0, active(x1), x2)
744.01/262.91	   U14(x0, x1, active(x2))
744.01/262.91	   U15(mark(x0), x1)
744.01/262.91	   U15(x0, mark(x1))
744.01/262.91	   U15(active(x0), x1)
744.01/262.91	   U15(x0, active(x1))
744.01/262.91	   U16(mark(x0))
744.01/262.91	   U16(active(x0))
744.01/262.91	   U21(mark(x0), x1)
744.01/262.91	   U21(x0, mark(x1))
744.01/262.91	   U21(active(x0), x1)
744.01/262.91	   U21(x0, active(x1))
744.01/262.91	   U22(mark(x0), x1)
744.01/262.91	   U22(x0, mark(x1))
744.01/262.91	   U22(active(x0), x1)
744.01/262.91	   U22(x0, active(x1))
744.01/262.91	   U23(mark(x0))
744.01/262.91	   U23(active(x0))
744.01/262.91	   U31(mark(x0), x1, x2)
744.01/262.91	   U31(x0, mark(x1), x2)
744.01/262.91	   U31(x0, x1, mark(x2))
744.01/262.91	   U31(active(x0), x1, x2)
744.01/262.91	   U31(x0, active(x1), x2)
744.01/262.91	   U31(x0, x1, active(x2))
744.01/262.91	   U32(mark(x0), x1, x2)
744.01/262.91	   U32(x0, mark(x1), x2)
744.01/262.91	   U32(x0, x1, mark(x2))
744.01/262.91	   U32(active(x0), x1, x2)
744.01/262.91	   U32(x0, active(x1), x2)
744.01/262.91	   U32(x0, x1, active(x2))
744.01/262.91	   U33(mark(x0), x1, x2)
744.01/262.91	   U33(x0, mark(x1), x2)
744.01/262.91	   U33(x0, x1, mark(x2))
744.01/262.91	   U33(active(x0), x1, x2)
744.01/262.91	   U33(x0, active(x1), x2)
744.01/262.91	   U33(x0, x1, active(x2))
744.01/262.91	   U34(mark(x0), x1, x2)
744.01/262.91	   U34(x0, mark(x1), x2)
744.01/262.91	   U34(x0, x1, mark(x2))
744.01/262.91	   U34(active(x0), x1, x2)
744.01/262.91	   U34(x0, active(x1), x2)
744.01/262.91	   U34(x0, x1, active(x2))
744.01/262.91	   U35(mark(x0), x1)
744.01/262.91	   U35(x0, mark(x1))
744.01/262.91	   U35(active(x0), x1)
744.01/262.91	   U35(x0, active(x1))
744.01/262.91	   U36(mark(x0))
744.01/262.91	   U36(active(x0))
744.01/262.91	   U41(mark(x0), x1)
744.01/262.91	   U41(x0, mark(x1))
744.01/262.91	   U41(active(x0), x1)
744.01/262.91	   U41(x0, active(x1))
744.01/262.91	   U42(mark(x0))
744.01/262.91	   U42(active(x0))
744.01/262.91	   U51(mark(x0))
744.01/262.91	   U51(active(x0))
744.01/262.91	   U61(mark(x0), x1)
744.01/262.91	   U61(x0, mark(x1))
744.01/262.91	   U61(active(x0), x1)
744.01/262.91	   U61(x0, active(x1))
744.01/262.91	   U62(mark(x0))
744.01/262.91	   U62(active(x0))
744.01/262.91	   U71(mark(x0), x1)
744.01/262.91	   U71(x0, mark(x1))
744.01/262.91	   U71(active(x0), x1)
744.01/262.91	   U71(x0, active(x1))
744.01/262.91	   U72(mark(x0), x1)
744.01/262.91	   U72(x0, mark(x1))
744.01/262.91	   U72(active(x0), x1)
744.01/262.91	   U72(x0, active(x1))
744.01/262.91	   U81(mark(x0), x1, x2)
744.01/262.91	   U81(x0, mark(x1), x2)
744.01/262.91	   U81(x0, x1, mark(x2))
744.01/262.91	   U81(active(x0), x1, x2)
744.01/262.91	   U81(x0, active(x1), x2)
744.01/262.91	   U81(x0, x1, active(x2))
744.01/262.91	   U82(mark(x0), x1, x2)
744.01/262.91	   U82(x0, mark(x1), x2)
744.01/262.91	   U82(x0, x1, mark(x2))
744.01/262.91	   U82(active(x0), x1, x2)
744.01/262.91	   U82(x0, active(x1), x2)
744.01/262.91	   U82(x0, x1, active(x2))
744.01/262.91	   U83(mark(x0), x1, x2)
744.01/262.91	   U83(x0, mark(x1), x2)
744.01/262.91	   U83(x0, x1, mark(x2))
744.01/262.91	   U83(active(x0), x1, x2)
744.01/262.91	   U83(x0, active(x1), x2)
744.01/262.91	   U83(x0, x1, active(x2))
744.01/262.91	   U84(mark(x0), x1, x2)
744.01/262.91	   U84(x0, mark(x1), x2)
744.01/262.91	   U84(x0, x1, mark(x2))
744.01/262.91	   U84(active(x0), x1, x2)
744.01/262.91	   U84(x0, active(x1), x2)
744.01/262.91	   U84(x0, x1, active(x2))
744.01/262.91	   s(mark(x0))
744.01/262.91	   s(active(x0))
744.01/262.91	   U91(mark(x0), x1)
744.01/262.91	   U91(x0, mark(x1))
744.01/262.91	   U91(active(x0), x1)
744.01/262.91	   U91(x0, active(x1))
744.01/262.91	   U92(mark(x0))
744.01/262.91	   U92(active(x0))
744.01/262.91	
744.01/262.91	
744.01/262.91	----------------------------------------
744.01/262.91	
744.01/262.91	(177)
744.01/262.91	Obligation:
744.01/262.91	Q DP problem:
744.01/262.91	The TRS P consists of the following rules:
744.01/262.91	
744.01/262.91	   U15^1(X1, mark(X2)) -> U15^1(X1, X2)
744.01/262.91	   U15^1(mark(X1), X2) -> U15^1(X1, X2)
744.01/262.91	   U15^1(active(X1), X2) -> U15^1(X1, X2)
744.01/262.91	   U15^1(X1, active(X2)) -> U15^1(X1, X2)
744.01/262.91	
744.01/262.91	R is empty.
744.01/262.91	The set Q consists of the following terms:
744.01/262.91	
744.01/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	
744.12/262.91	We have to consider all minimal (P,Q,R)-chains.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(178) QDPSizeChangeProof (EQUIVALENT)
744.12/262.91	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. 
744.12/262.91	
744.12/262.91	From the DPs we obtained the following set of size-change graphs:
744.12/262.91	*U15^1(X1, mark(X2)) -> U15^1(X1, X2)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.91	
744.12/262.91	
744.12/262.91	*U15^1(mark(X1), X2) -> U15^1(X1, X2)
744.12/262.91	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.91	
744.12/262.91	
744.12/262.91	*U15^1(active(X1), X2) -> U15^1(X1, X2)
744.12/262.91	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.91	
744.12/262.91	
744.12/262.91	*U15^1(X1, active(X2)) -> U15^1(X1, X2)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.91	
744.12/262.91	
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(179)
744.12/262.91	YES
744.12/262.91	
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(180)
744.12/262.91	Obligation:
744.12/262.91	Q DP problem:
744.12/262.91	The TRS P consists of the following rules:
744.12/262.91	
744.12/262.91	   U14^1(X1, mark(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(mark(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, mark(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(active(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, active(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, active(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	
744.12/262.91	The TRS R consists of the following rules:
744.12/262.91	
744.12/262.91	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.91	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.91	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.91	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.91	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.91	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.91	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.91	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.91	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.91	   active(U16(tt)) -> mark(tt)
744.12/262.91	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.91	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.91	   active(U23(tt)) -> mark(tt)
744.12/262.91	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.91	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.91	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.91	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.91	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.91	   active(U36(tt)) -> mark(tt)
744.12/262.91	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.91	   active(U42(tt)) -> mark(tt)
744.12/262.91	   active(U51(tt)) -> mark(tt)
744.12/262.91	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.91	   active(U62(tt)) -> mark(tt)
744.12/262.91	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.91	   active(U72(tt, N)) -> mark(N)
744.12/262.91	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.91	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.91	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.91	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.91	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.91	   active(U92(tt)) -> mark(0)
744.12/262.91	   active(isNat(0)) -> mark(tt)
744.12/262.91	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.91	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.91	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.91	   active(isNatKind(0)) -> mark(tt)
744.12/262.91	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.91	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.91	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.91	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.91	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.91	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.91	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.91	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.91	   mark(tt) -> active(tt)
744.12/262.91	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.91	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.91	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.91	   mark(isNat(X)) -> active(isNat(X))
744.12/262.91	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.91	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.91	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.91	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.91	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.91	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.91	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.91	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.91	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.91	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.91	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.91	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.91	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.91	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.91	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.91	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.91	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.91	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.91	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.91	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.91	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.91	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.91	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.91	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.91	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.91	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.91	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.91	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.91	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.91	   mark(s(X)) -> active(s(mark(X)))
744.12/262.91	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.91	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.91	   mark(0) -> active(0)
744.12/262.91	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.91	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.91	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.91	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.91	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.91	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.91	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.91	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.91	   isNat(mark(X)) -> isNat(X)
744.12/262.91	   isNat(active(X)) -> isNat(X)
744.12/262.91	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.91	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.91	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.91	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.91	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.91	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.91	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.91	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.91	   x(active(X1), X2) -> x(X1, X2)
744.12/262.91	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.91	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.91	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.91	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.91	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.91	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.91	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.91	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.91	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.91	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.91	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.91	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.91	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.91	   U16(mark(X)) -> U16(X)
744.12/262.91	   U16(active(X)) -> U16(X)
744.12/262.91	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.91	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.91	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.91	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.91	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.91	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.91	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.91	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.91	   U23(mark(X)) -> U23(X)
744.12/262.91	   U23(active(X)) -> U23(X)
744.12/262.91	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.91	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.91	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.91	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.91	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.91	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.91	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.91	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.91	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.91	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.91	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.91	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.91	   U36(mark(X)) -> U36(X)
744.12/262.91	   U36(active(X)) -> U36(X)
744.12/262.91	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.91	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.91	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.91	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.91	   U42(mark(X)) -> U42(X)
744.12/262.91	   U42(active(X)) -> U42(X)
744.12/262.91	   U51(mark(X)) -> U51(X)
744.12/262.91	   U51(active(X)) -> U51(X)
744.12/262.91	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.91	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.91	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.91	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.91	   U62(mark(X)) -> U62(X)
744.12/262.91	   U62(active(X)) -> U62(X)
744.12/262.91	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.91	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.91	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.91	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.91	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.91	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.91	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.91	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.91	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.91	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.91	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.91	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.91	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.91	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.91	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.91	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.91	   s(mark(X)) -> s(X)
744.12/262.91	   s(active(X)) -> s(X)
744.12/262.91	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.91	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.91	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.91	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.91	   U92(mark(X)) -> U92(X)
744.12/262.91	   U92(active(X)) -> U92(X)
744.12/262.91	
744.12/262.91	The set Q consists of the following terms:
744.12/262.91	
744.12/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	   U101(mark(x0), x1, x2)
744.12/262.91	   U101(x0, mark(x1), x2)
744.12/262.91	   U101(x0, x1, mark(x2))
744.12/262.91	   U101(active(x0), x1, x2)
744.12/262.91	   U101(x0, active(x1), x2)
744.12/262.91	   U101(x0, x1, active(x2))
744.12/262.91	   U102(mark(x0), x1, x2)
744.12/262.91	   U102(x0, mark(x1), x2)
744.12/262.91	   U102(x0, x1, mark(x2))
744.12/262.91	   U102(active(x0), x1, x2)
744.12/262.91	   U102(x0, active(x1), x2)
744.12/262.91	   U102(x0, x1, active(x2))
744.12/262.91	   isNatKind(mark(x0))
744.12/262.91	   isNatKind(active(x0))
744.12/262.91	   U103(mark(x0), x1, x2)
744.12/262.91	   U103(x0, mark(x1), x2)
744.12/262.91	   U103(x0, x1, mark(x2))
744.12/262.91	   U103(active(x0), x1, x2)
744.12/262.91	   U103(x0, active(x1), x2)
744.12/262.91	   U103(x0, x1, active(x2))
744.12/262.91	   isNat(mark(x0))
744.12/262.91	   isNat(active(x0))
744.12/262.91	   U104(mark(x0), x1, x2)
744.12/262.91	   U104(x0, mark(x1), x2)
744.12/262.91	   U104(x0, x1, mark(x2))
744.12/262.91	   U104(active(x0), x1, x2)
744.12/262.91	   U104(x0, active(x1), x2)
744.12/262.91	   U104(x0, x1, active(x2))
744.12/262.91	   plus(mark(x0), x1)
744.12/262.91	   plus(x0, mark(x1))
744.12/262.91	   plus(active(x0), x1)
744.12/262.91	   plus(x0, active(x1))
744.12/262.91	   x(mark(x0), x1)
744.12/262.91	   x(x0, mark(x1))
744.12/262.91	   x(active(x0), x1)
744.12/262.91	   x(x0, active(x1))
744.12/262.91	   U11(mark(x0), x1, x2)
744.12/262.91	   U11(x0, mark(x1), x2)
744.12/262.91	   U11(x0, x1, mark(x2))
744.12/262.91	   U11(active(x0), x1, x2)
744.12/262.91	   U11(x0, active(x1), x2)
744.12/262.91	   U11(x0, x1, active(x2))
744.12/262.91	   U12(mark(x0), x1, x2)
744.12/262.91	   U12(x0, mark(x1), x2)
744.12/262.91	   U12(x0, x1, mark(x2))
744.12/262.91	   U12(active(x0), x1, x2)
744.12/262.91	   U12(x0, active(x1), x2)
744.12/262.91	   U12(x0, x1, active(x2))
744.12/262.91	   U13(mark(x0), x1, x2)
744.12/262.91	   U13(x0, mark(x1), x2)
744.12/262.91	   U13(x0, x1, mark(x2))
744.12/262.91	   U13(active(x0), x1, x2)
744.12/262.91	   U13(x0, active(x1), x2)
744.12/262.91	   U13(x0, x1, active(x2))
744.12/262.91	   U14(mark(x0), x1, x2)
744.12/262.91	   U14(x0, mark(x1), x2)
744.12/262.91	   U14(x0, x1, mark(x2))
744.12/262.91	   U14(active(x0), x1, x2)
744.12/262.91	   U14(x0, active(x1), x2)
744.12/262.91	   U14(x0, x1, active(x2))
744.12/262.91	   U15(mark(x0), x1)
744.12/262.91	   U15(x0, mark(x1))
744.12/262.91	   U15(active(x0), x1)
744.12/262.91	   U15(x0, active(x1))
744.12/262.91	   U16(mark(x0))
744.12/262.91	   U16(active(x0))
744.12/262.91	   U21(mark(x0), x1)
744.12/262.91	   U21(x0, mark(x1))
744.12/262.91	   U21(active(x0), x1)
744.12/262.91	   U21(x0, active(x1))
744.12/262.91	   U22(mark(x0), x1)
744.12/262.91	   U22(x0, mark(x1))
744.12/262.91	   U22(active(x0), x1)
744.12/262.91	   U22(x0, active(x1))
744.12/262.91	   U23(mark(x0))
744.12/262.91	   U23(active(x0))
744.12/262.91	   U31(mark(x0), x1, x2)
744.12/262.91	   U31(x0, mark(x1), x2)
744.12/262.91	   U31(x0, x1, mark(x2))
744.12/262.91	   U31(active(x0), x1, x2)
744.12/262.91	   U31(x0, active(x1), x2)
744.12/262.91	   U31(x0, x1, active(x2))
744.12/262.91	   U32(mark(x0), x1, x2)
744.12/262.91	   U32(x0, mark(x1), x2)
744.12/262.91	   U32(x0, x1, mark(x2))
744.12/262.91	   U32(active(x0), x1, x2)
744.12/262.91	   U32(x0, active(x1), x2)
744.12/262.91	   U32(x0, x1, active(x2))
744.12/262.91	   U33(mark(x0), x1, x2)
744.12/262.91	   U33(x0, mark(x1), x2)
744.12/262.91	   U33(x0, x1, mark(x2))
744.12/262.91	   U33(active(x0), x1, x2)
744.12/262.91	   U33(x0, active(x1), x2)
744.12/262.91	   U33(x0, x1, active(x2))
744.12/262.91	   U34(mark(x0), x1, x2)
744.12/262.91	   U34(x0, mark(x1), x2)
744.12/262.91	   U34(x0, x1, mark(x2))
744.12/262.91	   U34(active(x0), x1, x2)
744.12/262.91	   U34(x0, active(x1), x2)
744.12/262.91	   U34(x0, x1, active(x2))
744.12/262.91	   U35(mark(x0), x1)
744.12/262.91	   U35(x0, mark(x1))
744.12/262.91	   U35(active(x0), x1)
744.12/262.91	   U35(x0, active(x1))
744.12/262.91	   U36(mark(x0))
744.12/262.91	   U36(active(x0))
744.12/262.91	   U41(mark(x0), x1)
744.12/262.91	   U41(x0, mark(x1))
744.12/262.91	   U41(active(x0), x1)
744.12/262.91	   U41(x0, active(x1))
744.12/262.91	   U42(mark(x0))
744.12/262.91	   U42(active(x0))
744.12/262.91	   U51(mark(x0))
744.12/262.91	   U51(active(x0))
744.12/262.91	   U61(mark(x0), x1)
744.12/262.91	   U61(x0, mark(x1))
744.12/262.91	   U61(active(x0), x1)
744.12/262.91	   U61(x0, active(x1))
744.12/262.91	   U62(mark(x0))
744.12/262.91	   U62(active(x0))
744.12/262.91	   U71(mark(x0), x1)
744.12/262.91	   U71(x0, mark(x1))
744.12/262.91	   U71(active(x0), x1)
744.12/262.91	   U71(x0, active(x1))
744.12/262.91	   U72(mark(x0), x1)
744.12/262.91	   U72(x0, mark(x1))
744.12/262.91	   U72(active(x0), x1)
744.12/262.91	   U72(x0, active(x1))
744.12/262.91	   U81(mark(x0), x1, x2)
744.12/262.91	   U81(x0, mark(x1), x2)
744.12/262.91	   U81(x0, x1, mark(x2))
744.12/262.91	   U81(active(x0), x1, x2)
744.12/262.91	   U81(x0, active(x1), x2)
744.12/262.91	   U81(x0, x1, active(x2))
744.12/262.91	   U82(mark(x0), x1, x2)
744.12/262.91	   U82(x0, mark(x1), x2)
744.12/262.91	   U82(x0, x1, mark(x2))
744.12/262.91	   U82(active(x0), x1, x2)
744.12/262.91	   U82(x0, active(x1), x2)
744.12/262.91	   U82(x0, x1, active(x2))
744.12/262.91	   U83(mark(x0), x1, x2)
744.12/262.91	   U83(x0, mark(x1), x2)
744.12/262.91	   U83(x0, x1, mark(x2))
744.12/262.91	   U83(active(x0), x1, x2)
744.12/262.91	   U83(x0, active(x1), x2)
744.12/262.91	   U83(x0, x1, active(x2))
744.12/262.91	   U84(mark(x0), x1, x2)
744.12/262.91	   U84(x0, mark(x1), x2)
744.12/262.91	   U84(x0, x1, mark(x2))
744.12/262.91	   U84(active(x0), x1, x2)
744.12/262.91	   U84(x0, active(x1), x2)
744.12/262.91	   U84(x0, x1, active(x2))
744.12/262.91	   s(mark(x0))
744.12/262.91	   s(active(x0))
744.12/262.91	   U91(mark(x0), x1)
744.12/262.91	   U91(x0, mark(x1))
744.12/262.91	   U91(active(x0), x1)
744.12/262.91	   U91(x0, active(x1))
744.12/262.91	   U92(mark(x0))
744.12/262.91	   U92(active(x0))
744.12/262.91	
744.12/262.91	We have to consider all minimal (P,Q,R)-chains.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(181) UsableRulesProof (EQUIVALENT)
744.12/262.91	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.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(182)
744.12/262.91	Obligation:
744.12/262.91	Q DP problem:
744.12/262.91	The TRS P consists of the following rules:
744.12/262.91	
744.12/262.91	   U14^1(X1, mark(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(mark(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, mark(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(active(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, active(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, active(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	
744.12/262.91	R is empty.
744.12/262.91	The set Q consists of the following terms:
744.12/262.91	
744.12/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	   U101(mark(x0), x1, x2)
744.12/262.91	   U101(x0, mark(x1), x2)
744.12/262.91	   U101(x0, x1, mark(x2))
744.12/262.91	   U101(active(x0), x1, x2)
744.12/262.91	   U101(x0, active(x1), x2)
744.12/262.91	   U101(x0, x1, active(x2))
744.12/262.91	   U102(mark(x0), x1, x2)
744.12/262.91	   U102(x0, mark(x1), x2)
744.12/262.91	   U102(x0, x1, mark(x2))
744.12/262.91	   U102(active(x0), x1, x2)
744.12/262.91	   U102(x0, active(x1), x2)
744.12/262.91	   U102(x0, x1, active(x2))
744.12/262.91	   isNatKind(mark(x0))
744.12/262.91	   isNatKind(active(x0))
744.12/262.91	   U103(mark(x0), x1, x2)
744.12/262.91	   U103(x0, mark(x1), x2)
744.12/262.91	   U103(x0, x1, mark(x2))
744.12/262.91	   U103(active(x0), x1, x2)
744.12/262.91	   U103(x0, active(x1), x2)
744.12/262.91	   U103(x0, x1, active(x2))
744.12/262.91	   isNat(mark(x0))
744.12/262.91	   isNat(active(x0))
744.12/262.91	   U104(mark(x0), x1, x2)
744.12/262.91	   U104(x0, mark(x1), x2)
744.12/262.91	   U104(x0, x1, mark(x2))
744.12/262.91	   U104(active(x0), x1, x2)
744.12/262.91	   U104(x0, active(x1), x2)
744.12/262.91	   U104(x0, x1, active(x2))
744.12/262.91	   plus(mark(x0), x1)
744.12/262.91	   plus(x0, mark(x1))
744.12/262.91	   plus(active(x0), x1)
744.12/262.91	   plus(x0, active(x1))
744.12/262.91	   x(mark(x0), x1)
744.12/262.91	   x(x0, mark(x1))
744.12/262.91	   x(active(x0), x1)
744.12/262.91	   x(x0, active(x1))
744.12/262.91	   U11(mark(x0), x1, x2)
744.12/262.91	   U11(x0, mark(x1), x2)
744.12/262.91	   U11(x0, x1, mark(x2))
744.12/262.91	   U11(active(x0), x1, x2)
744.12/262.91	   U11(x0, active(x1), x2)
744.12/262.91	   U11(x0, x1, active(x2))
744.12/262.91	   U12(mark(x0), x1, x2)
744.12/262.91	   U12(x0, mark(x1), x2)
744.12/262.91	   U12(x0, x1, mark(x2))
744.12/262.91	   U12(active(x0), x1, x2)
744.12/262.91	   U12(x0, active(x1), x2)
744.12/262.91	   U12(x0, x1, active(x2))
744.12/262.91	   U13(mark(x0), x1, x2)
744.12/262.91	   U13(x0, mark(x1), x2)
744.12/262.91	   U13(x0, x1, mark(x2))
744.12/262.91	   U13(active(x0), x1, x2)
744.12/262.91	   U13(x0, active(x1), x2)
744.12/262.91	   U13(x0, x1, active(x2))
744.12/262.91	   U14(mark(x0), x1, x2)
744.12/262.91	   U14(x0, mark(x1), x2)
744.12/262.91	   U14(x0, x1, mark(x2))
744.12/262.91	   U14(active(x0), x1, x2)
744.12/262.91	   U14(x0, active(x1), x2)
744.12/262.91	   U14(x0, x1, active(x2))
744.12/262.91	   U15(mark(x0), x1)
744.12/262.91	   U15(x0, mark(x1))
744.12/262.91	   U15(active(x0), x1)
744.12/262.91	   U15(x0, active(x1))
744.12/262.91	   U16(mark(x0))
744.12/262.91	   U16(active(x0))
744.12/262.91	   U21(mark(x0), x1)
744.12/262.91	   U21(x0, mark(x1))
744.12/262.91	   U21(active(x0), x1)
744.12/262.91	   U21(x0, active(x1))
744.12/262.91	   U22(mark(x0), x1)
744.12/262.91	   U22(x0, mark(x1))
744.12/262.91	   U22(active(x0), x1)
744.12/262.91	   U22(x0, active(x1))
744.12/262.91	   U23(mark(x0))
744.12/262.91	   U23(active(x0))
744.12/262.91	   U31(mark(x0), x1, x2)
744.12/262.91	   U31(x0, mark(x1), x2)
744.12/262.91	   U31(x0, x1, mark(x2))
744.12/262.91	   U31(active(x0), x1, x2)
744.12/262.91	   U31(x0, active(x1), x2)
744.12/262.91	   U31(x0, x1, active(x2))
744.12/262.91	   U32(mark(x0), x1, x2)
744.12/262.91	   U32(x0, mark(x1), x2)
744.12/262.91	   U32(x0, x1, mark(x2))
744.12/262.91	   U32(active(x0), x1, x2)
744.12/262.91	   U32(x0, active(x1), x2)
744.12/262.91	   U32(x0, x1, active(x2))
744.12/262.91	   U33(mark(x0), x1, x2)
744.12/262.91	   U33(x0, mark(x1), x2)
744.12/262.91	   U33(x0, x1, mark(x2))
744.12/262.91	   U33(active(x0), x1, x2)
744.12/262.91	   U33(x0, active(x1), x2)
744.12/262.91	   U33(x0, x1, active(x2))
744.12/262.91	   U34(mark(x0), x1, x2)
744.12/262.91	   U34(x0, mark(x1), x2)
744.12/262.91	   U34(x0, x1, mark(x2))
744.12/262.91	   U34(active(x0), x1, x2)
744.12/262.91	   U34(x0, active(x1), x2)
744.12/262.91	   U34(x0, x1, active(x2))
744.12/262.91	   U35(mark(x0), x1)
744.12/262.91	   U35(x0, mark(x1))
744.12/262.91	   U35(active(x0), x1)
744.12/262.91	   U35(x0, active(x1))
744.12/262.91	   U36(mark(x0))
744.12/262.91	   U36(active(x0))
744.12/262.91	   U41(mark(x0), x1)
744.12/262.91	   U41(x0, mark(x1))
744.12/262.91	   U41(active(x0), x1)
744.12/262.91	   U41(x0, active(x1))
744.12/262.91	   U42(mark(x0))
744.12/262.91	   U42(active(x0))
744.12/262.91	   U51(mark(x0))
744.12/262.91	   U51(active(x0))
744.12/262.91	   U61(mark(x0), x1)
744.12/262.91	   U61(x0, mark(x1))
744.12/262.91	   U61(active(x0), x1)
744.12/262.91	   U61(x0, active(x1))
744.12/262.91	   U62(mark(x0))
744.12/262.91	   U62(active(x0))
744.12/262.91	   U71(mark(x0), x1)
744.12/262.91	   U71(x0, mark(x1))
744.12/262.91	   U71(active(x0), x1)
744.12/262.91	   U71(x0, active(x1))
744.12/262.91	   U72(mark(x0), x1)
744.12/262.91	   U72(x0, mark(x1))
744.12/262.91	   U72(active(x0), x1)
744.12/262.91	   U72(x0, active(x1))
744.12/262.91	   U81(mark(x0), x1, x2)
744.12/262.91	   U81(x0, mark(x1), x2)
744.12/262.91	   U81(x0, x1, mark(x2))
744.12/262.91	   U81(active(x0), x1, x2)
744.12/262.91	   U81(x0, active(x1), x2)
744.12/262.91	   U81(x0, x1, active(x2))
744.12/262.91	   U82(mark(x0), x1, x2)
744.12/262.91	   U82(x0, mark(x1), x2)
744.12/262.91	   U82(x0, x1, mark(x2))
744.12/262.91	   U82(active(x0), x1, x2)
744.12/262.91	   U82(x0, active(x1), x2)
744.12/262.91	   U82(x0, x1, active(x2))
744.12/262.91	   U83(mark(x0), x1, x2)
744.12/262.91	   U83(x0, mark(x1), x2)
744.12/262.91	   U83(x0, x1, mark(x2))
744.12/262.91	   U83(active(x0), x1, x2)
744.12/262.91	   U83(x0, active(x1), x2)
744.12/262.91	   U83(x0, x1, active(x2))
744.12/262.91	   U84(mark(x0), x1, x2)
744.12/262.91	   U84(x0, mark(x1), x2)
744.12/262.91	   U84(x0, x1, mark(x2))
744.12/262.91	   U84(active(x0), x1, x2)
744.12/262.91	   U84(x0, active(x1), x2)
744.12/262.91	   U84(x0, x1, active(x2))
744.12/262.91	   s(mark(x0))
744.12/262.91	   s(active(x0))
744.12/262.91	   U91(mark(x0), x1)
744.12/262.91	   U91(x0, mark(x1))
744.12/262.91	   U91(active(x0), x1)
744.12/262.91	   U91(x0, active(x1))
744.12/262.91	   U92(mark(x0))
744.12/262.91	   U92(active(x0))
744.12/262.91	
744.12/262.91	We have to consider all minimal (P,Q,R)-chains.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(183) QReductionProof (EQUIVALENT)
744.12/262.91	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.91	
744.12/262.91	   U101(mark(x0), x1, x2)
744.12/262.91	   U101(x0, mark(x1), x2)
744.12/262.91	   U101(x0, x1, mark(x2))
744.12/262.91	   U101(active(x0), x1, x2)
744.12/262.91	   U101(x0, active(x1), x2)
744.12/262.91	   U101(x0, x1, active(x2))
744.12/262.91	   U102(mark(x0), x1, x2)
744.12/262.91	   U102(x0, mark(x1), x2)
744.12/262.91	   U102(x0, x1, mark(x2))
744.12/262.91	   U102(active(x0), x1, x2)
744.12/262.91	   U102(x0, active(x1), x2)
744.12/262.91	   U102(x0, x1, active(x2))
744.12/262.91	   isNatKind(mark(x0))
744.12/262.91	   isNatKind(active(x0))
744.12/262.91	   U103(mark(x0), x1, x2)
744.12/262.91	   U103(x0, mark(x1), x2)
744.12/262.91	   U103(x0, x1, mark(x2))
744.12/262.91	   U103(active(x0), x1, x2)
744.12/262.91	   U103(x0, active(x1), x2)
744.12/262.91	   U103(x0, x1, active(x2))
744.12/262.91	   isNat(mark(x0))
744.12/262.91	   isNat(active(x0))
744.12/262.91	   U104(mark(x0), x1, x2)
744.12/262.91	   U104(x0, mark(x1), x2)
744.12/262.91	   U104(x0, x1, mark(x2))
744.12/262.91	   U104(active(x0), x1, x2)
744.12/262.91	   U104(x0, active(x1), x2)
744.12/262.91	   U104(x0, x1, active(x2))
744.12/262.91	   plus(mark(x0), x1)
744.12/262.91	   plus(x0, mark(x1))
744.12/262.91	   plus(active(x0), x1)
744.12/262.91	   plus(x0, active(x1))
744.12/262.91	   x(mark(x0), x1)
744.12/262.91	   x(x0, mark(x1))
744.12/262.91	   x(active(x0), x1)
744.12/262.91	   x(x0, active(x1))
744.12/262.91	   U11(mark(x0), x1, x2)
744.12/262.91	   U11(x0, mark(x1), x2)
744.12/262.91	   U11(x0, x1, mark(x2))
744.12/262.91	   U11(active(x0), x1, x2)
744.12/262.91	   U11(x0, active(x1), x2)
744.12/262.91	   U11(x0, x1, active(x2))
744.12/262.91	   U12(mark(x0), x1, x2)
744.12/262.91	   U12(x0, mark(x1), x2)
744.12/262.91	   U12(x0, x1, mark(x2))
744.12/262.91	   U12(active(x0), x1, x2)
744.12/262.91	   U12(x0, active(x1), x2)
744.12/262.91	   U12(x0, x1, active(x2))
744.12/262.91	   U13(mark(x0), x1, x2)
744.12/262.91	   U13(x0, mark(x1), x2)
744.12/262.91	   U13(x0, x1, mark(x2))
744.12/262.91	   U13(active(x0), x1, x2)
744.12/262.91	   U13(x0, active(x1), x2)
744.12/262.91	   U13(x0, x1, active(x2))
744.12/262.91	   U14(mark(x0), x1, x2)
744.12/262.91	   U14(x0, mark(x1), x2)
744.12/262.91	   U14(x0, x1, mark(x2))
744.12/262.91	   U14(active(x0), x1, x2)
744.12/262.91	   U14(x0, active(x1), x2)
744.12/262.91	   U14(x0, x1, active(x2))
744.12/262.91	   U15(mark(x0), x1)
744.12/262.91	   U15(x0, mark(x1))
744.12/262.91	   U15(active(x0), x1)
744.12/262.91	   U15(x0, active(x1))
744.12/262.91	   U16(mark(x0))
744.12/262.91	   U16(active(x0))
744.12/262.91	   U21(mark(x0), x1)
744.12/262.91	   U21(x0, mark(x1))
744.12/262.91	   U21(active(x0), x1)
744.12/262.91	   U21(x0, active(x1))
744.12/262.91	   U22(mark(x0), x1)
744.12/262.91	   U22(x0, mark(x1))
744.12/262.91	   U22(active(x0), x1)
744.12/262.91	   U22(x0, active(x1))
744.12/262.91	   U23(mark(x0))
744.12/262.91	   U23(active(x0))
744.12/262.91	   U31(mark(x0), x1, x2)
744.12/262.91	   U31(x0, mark(x1), x2)
744.12/262.91	   U31(x0, x1, mark(x2))
744.12/262.91	   U31(active(x0), x1, x2)
744.12/262.91	   U31(x0, active(x1), x2)
744.12/262.91	   U31(x0, x1, active(x2))
744.12/262.91	   U32(mark(x0), x1, x2)
744.12/262.91	   U32(x0, mark(x1), x2)
744.12/262.91	   U32(x0, x1, mark(x2))
744.12/262.91	   U32(active(x0), x1, x2)
744.12/262.91	   U32(x0, active(x1), x2)
744.12/262.91	   U32(x0, x1, active(x2))
744.12/262.91	   U33(mark(x0), x1, x2)
744.12/262.91	   U33(x0, mark(x1), x2)
744.12/262.91	   U33(x0, x1, mark(x2))
744.12/262.91	   U33(active(x0), x1, x2)
744.12/262.91	   U33(x0, active(x1), x2)
744.12/262.91	   U33(x0, x1, active(x2))
744.12/262.91	   U34(mark(x0), x1, x2)
744.12/262.91	   U34(x0, mark(x1), x2)
744.12/262.91	   U34(x0, x1, mark(x2))
744.12/262.91	   U34(active(x0), x1, x2)
744.12/262.91	   U34(x0, active(x1), x2)
744.12/262.91	   U34(x0, x1, active(x2))
744.12/262.91	   U35(mark(x0), x1)
744.12/262.91	   U35(x0, mark(x1))
744.12/262.91	   U35(active(x0), x1)
744.12/262.91	   U35(x0, active(x1))
744.12/262.91	   U36(mark(x0))
744.12/262.91	   U36(active(x0))
744.12/262.91	   U41(mark(x0), x1)
744.12/262.91	   U41(x0, mark(x1))
744.12/262.91	   U41(active(x0), x1)
744.12/262.91	   U41(x0, active(x1))
744.12/262.91	   U42(mark(x0))
744.12/262.91	   U42(active(x0))
744.12/262.91	   U51(mark(x0))
744.12/262.91	   U51(active(x0))
744.12/262.91	   U61(mark(x0), x1)
744.12/262.91	   U61(x0, mark(x1))
744.12/262.91	   U61(active(x0), x1)
744.12/262.91	   U61(x0, active(x1))
744.12/262.91	   U62(mark(x0))
744.12/262.91	   U62(active(x0))
744.12/262.91	   U71(mark(x0), x1)
744.12/262.91	   U71(x0, mark(x1))
744.12/262.91	   U71(active(x0), x1)
744.12/262.91	   U71(x0, active(x1))
744.12/262.91	   U72(mark(x0), x1)
744.12/262.91	   U72(x0, mark(x1))
744.12/262.91	   U72(active(x0), x1)
744.12/262.91	   U72(x0, active(x1))
744.12/262.91	   U81(mark(x0), x1, x2)
744.12/262.91	   U81(x0, mark(x1), x2)
744.12/262.91	   U81(x0, x1, mark(x2))
744.12/262.91	   U81(active(x0), x1, x2)
744.12/262.91	   U81(x0, active(x1), x2)
744.12/262.91	   U81(x0, x1, active(x2))
744.12/262.91	   U82(mark(x0), x1, x2)
744.12/262.91	   U82(x0, mark(x1), x2)
744.12/262.91	   U82(x0, x1, mark(x2))
744.12/262.91	   U82(active(x0), x1, x2)
744.12/262.91	   U82(x0, active(x1), x2)
744.12/262.91	   U82(x0, x1, active(x2))
744.12/262.91	   U83(mark(x0), x1, x2)
744.12/262.91	   U83(x0, mark(x1), x2)
744.12/262.91	   U83(x0, x1, mark(x2))
744.12/262.91	   U83(active(x0), x1, x2)
744.12/262.91	   U83(x0, active(x1), x2)
744.12/262.91	   U83(x0, x1, active(x2))
744.12/262.91	   U84(mark(x0), x1, x2)
744.12/262.91	   U84(x0, mark(x1), x2)
744.12/262.91	   U84(x0, x1, mark(x2))
744.12/262.91	   U84(active(x0), x1, x2)
744.12/262.91	   U84(x0, active(x1), x2)
744.12/262.91	   U84(x0, x1, active(x2))
744.12/262.91	   s(mark(x0))
744.12/262.91	   s(active(x0))
744.12/262.91	   U91(mark(x0), x1)
744.12/262.91	   U91(x0, mark(x1))
744.12/262.91	   U91(active(x0), x1)
744.12/262.91	   U91(x0, active(x1))
744.12/262.91	   U92(mark(x0))
744.12/262.91	   U92(active(x0))
744.12/262.91	
744.12/262.91	
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(184)
744.12/262.91	Obligation:
744.12/262.91	Q DP problem:
744.12/262.91	The TRS P consists of the following rules:
744.12/262.91	
744.12/262.91	   U14^1(X1, mark(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(mark(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, mark(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(active(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, active(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	   U14^1(X1, X2, active(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	
744.12/262.91	R is empty.
744.12/262.91	The set Q consists of the following terms:
744.12/262.91	
744.12/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	
744.12/262.91	We have to consider all minimal (P,Q,R)-chains.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(185) QDPSizeChangeProof (EQUIVALENT)
744.12/262.91	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. 
744.12/262.91	
744.12/262.91	From the DPs we obtained the following set of size-change graphs:
744.12/262.91	*U14^1(X1, mark(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.91	
744.12/262.91	
744.12/262.91	*U14^1(mark(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.91	
744.12/262.91	
744.12/262.91	*U14^1(X1, X2, mark(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.91	
744.12/262.91	
744.12/262.91	*U14^1(active(X1), X2, X3) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.91	
744.12/262.91	
744.12/262.91	*U14^1(X1, active(X2), X3) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.91	
744.12/262.91	
744.12/262.91	*U14^1(X1, X2, active(X3)) -> U14^1(X1, X2, X3)
744.12/262.91	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.91	
744.12/262.91	
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(186)
744.12/262.91	YES
744.12/262.91	
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(187)
744.12/262.91	Obligation:
744.12/262.91	Q DP problem:
744.12/262.91	The TRS P consists of the following rules:
744.12/262.91	
744.12/262.91	   U13^1(X1, mark(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(mark(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, X2, mark(X3)) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(active(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, active(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, X2, active(X3)) -> U13^1(X1, X2, X3)
744.12/262.91	
744.12/262.91	The TRS R consists of the following rules:
744.12/262.91	
744.12/262.91	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.91	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.91	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.91	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.91	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.91	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.91	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.91	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.91	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.91	   active(U16(tt)) -> mark(tt)
744.12/262.91	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.91	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.91	   active(U23(tt)) -> mark(tt)
744.12/262.91	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.91	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.91	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.91	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.91	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.91	   active(U36(tt)) -> mark(tt)
744.12/262.91	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.91	   active(U42(tt)) -> mark(tt)
744.12/262.91	   active(U51(tt)) -> mark(tt)
744.12/262.91	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.91	   active(U62(tt)) -> mark(tt)
744.12/262.91	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.91	   active(U72(tt, N)) -> mark(N)
744.12/262.91	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.91	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.91	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.91	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.91	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.91	   active(U92(tt)) -> mark(0)
744.12/262.91	   active(isNat(0)) -> mark(tt)
744.12/262.91	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.91	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.91	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.91	   active(isNatKind(0)) -> mark(tt)
744.12/262.91	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.91	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.91	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.91	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.91	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.91	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.91	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.91	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.91	   mark(tt) -> active(tt)
744.12/262.91	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.91	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.91	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.91	   mark(isNat(X)) -> active(isNat(X))
744.12/262.91	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.91	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.91	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.91	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.91	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.91	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.91	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.91	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.91	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.91	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.91	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.91	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.91	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.91	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.91	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.91	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.91	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.91	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.91	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.91	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.91	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.91	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.91	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.91	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.91	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.91	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.91	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.91	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.91	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.91	   mark(s(X)) -> active(s(mark(X)))
744.12/262.91	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.91	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.91	   mark(0) -> active(0)
744.12/262.91	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.91	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.91	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.91	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.91	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.91	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.91	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.91	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.91	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.91	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.91	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.91	   isNat(mark(X)) -> isNat(X)
744.12/262.91	   isNat(active(X)) -> isNat(X)
744.12/262.91	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.91	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.91	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.91	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.91	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.91	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.91	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.91	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.91	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.91	   x(active(X1), X2) -> x(X1, X2)
744.12/262.91	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.91	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.91	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.91	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.91	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.91	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.91	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.91	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.91	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.91	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.91	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.91	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.91	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.91	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.91	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.91	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.91	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.91	   U16(mark(X)) -> U16(X)
744.12/262.91	   U16(active(X)) -> U16(X)
744.12/262.91	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.91	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.91	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.91	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.91	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.91	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.91	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.91	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.91	   U23(mark(X)) -> U23(X)
744.12/262.91	   U23(active(X)) -> U23(X)
744.12/262.91	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.91	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.91	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.91	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.91	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.91	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.91	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.91	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.91	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.91	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.91	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.91	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.91	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.91	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.91	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.91	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.91	   U36(mark(X)) -> U36(X)
744.12/262.91	   U36(active(X)) -> U36(X)
744.12/262.91	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.91	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.91	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.91	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.91	   U42(mark(X)) -> U42(X)
744.12/262.91	   U42(active(X)) -> U42(X)
744.12/262.91	   U51(mark(X)) -> U51(X)
744.12/262.91	   U51(active(X)) -> U51(X)
744.12/262.91	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.91	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.91	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.91	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.91	   U62(mark(X)) -> U62(X)
744.12/262.91	   U62(active(X)) -> U62(X)
744.12/262.91	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.91	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.91	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.91	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.91	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.91	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.91	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.91	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.91	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.91	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.91	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.91	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.91	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.91	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.91	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.91	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.91	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.91	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.91	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.91	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.91	   s(mark(X)) -> s(X)
744.12/262.91	   s(active(X)) -> s(X)
744.12/262.91	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.91	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.91	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.91	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.91	   U92(mark(X)) -> U92(X)
744.12/262.91	   U92(active(X)) -> U92(X)
744.12/262.91	
744.12/262.91	The set Q consists of the following terms:
744.12/262.91	
744.12/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	   U101(mark(x0), x1, x2)
744.12/262.91	   U101(x0, mark(x1), x2)
744.12/262.91	   U101(x0, x1, mark(x2))
744.12/262.91	   U101(active(x0), x1, x2)
744.12/262.91	   U101(x0, active(x1), x2)
744.12/262.91	   U101(x0, x1, active(x2))
744.12/262.91	   U102(mark(x0), x1, x2)
744.12/262.91	   U102(x0, mark(x1), x2)
744.12/262.91	   U102(x0, x1, mark(x2))
744.12/262.91	   U102(active(x0), x1, x2)
744.12/262.91	   U102(x0, active(x1), x2)
744.12/262.91	   U102(x0, x1, active(x2))
744.12/262.91	   isNatKind(mark(x0))
744.12/262.91	   isNatKind(active(x0))
744.12/262.91	   U103(mark(x0), x1, x2)
744.12/262.91	   U103(x0, mark(x1), x2)
744.12/262.91	   U103(x0, x1, mark(x2))
744.12/262.91	   U103(active(x0), x1, x2)
744.12/262.91	   U103(x0, active(x1), x2)
744.12/262.91	   U103(x0, x1, active(x2))
744.12/262.91	   isNat(mark(x0))
744.12/262.91	   isNat(active(x0))
744.12/262.91	   U104(mark(x0), x1, x2)
744.12/262.91	   U104(x0, mark(x1), x2)
744.12/262.91	   U104(x0, x1, mark(x2))
744.12/262.91	   U104(active(x0), x1, x2)
744.12/262.91	   U104(x0, active(x1), x2)
744.12/262.91	   U104(x0, x1, active(x2))
744.12/262.91	   plus(mark(x0), x1)
744.12/262.91	   plus(x0, mark(x1))
744.12/262.91	   plus(active(x0), x1)
744.12/262.91	   plus(x0, active(x1))
744.12/262.91	   x(mark(x0), x1)
744.12/262.91	   x(x0, mark(x1))
744.12/262.91	   x(active(x0), x1)
744.12/262.91	   x(x0, active(x1))
744.12/262.91	   U11(mark(x0), x1, x2)
744.12/262.91	   U11(x0, mark(x1), x2)
744.12/262.91	   U11(x0, x1, mark(x2))
744.12/262.91	   U11(active(x0), x1, x2)
744.12/262.91	   U11(x0, active(x1), x2)
744.12/262.91	   U11(x0, x1, active(x2))
744.12/262.91	   U12(mark(x0), x1, x2)
744.12/262.91	   U12(x0, mark(x1), x2)
744.12/262.91	   U12(x0, x1, mark(x2))
744.12/262.91	   U12(active(x0), x1, x2)
744.12/262.91	   U12(x0, active(x1), x2)
744.12/262.91	   U12(x0, x1, active(x2))
744.12/262.91	   U13(mark(x0), x1, x2)
744.12/262.91	   U13(x0, mark(x1), x2)
744.12/262.91	   U13(x0, x1, mark(x2))
744.12/262.91	   U13(active(x0), x1, x2)
744.12/262.91	   U13(x0, active(x1), x2)
744.12/262.91	   U13(x0, x1, active(x2))
744.12/262.91	   U14(mark(x0), x1, x2)
744.12/262.91	   U14(x0, mark(x1), x2)
744.12/262.91	   U14(x0, x1, mark(x2))
744.12/262.91	   U14(active(x0), x1, x2)
744.12/262.91	   U14(x0, active(x1), x2)
744.12/262.91	   U14(x0, x1, active(x2))
744.12/262.91	   U15(mark(x0), x1)
744.12/262.91	   U15(x0, mark(x1))
744.12/262.91	   U15(active(x0), x1)
744.12/262.91	   U15(x0, active(x1))
744.12/262.91	   U16(mark(x0))
744.12/262.91	   U16(active(x0))
744.12/262.91	   U21(mark(x0), x1)
744.12/262.91	   U21(x0, mark(x1))
744.12/262.91	   U21(active(x0), x1)
744.12/262.91	   U21(x0, active(x1))
744.12/262.91	   U22(mark(x0), x1)
744.12/262.91	   U22(x0, mark(x1))
744.12/262.91	   U22(active(x0), x1)
744.12/262.91	   U22(x0, active(x1))
744.12/262.91	   U23(mark(x0))
744.12/262.91	   U23(active(x0))
744.12/262.91	   U31(mark(x0), x1, x2)
744.12/262.91	   U31(x0, mark(x1), x2)
744.12/262.91	   U31(x0, x1, mark(x2))
744.12/262.91	   U31(active(x0), x1, x2)
744.12/262.91	   U31(x0, active(x1), x2)
744.12/262.91	   U31(x0, x1, active(x2))
744.12/262.91	   U32(mark(x0), x1, x2)
744.12/262.91	   U32(x0, mark(x1), x2)
744.12/262.91	   U32(x0, x1, mark(x2))
744.12/262.91	   U32(active(x0), x1, x2)
744.12/262.91	   U32(x0, active(x1), x2)
744.12/262.91	   U32(x0, x1, active(x2))
744.12/262.91	   U33(mark(x0), x1, x2)
744.12/262.91	   U33(x0, mark(x1), x2)
744.12/262.91	   U33(x0, x1, mark(x2))
744.12/262.91	   U33(active(x0), x1, x2)
744.12/262.91	   U33(x0, active(x1), x2)
744.12/262.91	   U33(x0, x1, active(x2))
744.12/262.91	   U34(mark(x0), x1, x2)
744.12/262.91	   U34(x0, mark(x1), x2)
744.12/262.91	   U34(x0, x1, mark(x2))
744.12/262.91	   U34(active(x0), x1, x2)
744.12/262.91	   U34(x0, active(x1), x2)
744.12/262.91	   U34(x0, x1, active(x2))
744.12/262.91	   U35(mark(x0), x1)
744.12/262.91	   U35(x0, mark(x1))
744.12/262.91	   U35(active(x0), x1)
744.12/262.91	   U35(x0, active(x1))
744.12/262.91	   U36(mark(x0))
744.12/262.91	   U36(active(x0))
744.12/262.91	   U41(mark(x0), x1)
744.12/262.91	   U41(x0, mark(x1))
744.12/262.91	   U41(active(x0), x1)
744.12/262.91	   U41(x0, active(x1))
744.12/262.91	   U42(mark(x0))
744.12/262.91	   U42(active(x0))
744.12/262.91	   U51(mark(x0))
744.12/262.91	   U51(active(x0))
744.12/262.91	   U61(mark(x0), x1)
744.12/262.91	   U61(x0, mark(x1))
744.12/262.91	   U61(active(x0), x1)
744.12/262.91	   U61(x0, active(x1))
744.12/262.91	   U62(mark(x0))
744.12/262.91	   U62(active(x0))
744.12/262.91	   U71(mark(x0), x1)
744.12/262.91	   U71(x0, mark(x1))
744.12/262.91	   U71(active(x0), x1)
744.12/262.91	   U71(x0, active(x1))
744.12/262.91	   U72(mark(x0), x1)
744.12/262.91	   U72(x0, mark(x1))
744.12/262.91	   U72(active(x0), x1)
744.12/262.91	   U72(x0, active(x1))
744.12/262.91	   U81(mark(x0), x1, x2)
744.12/262.91	   U81(x0, mark(x1), x2)
744.12/262.91	   U81(x0, x1, mark(x2))
744.12/262.91	   U81(active(x0), x1, x2)
744.12/262.91	   U81(x0, active(x1), x2)
744.12/262.91	   U81(x0, x1, active(x2))
744.12/262.91	   U82(mark(x0), x1, x2)
744.12/262.91	   U82(x0, mark(x1), x2)
744.12/262.91	   U82(x0, x1, mark(x2))
744.12/262.91	   U82(active(x0), x1, x2)
744.12/262.91	   U82(x0, active(x1), x2)
744.12/262.91	   U82(x0, x1, active(x2))
744.12/262.91	   U83(mark(x0), x1, x2)
744.12/262.91	   U83(x0, mark(x1), x2)
744.12/262.91	   U83(x0, x1, mark(x2))
744.12/262.91	   U83(active(x0), x1, x2)
744.12/262.91	   U83(x0, active(x1), x2)
744.12/262.91	   U83(x0, x1, active(x2))
744.12/262.91	   U84(mark(x0), x1, x2)
744.12/262.91	   U84(x0, mark(x1), x2)
744.12/262.91	   U84(x0, x1, mark(x2))
744.12/262.91	   U84(active(x0), x1, x2)
744.12/262.91	   U84(x0, active(x1), x2)
744.12/262.91	   U84(x0, x1, active(x2))
744.12/262.91	   s(mark(x0))
744.12/262.91	   s(active(x0))
744.12/262.91	   U91(mark(x0), x1)
744.12/262.91	   U91(x0, mark(x1))
744.12/262.91	   U91(active(x0), x1)
744.12/262.91	   U91(x0, active(x1))
744.12/262.91	   U92(mark(x0))
744.12/262.91	   U92(active(x0))
744.12/262.91	
744.12/262.91	We have to consider all minimal (P,Q,R)-chains.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(188) UsableRulesProof (EQUIVALENT)
744.12/262.91	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.
744.12/262.91	----------------------------------------
744.12/262.91	
744.12/262.91	(189)
744.12/262.91	Obligation:
744.12/262.91	Q DP problem:
744.12/262.91	The TRS P consists of the following rules:
744.12/262.91	
744.12/262.91	   U13^1(X1, mark(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(mark(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, X2, mark(X3)) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(active(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, active(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.91	   U13^1(X1, X2, active(X3)) -> U13^1(X1, X2, X3)
744.12/262.91	
744.12/262.91	R is empty.
744.12/262.91	The set Q consists of the following terms:
744.12/262.91	
744.12/262.91	   active(U101(tt, x0, x1))
744.12/262.91	   active(U102(tt, x0, x1))
744.12/262.91	   active(U103(tt, x0, x1))
744.12/262.91	   active(U104(tt, x0, x1))
744.12/262.91	   active(U11(tt, x0, x1))
744.12/262.91	   active(U12(tt, x0, x1))
744.12/262.91	   active(U13(tt, x0, x1))
744.12/262.91	   active(U14(tt, x0, x1))
744.12/262.91	   active(U15(tt, x0))
744.12/262.91	   active(U16(tt))
744.12/262.91	   active(U21(tt, x0))
744.12/262.91	   active(U22(tt, x0))
744.12/262.91	   active(U23(tt))
744.12/262.91	   active(U31(tt, x0, x1))
744.12/262.91	   active(U32(tt, x0, x1))
744.12/262.91	   active(U33(tt, x0, x1))
744.12/262.91	   active(U34(tt, x0, x1))
744.12/262.91	   active(U35(tt, x0))
744.12/262.91	   active(U36(tt))
744.12/262.91	   active(U41(tt, x0))
744.12/262.91	   active(U42(tt))
744.12/262.91	   active(U51(tt))
744.12/262.91	   active(U61(tt, x0))
744.12/262.91	   active(U62(tt))
744.12/262.91	   active(U71(tt, x0))
744.12/262.91	   active(U72(tt, x0))
744.12/262.91	   active(U81(tt, x0, x1))
744.12/262.91	   active(U82(tt, x0, x1))
744.12/262.91	   active(U83(tt, x0, x1))
744.12/262.91	   active(U84(tt, x0, x1))
744.12/262.91	   active(U91(tt, x0))
744.12/262.91	   active(U92(tt))
744.12/262.91	   active(isNat(0))
744.12/262.91	   active(isNat(plus(x0, x1)))
744.12/262.91	   active(isNat(s(x0)))
744.12/262.91	   active(isNat(x(x0, x1)))
744.12/262.91	   active(isNatKind(0))
744.12/262.91	   active(isNatKind(plus(x0, x1)))
744.12/262.91	   active(isNatKind(s(x0)))
744.12/262.91	   active(isNatKind(x(x0, x1)))
744.12/262.91	   active(plus(x0, 0))
744.12/262.91	   active(plus(x0, s(x1)))
744.12/262.91	   active(x(x0, 0))
744.12/262.91	   active(x(x0, s(x1)))
744.12/262.91	   mark(U101(x0, x1, x2))
744.12/262.91	   mark(tt)
744.12/262.91	   mark(U102(x0, x1, x2))
744.12/262.91	   mark(isNatKind(x0))
744.12/262.91	   mark(U103(x0, x1, x2))
744.12/262.91	   mark(isNat(x0))
744.12/262.91	   mark(U104(x0, x1, x2))
744.12/262.91	   mark(plus(x0, x1))
744.12/262.91	   mark(x(x0, x1))
744.12/262.91	   mark(U11(x0, x1, x2))
744.12/262.91	   mark(U12(x0, x1, x2))
744.12/262.91	   mark(U13(x0, x1, x2))
744.12/262.91	   mark(U14(x0, x1, x2))
744.12/262.91	   mark(U15(x0, x1))
744.12/262.91	   mark(U16(x0))
744.12/262.91	   mark(U21(x0, x1))
744.12/262.91	   mark(U22(x0, x1))
744.12/262.91	   mark(U23(x0))
744.12/262.91	   mark(U31(x0, x1, x2))
744.12/262.91	   mark(U32(x0, x1, x2))
744.12/262.91	   mark(U33(x0, x1, x2))
744.12/262.91	   mark(U34(x0, x1, x2))
744.12/262.91	   mark(U35(x0, x1))
744.12/262.91	   mark(U36(x0))
744.12/262.91	   mark(U41(x0, x1))
744.12/262.91	   mark(U42(x0))
744.12/262.91	   mark(U51(x0))
744.12/262.91	   mark(U61(x0, x1))
744.12/262.91	   mark(U62(x0))
744.12/262.91	   mark(U71(x0, x1))
744.12/262.91	   mark(U72(x0, x1))
744.12/262.91	   mark(U81(x0, x1, x2))
744.12/262.91	   mark(U82(x0, x1, x2))
744.12/262.91	   mark(U83(x0, x1, x2))
744.12/262.91	   mark(U84(x0, x1, x2))
744.12/262.91	   mark(s(x0))
744.12/262.91	   mark(U91(x0, x1))
744.12/262.91	   mark(U92(x0))
744.12/262.91	   mark(0)
744.12/262.91	   U101(mark(x0), x1, x2)
744.12/262.91	   U101(x0, mark(x1), x2)
744.12/262.91	   U101(x0, x1, mark(x2))
744.12/262.91	   U101(active(x0), x1, x2)
744.12/262.91	   U101(x0, active(x1), x2)
744.12/262.91	   U101(x0, x1, active(x2))
744.12/262.91	   U102(mark(x0), x1, x2)
744.12/262.91	   U102(x0, mark(x1), x2)
744.12/262.91	   U102(x0, x1, mark(x2))
744.12/262.91	   U102(active(x0), x1, x2)
744.12/262.91	   U102(x0, active(x1), x2)
744.12/262.91	   U102(x0, x1, active(x2))
744.12/262.91	   isNatKind(mark(x0))
744.12/262.91	   isNatKind(active(x0))
744.12/262.91	   U103(mark(x0), x1, x2)
744.12/262.91	   U103(x0, mark(x1), x2)
744.12/262.91	   U103(x0, x1, mark(x2))
744.12/262.91	   U103(active(x0), x1, x2)
744.12/262.91	   U103(x0, active(x1), x2)
744.12/262.91	   U103(x0, x1, active(x2))
744.12/262.91	   isNat(mark(x0))
744.12/262.91	   isNat(active(x0))
744.12/262.91	   U104(mark(x0), x1, x2)
744.12/262.91	   U104(x0, mark(x1), x2)
744.12/262.91	   U104(x0, x1, mark(x2))
744.12/262.91	   U104(active(x0), x1, x2)
744.12/262.91	   U104(x0, active(x1), x2)
744.12/262.91	   U104(x0, x1, active(x2))
744.12/262.91	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(190) QReductionProof (EQUIVALENT)
744.12/262.92	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.92	
744.12/262.92	   U101(mark(x0), x1, x2)
744.12/262.92	   U101(x0, mark(x1), x2)
744.12/262.92	   U101(x0, x1, mark(x2))
744.12/262.92	   U101(active(x0), x1, x2)
744.12/262.92	   U101(x0, active(x1), x2)
744.12/262.92	   U101(x0, x1, active(x2))
744.12/262.92	   U102(mark(x0), x1, x2)
744.12/262.92	   U102(x0, mark(x1), x2)
744.12/262.92	   U102(x0, x1, mark(x2))
744.12/262.92	   U102(active(x0), x1, x2)
744.12/262.92	   U102(x0, active(x1), x2)
744.12/262.92	   U102(x0, x1, active(x2))
744.12/262.92	   isNatKind(mark(x0))
744.12/262.92	   isNatKind(active(x0))
744.12/262.92	   U103(mark(x0), x1, x2)
744.12/262.92	   U103(x0, mark(x1), x2)
744.12/262.92	   U103(x0, x1, mark(x2))
744.12/262.92	   U103(active(x0), x1, x2)
744.12/262.92	   U103(x0, active(x1), x2)
744.12/262.92	   U103(x0, x1, active(x2))
744.12/262.92	   isNat(mark(x0))
744.12/262.92	   isNat(active(x0))
744.12/262.92	   U104(mark(x0), x1, x2)
744.12/262.92	   U104(x0, mark(x1), x2)
744.12/262.92	   U104(x0, x1, mark(x2))
744.12/262.92	   U104(active(x0), x1, x2)
744.12/262.92	   U104(x0, active(x1), x2)
744.12/262.92	   U104(x0, x1, active(x2))
744.12/262.92	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(191)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U13^1(X1, mark(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.92	   U13^1(mark(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.92	   U13^1(X1, X2, mark(X3)) -> U13^1(X1, X2, X3)
744.12/262.92	   U13^1(active(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.92	   U13^1(X1, active(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.92	   U13^1(X1, X2, active(X3)) -> U13^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	R is empty.
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.92	   active(isNat(x(x0, x1)))
744.12/262.92	   active(isNatKind(0))
744.12/262.92	   active(isNatKind(plus(x0, x1)))
744.12/262.92	   active(isNatKind(s(x0)))
744.12/262.92	   active(isNatKind(x(x0, x1)))
744.12/262.92	   active(plus(x0, 0))
744.12/262.92	   active(plus(x0, s(x1)))
744.12/262.92	   active(x(x0, 0))
744.12/262.92	   active(x(x0, s(x1)))
744.12/262.92	   mark(U101(x0, x1, x2))
744.12/262.92	   mark(tt)
744.12/262.92	   mark(U102(x0, x1, x2))
744.12/262.92	   mark(isNatKind(x0))
744.12/262.92	   mark(U103(x0, x1, x2))
744.12/262.92	   mark(isNat(x0))
744.12/262.92	   mark(U104(x0, x1, x2))
744.12/262.92	   mark(plus(x0, x1))
744.12/262.92	   mark(x(x0, x1))
744.12/262.92	   mark(U11(x0, x1, x2))
744.12/262.92	   mark(U12(x0, x1, x2))
744.12/262.92	   mark(U13(x0, x1, x2))
744.12/262.92	   mark(U14(x0, x1, x2))
744.12/262.92	   mark(U15(x0, x1))
744.12/262.92	   mark(U16(x0))
744.12/262.92	   mark(U21(x0, x1))
744.12/262.92	   mark(U22(x0, x1))
744.12/262.92	   mark(U23(x0))
744.12/262.92	   mark(U31(x0, x1, x2))
744.12/262.92	   mark(U32(x0, x1, x2))
744.12/262.92	   mark(U33(x0, x1, x2))
744.12/262.92	   mark(U34(x0, x1, x2))
744.12/262.92	   mark(U35(x0, x1))
744.12/262.92	   mark(U36(x0))
744.12/262.92	   mark(U41(x0, x1))
744.12/262.92	   mark(U42(x0))
744.12/262.92	   mark(U51(x0))
744.12/262.92	   mark(U61(x0, x1))
744.12/262.92	   mark(U62(x0))
744.12/262.92	   mark(U71(x0, x1))
744.12/262.92	   mark(U72(x0, x1))
744.12/262.92	   mark(U81(x0, x1, x2))
744.12/262.92	   mark(U82(x0, x1, x2))
744.12/262.92	   mark(U83(x0, x1, x2))
744.12/262.92	   mark(U84(x0, x1, x2))
744.12/262.92	   mark(s(x0))
744.12/262.92	   mark(U91(x0, x1))
744.12/262.92	   mark(U92(x0))
744.12/262.92	   mark(0)
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(192) QDPSizeChangeProof (EQUIVALENT)
744.12/262.92	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. 
744.12/262.92	
744.12/262.92	From the DPs we obtained the following set of size-change graphs:
744.12/262.92	*U13^1(X1, mark(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U13^1(mark(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U13^1(X1, X2, mark(X3)) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U13^1(active(X1), X2, X3) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U13^1(X1, active(X2), X3) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U13^1(X1, X2, active(X3)) -> U13^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.92	
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(193)
744.12/262.92	YES
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(194)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U12^1(X1, mark(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(mark(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, mark(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(active(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, active(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, active(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	The TRS R consists of the following rules:
744.12/262.92	
744.12/262.92	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.92	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.92	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.92	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.92	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.92	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.92	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.92	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.92	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.92	   active(U16(tt)) -> mark(tt)
744.12/262.92	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.92	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.92	   active(U23(tt)) -> mark(tt)
744.12/262.92	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.92	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.92	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.92	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.92	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.92	   active(U36(tt)) -> mark(tt)
744.12/262.92	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.92	   active(U42(tt)) -> mark(tt)
744.12/262.92	   active(U51(tt)) -> mark(tt)
744.12/262.92	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.92	   active(U62(tt)) -> mark(tt)
744.12/262.92	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.92	   active(U72(tt, N)) -> mark(N)
744.12/262.92	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.92	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.92	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.92	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.92	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.92	   active(U92(tt)) -> mark(0)
744.12/262.92	   active(isNat(0)) -> mark(tt)
744.12/262.92	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.92	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.92	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.92	   active(isNatKind(0)) -> mark(tt)
744.12/262.92	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.92	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.92	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.92	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.92	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.92	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.92	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.92	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.92	   mark(tt) -> active(tt)
744.12/262.92	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.92	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.92	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.92	   mark(isNat(X)) -> active(isNat(X))
744.12/262.92	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.92	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.92	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.92	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.92	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.92	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.92	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.92	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.92	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.92	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.92	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.92	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.92	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.92	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.92	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.92	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.92	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.92	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.92	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.92	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.92	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.92	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.92	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.92	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.92	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.92	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.92	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.92	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.92	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.92	   mark(s(X)) -> active(s(mark(X)))
744.12/262.92	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.92	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.92	   mark(0) -> active(0)
744.12/262.92	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.92	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.92	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.92	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.92	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.92	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.92	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.92	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.92	   isNat(mark(X)) -> isNat(X)
744.12/262.92	   isNat(active(X)) -> isNat(X)
744.12/262.92	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.92	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.92	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.92	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.92	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.92	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.92	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.92	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.92	   x(active(X1), X2) -> x(X1, X2)
744.12/262.92	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.92	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.92	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.92	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.92	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.92	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.92	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.92	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.92	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.92	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.92	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.92	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.92	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.92	   U16(mark(X)) -> U16(X)
744.12/262.92	   U16(active(X)) -> U16(X)
744.12/262.92	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.92	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.92	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.92	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.92	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.92	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.92	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.92	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.92	   U23(mark(X)) -> U23(X)
744.12/262.92	   U23(active(X)) -> U23(X)
744.12/262.92	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.92	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.92	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.92	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.92	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.92	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.92	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.92	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.92	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.92	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.92	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.92	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.92	   U36(mark(X)) -> U36(X)
744.12/262.92	   U36(active(X)) -> U36(X)
744.12/262.92	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.92	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.92	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.92	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.92	   U42(mark(X)) -> U42(X)
744.12/262.92	   U42(active(X)) -> U42(X)
744.12/262.92	   U51(mark(X)) -> U51(X)
744.12/262.92	   U51(active(X)) -> U51(X)
744.12/262.92	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.92	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.92	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.92	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.92	   U62(mark(X)) -> U62(X)
744.12/262.92	   U62(active(X)) -> U62(X)
744.12/262.92	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.92	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.92	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.92	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.92	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.92	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.92	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.92	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.92	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.92	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.92	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.92	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.92	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.92	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.92	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.92	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.92	   s(mark(X)) -> s(X)
744.12/262.92	   s(active(X)) -> s(X)
744.12/262.92	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.92	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.92	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.92	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.92	   U92(mark(X)) -> U92(X)
744.12/262.92	   U92(active(X)) -> U92(X)
744.12/262.92	
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.92	   active(isNat(x(x0, x1)))
744.12/262.92	   active(isNatKind(0))
744.12/262.92	   active(isNatKind(plus(x0, x1)))
744.12/262.92	   active(isNatKind(s(x0)))
744.12/262.92	   active(isNatKind(x(x0, x1)))
744.12/262.92	   active(plus(x0, 0))
744.12/262.92	   active(plus(x0, s(x1)))
744.12/262.92	   active(x(x0, 0))
744.12/262.92	   active(x(x0, s(x1)))
744.12/262.92	   mark(U101(x0, x1, x2))
744.12/262.92	   mark(tt)
744.12/262.92	   mark(U102(x0, x1, x2))
744.12/262.92	   mark(isNatKind(x0))
744.12/262.92	   mark(U103(x0, x1, x2))
744.12/262.92	   mark(isNat(x0))
744.12/262.92	   mark(U104(x0, x1, x2))
744.12/262.92	   mark(plus(x0, x1))
744.12/262.92	   mark(x(x0, x1))
744.12/262.92	   mark(U11(x0, x1, x2))
744.12/262.92	   mark(U12(x0, x1, x2))
744.12/262.92	   mark(U13(x0, x1, x2))
744.12/262.92	   mark(U14(x0, x1, x2))
744.12/262.92	   mark(U15(x0, x1))
744.12/262.92	   mark(U16(x0))
744.12/262.92	   mark(U21(x0, x1))
744.12/262.92	   mark(U22(x0, x1))
744.12/262.92	   mark(U23(x0))
744.12/262.92	   mark(U31(x0, x1, x2))
744.12/262.92	   mark(U32(x0, x1, x2))
744.12/262.92	   mark(U33(x0, x1, x2))
744.12/262.92	   mark(U34(x0, x1, x2))
744.12/262.92	   mark(U35(x0, x1))
744.12/262.92	   mark(U36(x0))
744.12/262.92	   mark(U41(x0, x1))
744.12/262.92	   mark(U42(x0))
744.12/262.92	   mark(U51(x0))
744.12/262.92	   mark(U61(x0, x1))
744.12/262.92	   mark(U62(x0))
744.12/262.92	   mark(U71(x0, x1))
744.12/262.92	   mark(U72(x0, x1))
744.12/262.92	   mark(U81(x0, x1, x2))
744.12/262.92	   mark(U82(x0, x1, x2))
744.12/262.92	   mark(U83(x0, x1, x2))
744.12/262.92	   mark(U84(x0, x1, x2))
744.12/262.92	   mark(s(x0))
744.12/262.92	   mark(U91(x0, x1))
744.12/262.92	   mark(U92(x0))
744.12/262.92	   mark(0)
744.12/262.92	   U101(mark(x0), x1, x2)
744.12/262.92	   U101(x0, mark(x1), x2)
744.12/262.92	   U101(x0, x1, mark(x2))
744.12/262.92	   U101(active(x0), x1, x2)
744.12/262.92	   U101(x0, active(x1), x2)
744.12/262.92	   U101(x0, x1, active(x2))
744.12/262.92	   U102(mark(x0), x1, x2)
744.12/262.92	   U102(x0, mark(x1), x2)
744.12/262.92	   U102(x0, x1, mark(x2))
744.12/262.92	   U102(active(x0), x1, x2)
744.12/262.92	   U102(x0, active(x1), x2)
744.12/262.92	   U102(x0, x1, active(x2))
744.12/262.92	   isNatKind(mark(x0))
744.12/262.92	   isNatKind(active(x0))
744.12/262.92	   U103(mark(x0), x1, x2)
744.12/262.92	   U103(x0, mark(x1), x2)
744.12/262.92	   U103(x0, x1, mark(x2))
744.12/262.92	   U103(active(x0), x1, x2)
744.12/262.92	   U103(x0, active(x1), x2)
744.12/262.92	   U103(x0, x1, active(x2))
744.12/262.92	   isNat(mark(x0))
744.12/262.92	   isNat(active(x0))
744.12/262.92	   U104(mark(x0), x1, x2)
744.12/262.92	   U104(x0, mark(x1), x2)
744.12/262.92	   U104(x0, x1, mark(x2))
744.12/262.92	   U104(active(x0), x1, x2)
744.12/262.92	   U104(x0, active(x1), x2)
744.12/262.92	   U104(x0, x1, active(x2))
744.12/262.92	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(195) UsableRulesProof (EQUIVALENT)
744.12/262.92	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.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(196)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U12^1(X1, mark(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(mark(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, mark(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(active(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, active(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, active(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	R is empty.
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.92	   active(isNat(x(x0, x1)))
744.12/262.92	   active(isNatKind(0))
744.12/262.92	   active(isNatKind(plus(x0, x1)))
744.12/262.92	   active(isNatKind(s(x0)))
744.12/262.92	   active(isNatKind(x(x0, x1)))
744.12/262.92	   active(plus(x0, 0))
744.12/262.92	   active(plus(x0, s(x1)))
744.12/262.92	   active(x(x0, 0))
744.12/262.92	   active(x(x0, s(x1)))
744.12/262.92	   mark(U101(x0, x1, x2))
744.12/262.92	   mark(tt)
744.12/262.92	   mark(U102(x0, x1, x2))
744.12/262.92	   mark(isNatKind(x0))
744.12/262.92	   mark(U103(x0, x1, x2))
744.12/262.92	   mark(isNat(x0))
744.12/262.92	   mark(U104(x0, x1, x2))
744.12/262.92	   mark(plus(x0, x1))
744.12/262.92	   mark(x(x0, x1))
744.12/262.92	   mark(U11(x0, x1, x2))
744.12/262.92	   mark(U12(x0, x1, x2))
744.12/262.92	   mark(U13(x0, x1, x2))
744.12/262.92	   mark(U14(x0, x1, x2))
744.12/262.92	   mark(U15(x0, x1))
744.12/262.92	   mark(U16(x0))
744.12/262.92	   mark(U21(x0, x1))
744.12/262.92	   mark(U22(x0, x1))
744.12/262.92	   mark(U23(x0))
744.12/262.92	   mark(U31(x0, x1, x2))
744.12/262.92	   mark(U32(x0, x1, x2))
744.12/262.92	   mark(U33(x0, x1, x2))
744.12/262.92	   mark(U34(x0, x1, x2))
744.12/262.92	   mark(U35(x0, x1))
744.12/262.92	   mark(U36(x0))
744.12/262.92	   mark(U41(x0, x1))
744.12/262.92	   mark(U42(x0))
744.12/262.92	   mark(U51(x0))
744.12/262.92	   mark(U61(x0, x1))
744.12/262.92	   mark(U62(x0))
744.12/262.92	   mark(U71(x0, x1))
744.12/262.92	   mark(U72(x0, x1))
744.12/262.92	   mark(U81(x0, x1, x2))
744.12/262.92	   mark(U82(x0, x1, x2))
744.12/262.92	   mark(U83(x0, x1, x2))
744.12/262.92	   mark(U84(x0, x1, x2))
744.12/262.92	   mark(s(x0))
744.12/262.92	   mark(U91(x0, x1))
744.12/262.92	   mark(U92(x0))
744.12/262.92	   mark(0)
744.12/262.92	   U101(mark(x0), x1, x2)
744.12/262.92	   U101(x0, mark(x1), x2)
744.12/262.92	   U101(x0, x1, mark(x2))
744.12/262.92	   U101(active(x0), x1, x2)
744.12/262.92	   U101(x0, active(x1), x2)
744.12/262.92	   U101(x0, x1, active(x2))
744.12/262.92	   U102(mark(x0), x1, x2)
744.12/262.92	   U102(x0, mark(x1), x2)
744.12/262.92	   U102(x0, x1, mark(x2))
744.12/262.92	   U102(active(x0), x1, x2)
744.12/262.92	   U102(x0, active(x1), x2)
744.12/262.92	   U102(x0, x1, active(x2))
744.12/262.92	   isNatKind(mark(x0))
744.12/262.92	   isNatKind(active(x0))
744.12/262.92	   U103(mark(x0), x1, x2)
744.12/262.92	   U103(x0, mark(x1), x2)
744.12/262.92	   U103(x0, x1, mark(x2))
744.12/262.92	   U103(active(x0), x1, x2)
744.12/262.92	   U103(x0, active(x1), x2)
744.12/262.92	   U103(x0, x1, active(x2))
744.12/262.92	   isNat(mark(x0))
744.12/262.92	   isNat(active(x0))
744.12/262.92	   U104(mark(x0), x1, x2)
744.12/262.92	   U104(x0, mark(x1), x2)
744.12/262.92	   U104(x0, x1, mark(x2))
744.12/262.92	   U104(active(x0), x1, x2)
744.12/262.92	   U104(x0, active(x1), x2)
744.12/262.92	   U104(x0, x1, active(x2))
744.12/262.92	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(197) QReductionProof (EQUIVALENT)
744.12/262.92	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.92	
744.12/262.92	   U101(mark(x0), x1, x2)
744.12/262.92	   U101(x0, mark(x1), x2)
744.12/262.92	   U101(x0, x1, mark(x2))
744.12/262.92	   U101(active(x0), x1, x2)
744.12/262.92	   U101(x0, active(x1), x2)
744.12/262.92	   U101(x0, x1, active(x2))
744.12/262.92	   U102(mark(x0), x1, x2)
744.12/262.92	   U102(x0, mark(x1), x2)
744.12/262.92	   U102(x0, x1, mark(x2))
744.12/262.92	   U102(active(x0), x1, x2)
744.12/262.92	   U102(x0, active(x1), x2)
744.12/262.92	   U102(x0, x1, active(x2))
744.12/262.92	   isNatKind(mark(x0))
744.12/262.92	   isNatKind(active(x0))
744.12/262.92	   U103(mark(x0), x1, x2)
744.12/262.92	   U103(x0, mark(x1), x2)
744.12/262.92	   U103(x0, x1, mark(x2))
744.12/262.92	   U103(active(x0), x1, x2)
744.12/262.92	   U103(x0, active(x1), x2)
744.12/262.92	   U103(x0, x1, active(x2))
744.12/262.92	   isNat(mark(x0))
744.12/262.92	   isNat(active(x0))
744.12/262.92	   U104(mark(x0), x1, x2)
744.12/262.92	   U104(x0, mark(x1), x2)
744.12/262.92	   U104(x0, x1, mark(x2))
744.12/262.92	   U104(active(x0), x1, x2)
744.12/262.92	   U104(x0, active(x1), x2)
744.12/262.92	   U104(x0, x1, active(x2))
744.12/262.92	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(198)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U12^1(X1, mark(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(mark(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, mark(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(active(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, active(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	   U12^1(X1, X2, active(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	R is empty.
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.92	   active(isNat(x(x0, x1)))
744.12/262.92	   active(isNatKind(0))
744.12/262.92	   active(isNatKind(plus(x0, x1)))
744.12/262.92	   active(isNatKind(s(x0)))
744.12/262.92	   active(isNatKind(x(x0, x1)))
744.12/262.92	   active(plus(x0, 0))
744.12/262.92	   active(plus(x0, s(x1)))
744.12/262.92	   active(x(x0, 0))
744.12/262.92	   active(x(x0, s(x1)))
744.12/262.92	   mark(U101(x0, x1, x2))
744.12/262.92	   mark(tt)
744.12/262.92	   mark(U102(x0, x1, x2))
744.12/262.92	   mark(isNatKind(x0))
744.12/262.92	   mark(U103(x0, x1, x2))
744.12/262.92	   mark(isNat(x0))
744.12/262.92	   mark(U104(x0, x1, x2))
744.12/262.92	   mark(plus(x0, x1))
744.12/262.92	   mark(x(x0, x1))
744.12/262.92	   mark(U11(x0, x1, x2))
744.12/262.92	   mark(U12(x0, x1, x2))
744.12/262.92	   mark(U13(x0, x1, x2))
744.12/262.92	   mark(U14(x0, x1, x2))
744.12/262.92	   mark(U15(x0, x1))
744.12/262.92	   mark(U16(x0))
744.12/262.92	   mark(U21(x0, x1))
744.12/262.92	   mark(U22(x0, x1))
744.12/262.92	   mark(U23(x0))
744.12/262.92	   mark(U31(x0, x1, x2))
744.12/262.92	   mark(U32(x0, x1, x2))
744.12/262.92	   mark(U33(x0, x1, x2))
744.12/262.92	   mark(U34(x0, x1, x2))
744.12/262.92	   mark(U35(x0, x1))
744.12/262.92	   mark(U36(x0))
744.12/262.92	   mark(U41(x0, x1))
744.12/262.92	   mark(U42(x0))
744.12/262.92	   mark(U51(x0))
744.12/262.92	   mark(U61(x0, x1))
744.12/262.92	   mark(U62(x0))
744.12/262.92	   mark(U71(x0, x1))
744.12/262.92	   mark(U72(x0, x1))
744.12/262.92	   mark(U81(x0, x1, x2))
744.12/262.92	   mark(U82(x0, x1, x2))
744.12/262.92	   mark(U83(x0, x1, x2))
744.12/262.92	   mark(U84(x0, x1, x2))
744.12/262.92	   mark(s(x0))
744.12/262.92	   mark(U91(x0, x1))
744.12/262.92	   mark(U92(x0))
744.12/262.92	   mark(0)
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(199) QDPSizeChangeProof (EQUIVALENT)
744.12/262.92	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. 
744.12/262.92	
744.12/262.92	From the DPs we obtained the following set of size-change graphs:
744.12/262.92	*U12^1(X1, mark(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U12^1(mark(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U12^1(X1, X2, mark(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U12^1(active(X1), X2, X3) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U12^1(X1, active(X2), X3) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.92	
744.12/262.92	
744.12/262.92	*U12^1(X1, X2, active(X3)) -> U12^1(X1, X2, X3)
744.12/262.92	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.92	
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(200)
744.12/262.92	YES
744.12/262.92	
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(201)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U11^1(X1, mark(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(mark(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, X2, mark(X3)) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(active(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, active(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, X2, active(X3)) -> U11^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	The TRS R consists of the following rules:
744.12/262.92	
744.12/262.92	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.92	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.92	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.92	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.92	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.92	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.92	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.92	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.92	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.92	   active(U16(tt)) -> mark(tt)
744.12/262.92	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.92	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.92	   active(U23(tt)) -> mark(tt)
744.12/262.92	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.92	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.92	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.92	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.92	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.92	   active(U36(tt)) -> mark(tt)
744.12/262.92	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.92	   active(U42(tt)) -> mark(tt)
744.12/262.92	   active(U51(tt)) -> mark(tt)
744.12/262.92	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.92	   active(U62(tt)) -> mark(tt)
744.12/262.92	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.92	   active(U72(tt, N)) -> mark(N)
744.12/262.92	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.92	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.92	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.92	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.92	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.92	   active(U92(tt)) -> mark(0)
744.12/262.92	   active(isNat(0)) -> mark(tt)
744.12/262.92	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.92	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.92	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.92	   active(isNatKind(0)) -> mark(tt)
744.12/262.92	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.92	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.92	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.92	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.92	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.92	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.92	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.92	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.92	   mark(tt) -> active(tt)
744.12/262.92	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.92	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.92	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.92	   mark(isNat(X)) -> active(isNat(X))
744.12/262.92	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.92	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.92	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.92	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.92	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.92	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.92	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.92	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.92	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.92	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.92	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.92	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.92	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.92	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.92	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.92	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.92	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.92	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.92	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.92	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.92	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.92	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.92	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.92	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.92	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.92	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.92	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.92	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.92	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.92	   mark(s(X)) -> active(s(mark(X)))
744.12/262.92	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.92	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.92	   mark(0) -> active(0)
744.12/262.92	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.92	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.92	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.92	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.92	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.92	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.92	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.92	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.92	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.92	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.92	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.92	   isNat(mark(X)) -> isNat(X)
744.12/262.92	   isNat(active(X)) -> isNat(X)
744.12/262.92	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.92	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.92	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.92	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.92	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.92	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.92	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.92	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.92	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.92	   x(active(X1), X2) -> x(X1, X2)
744.12/262.92	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.92	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.92	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.92	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.92	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.92	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.92	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.92	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.92	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.92	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.92	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.92	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.92	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.92	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.92	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.92	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.92	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.92	   U16(mark(X)) -> U16(X)
744.12/262.92	   U16(active(X)) -> U16(X)
744.12/262.92	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.92	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.92	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.92	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.92	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.92	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.92	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.92	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.92	   U23(mark(X)) -> U23(X)
744.12/262.92	   U23(active(X)) -> U23(X)
744.12/262.92	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.92	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.92	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.92	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.92	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.92	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.92	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.92	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.92	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.92	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.92	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.92	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.92	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.92	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.92	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.92	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.92	   U36(mark(X)) -> U36(X)
744.12/262.92	   U36(active(X)) -> U36(X)
744.12/262.92	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.92	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.92	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.92	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.92	   U42(mark(X)) -> U42(X)
744.12/262.92	   U42(active(X)) -> U42(X)
744.12/262.92	   U51(mark(X)) -> U51(X)
744.12/262.92	   U51(active(X)) -> U51(X)
744.12/262.92	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.92	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.92	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.92	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.92	   U62(mark(X)) -> U62(X)
744.12/262.92	   U62(active(X)) -> U62(X)
744.12/262.92	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.92	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.92	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.92	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.92	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.92	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.92	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.92	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.92	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.92	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.92	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.92	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.92	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.92	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.92	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.92	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.92	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.92	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.92	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.92	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.92	   s(mark(X)) -> s(X)
744.12/262.92	   s(active(X)) -> s(X)
744.12/262.92	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.92	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.92	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.92	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.92	   U92(mark(X)) -> U92(X)
744.12/262.92	   U92(active(X)) -> U92(X)
744.12/262.92	
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.92	   active(isNat(x(x0, x1)))
744.12/262.92	   active(isNatKind(0))
744.12/262.92	   active(isNatKind(plus(x0, x1)))
744.12/262.92	   active(isNatKind(s(x0)))
744.12/262.92	   active(isNatKind(x(x0, x1)))
744.12/262.92	   active(plus(x0, 0))
744.12/262.92	   active(plus(x0, s(x1)))
744.12/262.92	   active(x(x0, 0))
744.12/262.92	   active(x(x0, s(x1)))
744.12/262.92	   mark(U101(x0, x1, x2))
744.12/262.92	   mark(tt)
744.12/262.92	   mark(U102(x0, x1, x2))
744.12/262.92	   mark(isNatKind(x0))
744.12/262.92	   mark(U103(x0, x1, x2))
744.12/262.92	   mark(isNat(x0))
744.12/262.92	   mark(U104(x0, x1, x2))
744.12/262.92	   mark(plus(x0, x1))
744.12/262.92	   mark(x(x0, x1))
744.12/262.92	   mark(U11(x0, x1, x2))
744.12/262.92	   mark(U12(x0, x1, x2))
744.12/262.92	   mark(U13(x0, x1, x2))
744.12/262.92	   mark(U14(x0, x1, x2))
744.12/262.92	   mark(U15(x0, x1))
744.12/262.92	   mark(U16(x0))
744.12/262.92	   mark(U21(x0, x1))
744.12/262.92	   mark(U22(x0, x1))
744.12/262.92	   mark(U23(x0))
744.12/262.92	   mark(U31(x0, x1, x2))
744.12/262.92	   mark(U32(x0, x1, x2))
744.12/262.92	   mark(U33(x0, x1, x2))
744.12/262.92	   mark(U34(x0, x1, x2))
744.12/262.92	   mark(U35(x0, x1))
744.12/262.92	   mark(U36(x0))
744.12/262.92	   mark(U41(x0, x1))
744.12/262.92	   mark(U42(x0))
744.12/262.92	   mark(U51(x0))
744.12/262.92	   mark(U61(x0, x1))
744.12/262.92	   mark(U62(x0))
744.12/262.92	   mark(U71(x0, x1))
744.12/262.92	   mark(U72(x0, x1))
744.12/262.92	   mark(U81(x0, x1, x2))
744.12/262.92	   mark(U82(x0, x1, x2))
744.12/262.92	   mark(U83(x0, x1, x2))
744.12/262.92	   mark(U84(x0, x1, x2))
744.12/262.92	   mark(s(x0))
744.12/262.92	   mark(U91(x0, x1))
744.12/262.92	   mark(U92(x0))
744.12/262.92	   mark(0)
744.12/262.92	   U101(mark(x0), x1, x2)
744.12/262.92	   U101(x0, mark(x1), x2)
744.12/262.92	   U101(x0, x1, mark(x2))
744.12/262.92	   U101(active(x0), x1, x2)
744.12/262.92	   U101(x0, active(x1), x2)
744.12/262.92	   U101(x0, x1, active(x2))
744.12/262.92	   U102(mark(x0), x1, x2)
744.12/262.92	   U102(x0, mark(x1), x2)
744.12/262.92	   U102(x0, x1, mark(x2))
744.12/262.92	   U102(active(x0), x1, x2)
744.12/262.92	   U102(x0, active(x1), x2)
744.12/262.92	   U102(x0, x1, active(x2))
744.12/262.92	   isNatKind(mark(x0))
744.12/262.92	   isNatKind(active(x0))
744.12/262.92	   U103(mark(x0), x1, x2)
744.12/262.92	   U103(x0, mark(x1), x2)
744.12/262.92	   U103(x0, x1, mark(x2))
744.12/262.92	   U103(active(x0), x1, x2)
744.12/262.92	   U103(x0, active(x1), x2)
744.12/262.92	   U103(x0, x1, active(x2))
744.12/262.92	   isNat(mark(x0))
744.12/262.92	   isNat(active(x0))
744.12/262.92	   U104(mark(x0), x1, x2)
744.12/262.92	   U104(x0, mark(x1), x2)
744.12/262.92	   U104(x0, x1, mark(x2))
744.12/262.92	   U104(active(x0), x1, x2)
744.12/262.92	   U104(x0, active(x1), x2)
744.12/262.92	   U104(x0, x1, active(x2))
744.12/262.92	   plus(mark(x0), x1)
744.12/262.92	   plus(x0, mark(x1))
744.12/262.92	   plus(active(x0), x1)
744.12/262.92	   plus(x0, active(x1))
744.12/262.92	   x(mark(x0), x1)
744.12/262.92	   x(x0, mark(x1))
744.12/262.92	   x(active(x0), x1)
744.12/262.92	   x(x0, active(x1))
744.12/262.92	   U11(mark(x0), x1, x2)
744.12/262.92	   U11(x0, mark(x1), x2)
744.12/262.92	   U11(x0, x1, mark(x2))
744.12/262.92	   U11(active(x0), x1, x2)
744.12/262.92	   U11(x0, active(x1), x2)
744.12/262.92	   U11(x0, x1, active(x2))
744.12/262.92	   U12(mark(x0), x1, x2)
744.12/262.92	   U12(x0, mark(x1), x2)
744.12/262.92	   U12(x0, x1, mark(x2))
744.12/262.92	   U12(active(x0), x1, x2)
744.12/262.92	   U12(x0, active(x1), x2)
744.12/262.92	   U12(x0, x1, active(x2))
744.12/262.92	   U13(mark(x0), x1, x2)
744.12/262.92	   U13(x0, mark(x1), x2)
744.12/262.92	   U13(x0, x1, mark(x2))
744.12/262.92	   U13(active(x0), x1, x2)
744.12/262.92	   U13(x0, active(x1), x2)
744.12/262.92	   U13(x0, x1, active(x2))
744.12/262.92	   U14(mark(x0), x1, x2)
744.12/262.92	   U14(x0, mark(x1), x2)
744.12/262.92	   U14(x0, x1, mark(x2))
744.12/262.92	   U14(active(x0), x1, x2)
744.12/262.92	   U14(x0, active(x1), x2)
744.12/262.92	   U14(x0, x1, active(x2))
744.12/262.92	   U15(mark(x0), x1)
744.12/262.92	   U15(x0, mark(x1))
744.12/262.92	   U15(active(x0), x1)
744.12/262.92	   U15(x0, active(x1))
744.12/262.92	   U16(mark(x0))
744.12/262.92	   U16(active(x0))
744.12/262.92	   U21(mark(x0), x1)
744.12/262.92	   U21(x0, mark(x1))
744.12/262.92	   U21(active(x0), x1)
744.12/262.92	   U21(x0, active(x1))
744.12/262.92	   U22(mark(x0), x1)
744.12/262.92	   U22(x0, mark(x1))
744.12/262.92	   U22(active(x0), x1)
744.12/262.92	   U22(x0, active(x1))
744.12/262.92	   U23(mark(x0))
744.12/262.92	   U23(active(x0))
744.12/262.92	   U31(mark(x0), x1, x2)
744.12/262.92	   U31(x0, mark(x1), x2)
744.12/262.92	   U31(x0, x1, mark(x2))
744.12/262.92	   U31(active(x0), x1, x2)
744.12/262.92	   U31(x0, active(x1), x2)
744.12/262.92	   U31(x0, x1, active(x2))
744.12/262.92	   U32(mark(x0), x1, x2)
744.12/262.92	   U32(x0, mark(x1), x2)
744.12/262.92	   U32(x0, x1, mark(x2))
744.12/262.92	   U32(active(x0), x1, x2)
744.12/262.92	   U32(x0, active(x1), x2)
744.12/262.92	   U32(x0, x1, active(x2))
744.12/262.92	   U33(mark(x0), x1, x2)
744.12/262.92	   U33(x0, mark(x1), x2)
744.12/262.92	   U33(x0, x1, mark(x2))
744.12/262.92	   U33(active(x0), x1, x2)
744.12/262.92	   U33(x0, active(x1), x2)
744.12/262.92	   U33(x0, x1, active(x2))
744.12/262.92	   U34(mark(x0), x1, x2)
744.12/262.92	   U34(x0, mark(x1), x2)
744.12/262.92	   U34(x0, x1, mark(x2))
744.12/262.92	   U34(active(x0), x1, x2)
744.12/262.92	   U34(x0, active(x1), x2)
744.12/262.92	   U34(x0, x1, active(x2))
744.12/262.92	   U35(mark(x0), x1)
744.12/262.92	   U35(x0, mark(x1))
744.12/262.92	   U35(active(x0), x1)
744.12/262.92	   U35(x0, active(x1))
744.12/262.92	   U36(mark(x0))
744.12/262.92	   U36(active(x0))
744.12/262.92	   U41(mark(x0), x1)
744.12/262.92	   U41(x0, mark(x1))
744.12/262.92	   U41(active(x0), x1)
744.12/262.92	   U41(x0, active(x1))
744.12/262.92	   U42(mark(x0))
744.12/262.92	   U42(active(x0))
744.12/262.92	   U51(mark(x0))
744.12/262.92	   U51(active(x0))
744.12/262.92	   U61(mark(x0), x1)
744.12/262.92	   U61(x0, mark(x1))
744.12/262.92	   U61(active(x0), x1)
744.12/262.92	   U61(x0, active(x1))
744.12/262.92	   U62(mark(x0))
744.12/262.92	   U62(active(x0))
744.12/262.92	   U71(mark(x0), x1)
744.12/262.92	   U71(x0, mark(x1))
744.12/262.92	   U71(active(x0), x1)
744.12/262.92	   U71(x0, active(x1))
744.12/262.92	   U72(mark(x0), x1)
744.12/262.92	   U72(x0, mark(x1))
744.12/262.92	   U72(active(x0), x1)
744.12/262.92	   U72(x0, active(x1))
744.12/262.92	   U81(mark(x0), x1, x2)
744.12/262.92	   U81(x0, mark(x1), x2)
744.12/262.92	   U81(x0, x1, mark(x2))
744.12/262.92	   U81(active(x0), x1, x2)
744.12/262.92	   U81(x0, active(x1), x2)
744.12/262.92	   U81(x0, x1, active(x2))
744.12/262.92	   U82(mark(x0), x1, x2)
744.12/262.92	   U82(x0, mark(x1), x2)
744.12/262.92	   U82(x0, x1, mark(x2))
744.12/262.92	   U82(active(x0), x1, x2)
744.12/262.92	   U82(x0, active(x1), x2)
744.12/262.92	   U82(x0, x1, active(x2))
744.12/262.92	   U83(mark(x0), x1, x2)
744.12/262.92	   U83(x0, mark(x1), x2)
744.12/262.92	   U83(x0, x1, mark(x2))
744.12/262.92	   U83(active(x0), x1, x2)
744.12/262.92	   U83(x0, active(x1), x2)
744.12/262.92	   U83(x0, x1, active(x2))
744.12/262.92	   U84(mark(x0), x1, x2)
744.12/262.92	   U84(x0, mark(x1), x2)
744.12/262.92	   U84(x0, x1, mark(x2))
744.12/262.92	   U84(active(x0), x1, x2)
744.12/262.92	   U84(x0, active(x1), x2)
744.12/262.92	   U84(x0, x1, active(x2))
744.12/262.92	   s(mark(x0))
744.12/262.92	   s(active(x0))
744.12/262.92	   U91(mark(x0), x1)
744.12/262.92	   U91(x0, mark(x1))
744.12/262.92	   U91(active(x0), x1)
744.12/262.92	   U91(x0, active(x1))
744.12/262.92	   U92(mark(x0))
744.12/262.92	   U92(active(x0))
744.12/262.92	
744.12/262.92	We have to consider all minimal (P,Q,R)-chains.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(202) UsableRulesProof (EQUIVALENT)
744.12/262.92	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.
744.12/262.92	----------------------------------------
744.12/262.92	
744.12/262.92	(203)
744.12/262.92	Obligation:
744.12/262.92	Q DP problem:
744.12/262.92	The TRS P consists of the following rules:
744.12/262.92	
744.12/262.92	   U11^1(X1, mark(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(mark(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, X2, mark(X3)) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(active(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, active(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.92	   U11^1(X1, X2, active(X3)) -> U11^1(X1, X2, X3)
744.12/262.92	
744.12/262.92	R is empty.
744.12/262.92	The set Q consists of the following terms:
744.12/262.92	
744.12/262.92	   active(U101(tt, x0, x1))
744.12/262.92	   active(U102(tt, x0, x1))
744.12/262.92	   active(U103(tt, x0, x1))
744.12/262.92	   active(U104(tt, x0, x1))
744.12/262.92	   active(U11(tt, x0, x1))
744.12/262.92	   active(U12(tt, x0, x1))
744.12/262.92	   active(U13(tt, x0, x1))
744.12/262.92	   active(U14(tt, x0, x1))
744.12/262.92	   active(U15(tt, x0))
744.12/262.92	   active(U16(tt))
744.12/262.92	   active(U21(tt, x0))
744.12/262.92	   active(U22(tt, x0))
744.12/262.92	   active(U23(tt))
744.12/262.92	   active(U31(tt, x0, x1))
744.12/262.92	   active(U32(tt, x0, x1))
744.12/262.92	   active(U33(tt, x0, x1))
744.12/262.92	   active(U34(tt, x0, x1))
744.12/262.92	   active(U35(tt, x0))
744.12/262.92	   active(U36(tt))
744.12/262.92	   active(U41(tt, x0))
744.12/262.92	   active(U42(tt))
744.12/262.92	   active(U51(tt))
744.12/262.92	   active(U61(tt, x0))
744.12/262.92	   active(U62(tt))
744.12/262.92	   active(U71(tt, x0))
744.12/262.92	   active(U72(tt, x0))
744.12/262.92	   active(U81(tt, x0, x1))
744.12/262.92	   active(U82(tt, x0, x1))
744.12/262.92	   active(U83(tt, x0, x1))
744.12/262.92	   active(U84(tt, x0, x1))
744.12/262.92	   active(U91(tt, x0))
744.12/262.92	   active(U92(tt))
744.12/262.92	   active(isNat(0))
744.12/262.92	   active(isNat(plus(x0, x1)))
744.12/262.92	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.93	   U84(mark(x0), x1, x2)
744.12/262.93	   U84(x0, mark(x1), x2)
744.12/262.93	   U84(x0, x1, mark(x2))
744.12/262.93	   U84(active(x0), x1, x2)
744.12/262.93	   U84(x0, active(x1), x2)
744.12/262.93	   U84(x0, x1, active(x2))
744.12/262.93	   s(mark(x0))
744.12/262.93	   s(active(x0))
744.12/262.93	   U91(mark(x0), x1)
744.12/262.93	   U91(x0, mark(x1))
744.12/262.93	   U91(active(x0), x1)
744.12/262.93	   U91(x0, active(x1))
744.12/262.93	   U92(mark(x0))
744.12/262.93	   U92(active(x0))
744.12/262.93	
744.12/262.93	We have to consider all minimal (P,Q,R)-chains.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(204) QReductionProof (EQUIVALENT)
744.12/262.93	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.93	
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.93	   U84(mark(x0), x1, x2)
744.12/262.93	   U84(x0, mark(x1), x2)
744.12/262.93	   U84(x0, x1, mark(x2))
744.12/262.93	   U84(active(x0), x1, x2)
744.12/262.93	   U84(x0, active(x1), x2)
744.12/262.93	   U84(x0, x1, active(x2))
744.12/262.93	   s(mark(x0))
744.12/262.93	   s(active(x0))
744.12/262.93	   U91(mark(x0), x1)
744.12/262.93	   U91(x0, mark(x1))
744.12/262.93	   U91(active(x0), x1)
744.12/262.93	   U91(x0, active(x1))
744.12/262.93	   U92(mark(x0))
744.12/262.93	   U92(active(x0))
744.12/262.93	
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(205)
744.12/262.93	Obligation:
744.12/262.93	Q DP problem:
744.12/262.93	The TRS P consists of the following rules:
744.12/262.93	
744.12/262.93	   U11^1(X1, mark(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.93	   U11^1(mark(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.93	   U11^1(X1, X2, mark(X3)) -> U11^1(X1, X2, X3)
744.12/262.93	   U11^1(active(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.93	   U11^1(X1, active(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.93	   U11^1(X1, X2, active(X3)) -> U11^1(X1, X2, X3)
744.12/262.93	
744.12/262.93	R is empty.
744.12/262.93	The set Q consists of the following terms:
744.12/262.93	
744.12/262.93	   active(U101(tt, x0, x1))
744.12/262.93	   active(U102(tt, x0, x1))
744.12/262.93	   active(U103(tt, x0, x1))
744.12/262.93	   active(U104(tt, x0, x1))
744.12/262.93	   active(U11(tt, x0, x1))
744.12/262.93	   active(U12(tt, x0, x1))
744.12/262.93	   active(U13(tt, x0, x1))
744.12/262.93	   active(U14(tt, x0, x1))
744.12/262.93	   active(U15(tt, x0))
744.12/262.93	   active(U16(tt))
744.12/262.93	   active(U21(tt, x0))
744.12/262.93	   active(U22(tt, x0))
744.12/262.93	   active(U23(tt))
744.12/262.93	   active(U31(tt, x0, x1))
744.12/262.93	   active(U32(tt, x0, x1))
744.12/262.93	   active(U33(tt, x0, x1))
744.12/262.93	   active(U34(tt, x0, x1))
744.12/262.93	   active(U35(tt, x0))
744.12/262.93	   active(U36(tt))
744.12/262.93	   active(U41(tt, x0))
744.12/262.93	   active(U42(tt))
744.12/262.93	   active(U51(tt))
744.12/262.93	   active(U61(tt, x0))
744.12/262.93	   active(U62(tt))
744.12/262.93	   active(U71(tt, x0))
744.12/262.93	   active(U72(tt, x0))
744.12/262.93	   active(U81(tt, x0, x1))
744.12/262.93	   active(U82(tt, x0, x1))
744.12/262.93	   active(U83(tt, x0, x1))
744.12/262.93	   active(U84(tt, x0, x1))
744.12/262.93	   active(U91(tt, x0))
744.12/262.93	   active(U92(tt))
744.12/262.93	   active(isNat(0))
744.12/262.93	   active(isNat(plus(x0, x1)))
744.12/262.93	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	
744.12/262.93	We have to consider all minimal (P,Q,R)-chains.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(206) QDPSizeChangeProof (EQUIVALENT)
744.12/262.93	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. 
744.12/262.93	
744.12/262.93	From the DPs we obtained the following set of size-change graphs:
744.12/262.93	*U11^1(X1, mark(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.93	
744.12/262.93	
744.12/262.93	*U11^1(mark(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.93	
744.12/262.93	
744.12/262.93	*U11^1(X1, X2, mark(X3)) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.93	
744.12/262.93	
744.12/262.93	*U11^1(active(X1), X2, X3) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.93	
744.12/262.93	
744.12/262.93	*U11^1(X1, active(X2), X3) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.93	
744.12/262.93	
744.12/262.93	*U11^1(X1, X2, active(X3)) -> U11^1(X1, X2, X3)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.93	
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(207)
744.12/262.93	YES
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(208)
744.12/262.93	Obligation:
744.12/262.93	Q DP problem:
744.12/262.93	The TRS P consists of the following rules:
744.12/262.93	
744.12/262.93	   X(X1, mark(X2)) -> X(X1, X2)
744.12/262.93	   X(mark(X1), X2) -> X(X1, X2)
744.12/262.93	   X(active(X1), X2) -> X(X1, X2)
744.12/262.93	   X(X1, active(X2)) -> X(X1, X2)
744.12/262.93	
744.12/262.93	The TRS R consists of the following rules:
744.12/262.93	
744.12/262.93	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.93	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.93	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.93	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.93	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.93	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.93	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.93	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.93	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.93	   active(U16(tt)) -> mark(tt)
744.12/262.93	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.93	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.93	   active(U23(tt)) -> mark(tt)
744.12/262.93	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.93	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.93	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.93	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.93	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.93	   active(U36(tt)) -> mark(tt)
744.12/262.93	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.93	   active(U42(tt)) -> mark(tt)
744.12/262.93	   active(U51(tt)) -> mark(tt)
744.12/262.93	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.93	   active(U62(tt)) -> mark(tt)
744.12/262.93	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.93	   active(U72(tt, N)) -> mark(N)
744.12/262.93	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.93	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.93	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.93	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.93	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.93	   active(U92(tt)) -> mark(0)
744.12/262.93	   active(isNat(0)) -> mark(tt)
744.12/262.93	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.93	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.93	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.93	   active(isNatKind(0)) -> mark(tt)
744.12/262.93	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.93	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.93	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.93	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.93	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.93	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.93	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.93	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.93	   mark(tt) -> active(tt)
744.12/262.93	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.93	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.93	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.93	   mark(isNat(X)) -> active(isNat(X))
744.12/262.93	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.93	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.93	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.93	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.93	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.93	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.93	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.93	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.93	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.93	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.93	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.93	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.93	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.93	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.93	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.93	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.93	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.93	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.93	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.93	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.93	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.93	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.93	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.93	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.93	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.93	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.93	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.93	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.93	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.93	   mark(s(X)) -> active(s(mark(X)))
744.12/262.93	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.93	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.93	   mark(0) -> active(0)
744.12/262.93	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.93	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.93	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.93	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.93	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.93	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.93	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.93	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.93	   isNat(mark(X)) -> isNat(X)
744.12/262.93	   isNat(active(X)) -> isNat(X)
744.12/262.93	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.93	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.93	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.93	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.93	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.93	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.93	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.93	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.93	   x(active(X1), X2) -> x(X1, X2)
744.12/262.93	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.93	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.93	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.93	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.93	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.93	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.93	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.93	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.93	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.93	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.93	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.93	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.93	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.93	   U16(mark(X)) -> U16(X)
744.12/262.93	   U16(active(X)) -> U16(X)
744.12/262.93	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.93	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.93	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.93	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.93	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.93	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.93	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.93	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.93	   U23(mark(X)) -> U23(X)
744.12/262.93	   U23(active(X)) -> U23(X)
744.12/262.93	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.93	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.93	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.93	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.93	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.93	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.93	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.93	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.93	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.93	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.93	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.93	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.93	   U36(mark(X)) -> U36(X)
744.12/262.93	   U36(active(X)) -> U36(X)
744.12/262.93	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.93	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.93	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.93	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.93	   U42(mark(X)) -> U42(X)
744.12/262.93	   U42(active(X)) -> U42(X)
744.12/262.93	   U51(mark(X)) -> U51(X)
744.12/262.93	   U51(active(X)) -> U51(X)
744.12/262.93	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.93	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.93	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.93	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.93	   U62(mark(X)) -> U62(X)
744.12/262.93	   U62(active(X)) -> U62(X)
744.12/262.93	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.93	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.93	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.93	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.93	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.93	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.93	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.93	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.93	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.93	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.93	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.93	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.93	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.93	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.93	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.93	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.93	   s(mark(X)) -> s(X)
744.12/262.93	   s(active(X)) -> s(X)
744.12/262.93	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.93	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.93	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.93	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.93	   U92(mark(X)) -> U92(X)
744.12/262.93	   U92(active(X)) -> U92(X)
744.12/262.93	
744.12/262.93	The set Q consists of the following terms:
744.12/262.93	
744.12/262.93	   active(U101(tt, x0, x1))
744.12/262.93	   active(U102(tt, x0, x1))
744.12/262.93	   active(U103(tt, x0, x1))
744.12/262.93	   active(U104(tt, x0, x1))
744.12/262.93	   active(U11(tt, x0, x1))
744.12/262.93	   active(U12(tt, x0, x1))
744.12/262.93	   active(U13(tt, x0, x1))
744.12/262.93	   active(U14(tt, x0, x1))
744.12/262.93	   active(U15(tt, x0))
744.12/262.93	   active(U16(tt))
744.12/262.93	   active(U21(tt, x0))
744.12/262.93	   active(U22(tt, x0))
744.12/262.93	   active(U23(tt))
744.12/262.93	   active(U31(tt, x0, x1))
744.12/262.93	   active(U32(tt, x0, x1))
744.12/262.93	   active(U33(tt, x0, x1))
744.12/262.93	   active(U34(tt, x0, x1))
744.12/262.93	   active(U35(tt, x0))
744.12/262.93	   active(U36(tt))
744.12/262.93	   active(U41(tt, x0))
744.12/262.93	   active(U42(tt))
744.12/262.93	   active(U51(tt))
744.12/262.93	   active(U61(tt, x0))
744.12/262.93	   active(U62(tt))
744.12/262.93	   active(U71(tt, x0))
744.12/262.93	   active(U72(tt, x0))
744.12/262.93	   active(U81(tt, x0, x1))
744.12/262.93	   active(U82(tt, x0, x1))
744.12/262.93	   active(U83(tt, x0, x1))
744.12/262.93	   active(U84(tt, x0, x1))
744.12/262.93	   active(U91(tt, x0))
744.12/262.93	   active(U92(tt))
744.12/262.93	   active(isNat(0))
744.12/262.93	   active(isNat(plus(x0, x1)))
744.12/262.93	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.93	   U84(mark(x0), x1, x2)
744.12/262.93	   U84(x0, mark(x1), x2)
744.12/262.93	   U84(x0, x1, mark(x2))
744.12/262.93	   U84(active(x0), x1, x2)
744.12/262.93	   U84(x0, active(x1), x2)
744.12/262.93	   U84(x0, x1, active(x2))
744.12/262.93	   s(mark(x0))
744.12/262.93	   s(active(x0))
744.12/262.93	   U91(mark(x0), x1)
744.12/262.93	   U91(x0, mark(x1))
744.12/262.93	   U91(active(x0), x1)
744.12/262.93	   U91(x0, active(x1))
744.12/262.93	   U92(mark(x0))
744.12/262.93	   U92(active(x0))
744.12/262.93	
744.12/262.93	We have to consider all minimal (P,Q,R)-chains.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(209) UsableRulesProof (EQUIVALENT)
744.12/262.93	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.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(210)
744.12/262.93	Obligation:
744.12/262.93	Q DP problem:
744.12/262.93	The TRS P consists of the following rules:
744.12/262.93	
744.12/262.93	   X(X1, mark(X2)) -> X(X1, X2)
744.12/262.93	   X(mark(X1), X2) -> X(X1, X2)
744.12/262.93	   X(active(X1), X2) -> X(X1, X2)
744.12/262.93	   X(X1, active(X2)) -> X(X1, X2)
744.12/262.93	
744.12/262.93	R is empty.
744.12/262.93	The set Q consists of the following terms:
744.12/262.93	
744.12/262.93	   active(U101(tt, x0, x1))
744.12/262.93	   active(U102(tt, x0, x1))
744.12/262.93	   active(U103(tt, x0, x1))
744.12/262.93	   active(U104(tt, x0, x1))
744.12/262.93	   active(U11(tt, x0, x1))
744.12/262.93	   active(U12(tt, x0, x1))
744.12/262.93	   active(U13(tt, x0, x1))
744.12/262.93	   active(U14(tt, x0, x1))
744.12/262.93	   active(U15(tt, x0))
744.12/262.93	   active(U16(tt))
744.12/262.93	   active(U21(tt, x0))
744.12/262.93	   active(U22(tt, x0))
744.12/262.93	   active(U23(tt))
744.12/262.93	   active(U31(tt, x0, x1))
744.12/262.93	   active(U32(tt, x0, x1))
744.12/262.93	   active(U33(tt, x0, x1))
744.12/262.93	   active(U34(tt, x0, x1))
744.12/262.93	   active(U35(tt, x0))
744.12/262.93	   active(U36(tt))
744.12/262.93	   active(U41(tt, x0))
744.12/262.93	   active(U42(tt))
744.12/262.93	   active(U51(tt))
744.12/262.93	   active(U61(tt, x0))
744.12/262.93	   active(U62(tt))
744.12/262.93	   active(U71(tt, x0))
744.12/262.93	   active(U72(tt, x0))
744.12/262.93	   active(U81(tt, x0, x1))
744.12/262.93	   active(U82(tt, x0, x1))
744.12/262.93	   active(U83(tt, x0, x1))
744.12/262.93	   active(U84(tt, x0, x1))
744.12/262.93	   active(U91(tt, x0))
744.12/262.93	   active(U92(tt))
744.12/262.93	   active(isNat(0))
744.12/262.93	   active(isNat(plus(x0, x1)))
744.12/262.93	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.93	   U84(mark(x0), x1, x2)
744.12/262.93	   U84(x0, mark(x1), x2)
744.12/262.93	   U84(x0, x1, mark(x2))
744.12/262.93	   U84(active(x0), x1, x2)
744.12/262.93	   U84(x0, active(x1), x2)
744.12/262.93	   U84(x0, x1, active(x2))
744.12/262.93	   s(mark(x0))
744.12/262.93	   s(active(x0))
744.12/262.93	   U91(mark(x0), x1)
744.12/262.93	   U91(x0, mark(x1))
744.12/262.93	   U91(active(x0), x1)
744.12/262.93	   U91(x0, active(x1))
744.12/262.93	   U92(mark(x0))
744.12/262.93	   U92(active(x0))
744.12/262.93	
744.12/262.93	We have to consider all minimal (P,Q,R)-chains.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(211) QReductionProof (EQUIVALENT)
744.12/262.93	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.93	
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.93	   U84(mark(x0), x1, x2)
744.12/262.93	   U84(x0, mark(x1), x2)
744.12/262.93	   U84(x0, x1, mark(x2))
744.12/262.93	   U84(active(x0), x1, x2)
744.12/262.93	   U84(x0, active(x1), x2)
744.12/262.93	   U84(x0, x1, active(x2))
744.12/262.93	   s(mark(x0))
744.12/262.93	   s(active(x0))
744.12/262.93	   U91(mark(x0), x1)
744.12/262.93	   U91(x0, mark(x1))
744.12/262.93	   U91(active(x0), x1)
744.12/262.93	   U91(x0, active(x1))
744.12/262.93	   U92(mark(x0))
744.12/262.93	   U92(active(x0))
744.12/262.93	
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(212)
744.12/262.93	Obligation:
744.12/262.93	Q DP problem:
744.12/262.93	The TRS P consists of the following rules:
744.12/262.93	
744.12/262.93	   X(X1, mark(X2)) -> X(X1, X2)
744.12/262.93	   X(mark(X1), X2) -> X(X1, X2)
744.12/262.93	   X(active(X1), X2) -> X(X1, X2)
744.12/262.93	   X(X1, active(X2)) -> X(X1, X2)
744.12/262.93	
744.12/262.93	R is empty.
744.12/262.93	The set Q consists of the following terms:
744.12/262.93	
744.12/262.93	   active(U101(tt, x0, x1))
744.12/262.93	   active(U102(tt, x0, x1))
744.12/262.93	   active(U103(tt, x0, x1))
744.12/262.93	   active(U104(tt, x0, x1))
744.12/262.93	   active(U11(tt, x0, x1))
744.12/262.93	   active(U12(tt, x0, x1))
744.12/262.93	   active(U13(tt, x0, x1))
744.12/262.93	   active(U14(tt, x0, x1))
744.12/262.93	   active(U15(tt, x0))
744.12/262.93	   active(U16(tt))
744.12/262.93	   active(U21(tt, x0))
744.12/262.93	   active(U22(tt, x0))
744.12/262.93	   active(U23(tt))
744.12/262.93	   active(U31(tt, x0, x1))
744.12/262.93	   active(U32(tt, x0, x1))
744.12/262.93	   active(U33(tt, x0, x1))
744.12/262.93	   active(U34(tt, x0, x1))
744.12/262.93	   active(U35(tt, x0))
744.12/262.93	   active(U36(tt))
744.12/262.93	   active(U41(tt, x0))
744.12/262.93	   active(U42(tt))
744.12/262.93	   active(U51(tt))
744.12/262.93	   active(U61(tt, x0))
744.12/262.93	   active(U62(tt))
744.12/262.93	   active(U71(tt, x0))
744.12/262.93	   active(U72(tt, x0))
744.12/262.93	   active(U81(tt, x0, x1))
744.12/262.93	   active(U82(tt, x0, x1))
744.12/262.93	   active(U83(tt, x0, x1))
744.12/262.93	   active(U84(tt, x0, x1))
744.12/262.93	   active(U91(tt, x0))
744.12/262.93	   active(U92(tt))
744.12/262.93	   active(isNat(0))
744.12/262.93	   active(isNat(plus(x0, x1)))
744.12/262.93	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	
744.12/262.93	We have to consider all minimal (P,Q,R)-chains.
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(213) QDPSizeChangeProof (EQUIVALENT)
744.12/262.93	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. 
744.12/262.93	
744.12/262.93	From the DPs we obtained the following set of size-change graphs:
744.12/262.93	*X(X1, mark(X2)) -> X(X1, X2)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.93	
744.12/262.93	
744.12/262.93	*X(mark(X1), X2) -> X(X1, X2)
744.12/262.93	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.93	
744.12/262.93	
744.12/262.93	*X(active(X1), X2) -> X(X1, X2)
744.12/262.93	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.93	
744.12/262.93	
744.12/262.93	*X(X1, active(X2)) -> X(X1, X2)
744.12/262.93	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.93	
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(214)
744.12/262.93	YES
744.12/262.93	
744.12/262.93	----------------------------------------
744.12/262.93	
744.12/262.93	(215)
744.12/262.93	Obligation:
744.12/262.93	Q DP problem:
744.12/262.93	The TRS P consists of the following rules:
744.12/262.93	
744.12/262.93	   PLUS(X1, mark(X2)) -> PLUS(X1, X2)
744.12/262.93	   PLUS(mark(X1), X2) -> PLUS(X1, X2)
744.12/262.93	   PLUS(active(X1), X2) -> PLUS(X1, X2)
744.12/262.93	   PLUS(X1, active(X2)) -> PLUS(X1, X2)
744.12/262.93	
744.12/262.93	The TRS R consists of the following rules:
744.12/262.93	
744.12/262.93	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.93	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.93	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.93	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.93	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.93	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.93	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.93	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.93	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.93	   active(U16(tt)) -> mark(tt)
744.12/262.93	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.93	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.93	   active(U23(tt)) -> mark(tt)
744.12/262.93	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.93	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.93	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.93	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.93	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.93	   active(U36(tt)) -> mark(tt)
744.12/262.93	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.93	   active(U42(tt)) -> mark(tt)
744.12/262.93	   active(U51(tt)) -> mark(tt)
744.12/262.93	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.93	   active(U62(tt)) -> mark(tt)
744.12/262.93	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.93	   active(U72(tt, N)) -> mark(N)
744.12/262.93	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.93	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.93	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.93	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.93	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.93	   active(U92(tt)) -> mark(0)
744.12/262.93	   active(isNat(0)) -> mark(tt)
744.12/262.93	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.93	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.93	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.93	   active(isNatKind(0)) -> mark(tt)
744.12/262.93	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.93	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.93	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.93	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.93	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.93	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.93	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.93	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.93	   mark(tt) -> active(tt)
744.12/262.93	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.93	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.93	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.93	   mark(isNat(X)) -> active(isNat(X))
744.12/262.93	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.93	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.93	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.93	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.93	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.93	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.93	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.93	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.93	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.93	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.93	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.93	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.93	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.93	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.93	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.93	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.93	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.93	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.93	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.93	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.93	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.93	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.93	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.93	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.93	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.93	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.93	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.93	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.93	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.93	   mark(s(X)) -> active(s(mark(X)))
744.12/262.93	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.93	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.93	   mark(0) -> active(0)
744.12/262.93	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.93	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.93	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.93	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.93	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.93	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.93	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.93	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.93	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.93	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.93	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.93	   isNat(mark(X)) -> isNat(X)
744.12/262.93	   isNat(active(X)) -> isNat(X)
744.12/262.93	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.93	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.93	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.93	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.93	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.93	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.93	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.93	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.93	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.93	   x(active(X1), X2) -> x(X1, X2)
744.12/262.93	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.93	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.93	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.93	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.93	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.93	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.93	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.93	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.93	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.93	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.93	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.93	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.93	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.93	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.93	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.93	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.93	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.93	   U16(mark(X)) -> U16(X)
744.12/262.93	   U16(active(X)) -> U16(X)
744.12/262.93	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.93	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.93	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.93	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.93	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.93	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.93	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.93	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.93	   U23(mark(X)) -> U23(X)
744.12/262.93	   U23(active(X)) -> U23(X)
744.12/262.93	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.93	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.93	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.93	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.93	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.93	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.93	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.93	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.93	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.93	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.93	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.93	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.93	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.93	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.93	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.93	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.93	   U36(mark(X)) -> U36(X)
744.12/262.93	   U36(active(X)) -> U36(X)
744.12/262.93	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.93	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.93	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.93	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.93	   U42(mark(X)) -> U42(X)
744.12/262.93	   U42(active(X)) -> U42(X)
744.12/262.93	   U51(mark(X)) -> U51(X)
744.12/262.93	   U51(active(X)) -> U51(X)
744.12/262.93	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.93	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.93	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.93	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.93	   U62(mark(X)) -> U62(X)
744.12/262.93	   U62(active(X)) -> U62(X)
744.12/262.93	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.93	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.93	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.93	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.93	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.93	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.93	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.93	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.93	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.93	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.93	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.93	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.93	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.93	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.93	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.93	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.93	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.93	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.93	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.93	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.93	   s(mark(X)) -> s(X)
744.12/262.93	   s(active(X)) -> s(X)
744.12/262.93	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.93	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.93	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.93	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.93	   U92(mark(X)) -> U92(X)
744.12/262.93	   U92(active(X)) -> U92(X)
744.12/262.93	
744.12/262.93	The set Q consists of the following terms:
744.12/262.93	
744.12/262.93	   active(U101(tt, x0, x1))
744.12/262.93	   active(U102(tt, x0, x1))
744.12/262.93	   active(U103(tt, x0, x1))
744.12/262.93	   active(U104(tt, x0, x1))
744.12/262.93	   active(U11(tt, x0, x1))
744.12/262.93	   active(U12(tt, x0, x1))
744.12/262.93	   active(U13(tt, x0, x1))
744.12/262.93	   active(U14(tt, x0, x1))
744.12/262.93	   active(U15(tt, x0))
744.12/262.93	   active(U16(tt))
744.12/262.93	   active(U21(tt, x0))
744.12/262.93	   active(U22(tt, x0))
744.12/262.93	   active(U23(tt))
744.12/262.93	   active(U31(tt, x0, x1))
744.12/262.93	   active(U32(tt, x0, x1))
744.12/262.93	   active(U33(tt, x0, x1))
744.12/262.93	   active(U34(tt, x0, x1))
744.12/262.93	   active(U35(tt, x0))
744.12/262.93	   active(U36(tt))
744.12/262.93	   active(U41(tt, x0))
744.12/262.93	   active(U42(tt))
744.12/262.93	   active(U51(tt))
744.12/262.93	   active(U61(tt, x0))
744.12/262.93	   active(U62(tt))
744.12/262.93	   active(U71(tt, x0))
744.12/262.93	   active(U72(tt, x0))
744.12/262.93	   active(U81(tt, x0, x1))
744.12/262.93	   active(U82(tt, x0, x1))
744.12/262.93	   active(U83(tt, x0, x1))
744.12/262.93	   active(U84(tt, x0, x1))
744.12/262.93	   active(U91(tt, x0))
744.12/262.93	   active(U92(tt))
744.12/262.93	   active(isNat(0))
744.12/262.93	   active(isNat(plus(x0, x1)))
744.12/262.93	   active(isNat(s(x0)))
744.12/262.93	   active(isNat(x(x0, x1)))
744.12/262.93	   active(isNatKind(0))
744.12/262.93	   active(isNatKind(plus(x0, x1)))
744.12/262.93	   active(isNatKind(s(x0)))
744.12/262.93	   active(isNatKind(x(x0, x1)))
744.12/262.93	   active(plus(x0, 0))
744.12/262.93	   active(plus(x0, s(x1)))
744.12/262.93	   active(x(x0, 0))
744.12/262.93	   active(x(x0, s(x1)))
744.12/262.93	   mark(U101(x0, x1, x2))
744.12/262.93	   mark(tt)
744.12/262.93	   mark(U102(x0, x1, x2))
744.12/262.93	   mark(isNatKind(x0))
744.12/262.93	   mark(U103(x0, x1, x2))
744.12/262.93	   mark(isNat(x0))
744.12/262.93	   mark(U104(x0, x1, x2))
744.12/262.93	   mark(plus(x0, x1))
744.12/262.93	   mark(x(x0, x1))
744.12/262.93	   mark(U11(x0, x1, x2))
744.12/262.93	   mark(U12(x0, x1, x2))
744.12/262.93	   mark(U13(x0, x1, x2))
744.12/262.93	   mark(U14(x0, x1, x2))
744.12/262.93	   mark(U15(x0, x1))
744.12/262.93	   mark(U16(x0))
744.12/262.93	   mark(U21(x0, x1))
744.12/262.93	   mark(U22(x0, x1))
744.12/262.93	   mark(U23(x0))
744.12/262.93	   mark(U31(x0, x1, x2))
744.12/262.93	   mark(U32(x0, x1, x2))
744.12/262.93	   mark(U33(x0, x1, x2))
744.12/262.93	   mark(U34(x0, x1, x2))
744.12/262.93	   mark(U35(x0, x1))
744.12/262.93	   mark(U36(x0))
744.12/262.93	   mark(U41(x0, x1))
744.12/262.93	   mark(U42(x0))
744.12/262.93	   mark(U51(x0))
744.12/262.93	   mark(U61(x0, x1))
744.12/262.93	   mark(U62(x0))
744.12/262.93	   mark(U71(x0, x1))
744.12/262.93	   mark(U72(x0, x1))
744.12/262.93	   mark(U81(x0, x1, x2))
744.12/262.93	   mark(U82(x0, x1, x2))
744.12/262.93	   mark(U83(x0, x1, x2))
744.12/262.93	   mark(U84(x0, x1, x2))
744.12/262.93	   mark(s(x0))
744.12/262.93	   mark(U91(x0, x1))
744.12/262.93	   mark(U92(x0))
744.12/262.93	   mark(0)
744.12/262.93	   U101(mark(x0), x1, x2)
744.12/262.93	   U101(x0, mark(x1), x2)
744.12/262.93	   U101(x0, x1, mark(x2))
744.12/262.93	   U101(active(x0), x1, x2)
744.12/262.93	   U101(x0, active(x1), x2)
744.12/262.93	   U101(x0, x1, active(x2))
744.12/262.93	   U102(mark(x0), x1, x2)
744.12/262.93	   U102(x0, mark(x1), x2)
744.12/262.93	   U102(x0, x1, mark(x2))
744.12/262.93	   U102(active(x0), x1, x2)
744.12/262.93	   U102(x0, active(x1), x2)
744.12/262.93	   U102(x0, x1, active(x2))
744.12/262.93	   isNatKind(mark(x0))
744.12/262.93	   isNatKind(active(x0))
744.12/262.93	   U103(mark(x0), x1, x2)
744.12/262.93	   U103(x0, mark(x1), x2)
744.12/262.93	   U103(x0, x1, mark(x2))
744.12/262.93	   U103(active(x0), x1, x2)
744.12/262.93	   U103(x0, active(x1), x2)
744.12/262.93	   U103(x0, x1, active(x2))
744.12/262.93	   isNat(mark(x0))
744.12/262.93	   isNat(active(x0))
744.12/262.93	   U104(mark(x0), x1, x2)
744.12/262.93	   U104(x0, mark(x1), x2)
744.12/262.93	   U104(x0, x1, mark(x2))
744.12/262.93	   U104(active(x0), x1, x2)
744.12/262.93	   U104(x0, active(x1), x2)
744.12/262.93	   U104(x0, x1, active(x2))
744.12/262.93	   plus(mark(x0), x1)
744.12/262.93	   plus(x0, mark(x1))
744.12/262.93	   plus(active(x0), x1)
744.12/262.93	   plus(x0, active(x1))
744.12/262.93	   x(mark(x0), x1)
744.12/262.93	   x(x0, mark(x1))
744.12/262.93	   x(active(x0), x1)
744.12/262.93	   x(x0, active(x1))
744.12/262.93	   U11(mark(x0), x1, x2)
744.12/262.93	   U11(x0, mark(x1), x2)
744.12/262.93	   U11(x0, x1, mark(x2))
744.12/262.93	   U11(active(x0), x1, x2)
744.12/262.93	   U11(x0, active(x1), x2)
744.12/262.93	   U11(x0, x1, active(x2))
744.12/262.93	   U12(mark(x0), x1, x2)
744.12/262.93	   U12(x0, mark(x1), x2)
744.12/262.93	   U12(x0, x1, mark(x2))
744.12/262.93	   U12(active(x0), x1, x2)
744.12/262.93	   U12(x0, active(x1), x2)
744.12/262.93	   U12(x0, x1, active(x2))
744.12/262.93	   U13(mark(x0), x1, x2)
744.12/262.93	   U13(x0, mark(x1), x2)
744.12/262.93	   U13(x0, x1, mark(x2))
744.12/262.93	   U13(active(x0), x1, x2)
744.12/262.93	   U13(x0, active(x1), x2)
744.12/262.93	   U13(x0, x1, active(x2))
744.12/262.93	   U14(mark(x0), x1, x2)
744.12/262.93	   U14(x0, mark(x1), x2)
744.12/262.93	   U14(x0, x1, mark(x2))
744.12/262.93	   U14(active(x0), x1, x2)
744.12/262.93	   U14(x0, active(x1), x2)
744.12/262.93	   U14(x0, x1, active(x2))
744.12/262.93	   U15(mark(x0), x1)
744.12/262.93	   U15(x0, mark(x1))
744.12/262.93	   U15(active(x0), x1)
744.12/262.93	   U15(x0, active(x1))
744.12/262.93	   U16(mark(x0))
744.12/262.93	   U16(active(x0))
744.12/262.93	   U21(mark(x0), x1)
744.12/262.93	   U21(x0, mark(x1))
744.12/262.93	   U21(active(x0), x1)
744.12/262.93	   U21(x0, active(x1))
744.12/262.93	   U22(mark(x0), x1)
744.12/262.93	   U22(x0, mark(x1))
744.12/262.93	   U22(active(x0), x1)
744.12/262.93	   U22(x0, active(x1))
744.12/262.93	   U23(mark(x0))
744.12/262.93	   U23(active(x0))
744.12/262.93	   U31(mark(x0), x1, x2)
744.12/262.93	   U31(x0, mark(x1), x2)
744.12/262.93	   U31(x0, x1, mark(x2))
744.12/262.93	   U31(active(x0), x1, x2)
744.12/262.93	   U31(x0, active(x1), x2)
744.12/262.93	   U31(x0, x1, active(x2))
744.12/262.93	   U32(mark(x0), x1, x2)
744.12/262.93	   U32(x0, mark(x1), x2)
744.12/262.93	   U32(x0, x1, mark(x2))
744.12/262.93	   U32(active(x0), x1, x2)
744.12/262.93	   U32(x0, active(x1), x2)
744.12/262.93	   U32(x0, x1, active(x2))
744.12/262.93	   U33(mark(x0), x1, x2)
744.12/262.93	   U33(x0, mark(x1), x2)
744.12/262.93	   U33(x0, x1, mark(x2))
744.12/262.93	   U33(active(x0), x1, x2)
744.12/262.93	   U33(x0, active(x1), x2)
744.12/262.93	   U33(x0, x1, active(x2))
744.12/262.93	   U34(mark(x0), x1, x2)
744.12/262.93	   U34(x0, mark(x1), x2)
744.12/262.93	   U34(x0, x1, mark(x2))
744.12/262.93	   U34(active(x0), x1, x2)
744.12/262.93	   U34(x0, active(x1), x2)
744.12/262.93	   U34(x0, x1, active(x2))
744.12/262.93	   U35(mark(x0), x1)
744.12/262.93	   U35(x0, mark(x1))
744.12/262.93	   U35(active(x0), x1)
744.12/262.93	   U35(x0, active(x1))
744.12/262.93	   U36(mark(x0))
744.12/262.93	   U36(active(x0))
744.12/262.93	   U41(mark(x0), x1)
744.12/262.93	   U41(x0, mark(x1))
744.12/262.93	   U41(active(x0), x1)
744.12/262.93	   U41(x0, active(x1))
744.12/262.93	   U42(mark(x0))
744.12/262.93	   U42(active(x0))
744.12/262.93	   U51(mark(x0))
744.12/262.93	   U51(active(x0))
744.12/262.93	   U61(mark(x0), x1)
744.12/262.93	   U61(x0, mark(x1))
744.12/262.93	   U61(active(x0), x1)
744.12/262.93	   U61(x0, active(x1))
744.12/262.93	   U62(mark(x0))
744.12/262.93	   U62(active(x0))
744.12/262.93	   U71(mark(x0), x1)
744.12/262.93	   U71(x0, mark(x1))
744.12/262.93	   U71(active(x0), x1)
744.12/262.93	   U71(x0, active(x1))
744.12/262.93	   U72(mark(x0), x1)
744.12/262.93	   U72(x0, mark(x1))
744.12/262.93	   U72(active(x0), x1)
744.12/262.93	   U72(x0, active(x1))
744.12/262.93	   U81(mark(x0), x1, x2)
744.12/262.93	   U81(x0, mark(x1), x2)
744.12/262.93	   U81(x0, x1, mark(x2))
744.12/262.93	   U81(active(x0), x1, x2)
744.12/262.93	   U81(x0, active(x1), x2)
744.12/262.93	   U81(x0, x1, active(x2))
744.12/262.93	   U82(mark(x0), x1, x2)
744.12/262.93	   U82(x0, mark(x1), x2)
744.12/262.93	   U82(x0, x1, mark(x2))
744.12/262.93	   U82(active(x0), x1, x2)
744.12/262.93	   U82(x0, active(x1), x2)
744.12/262.93	   U82(x0, x1, active(x2))
744.12/262.93	   U83(mark(x0), x1, x2)
744.12/262.93	   U83(x0, mark(x1), x2)
744.12/262.93	   U83(x0, x1, mark(x2))
744.12/262.93	   U83(active(x0), x1, x2)
744.12/262.93	   U83(x0, active(x1), x2)
744.12/262.93	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(216) UsableRulesProof (EQUIVALENT)
744.12/262.94	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.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(217)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   PLUS(X1, mark(X2)) -> PLUS(X1, X2)
744.12/262.94	   PLUS(mark(X1), X2) -> PLUS(X1, X2)
744.12/262.94	   PLUS(active(X1), X2) -> PLUS(X1, X2)
744.12/262.94	   PLUS(X1, active(X2)) -> PLUS(X1, X2)
744.12/262.94	
744.12/262.94	R is empty.
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.94	   U14(x0, x1, mark(x2))
744.12/262.94	   U14(active(x0), x1, x2)
744.12/262.94	   U14(x0, active(x1), x2)
744.12/262.94	   U14(x0, x1, active(x2))
744.12/262.94	   U15(mark(x0), x1)
744.12/262.94	   U15(x0, mark(x1))
744.12/262.94	   U15(active(x0), x1)
744.12/262.94	   U15(x0, active(x1))
744.12/262.94	   U16(mark(x0))
744.12/262.94	   U16(active(x0))
744.12/262.94	   U21(mark(x0), x1)
744.12/262.94	   U21(x0, mark(x1))
744.12/262.94	   U21(active(x0), x1)
744.12/262.94	   U21(x0, active(x1))
744.12/262.94	   U22(mark(x0), x1)
744.12/262.94	   U22(x0, mark(x1))
744.12/262.94	   U22(active(x0), x1)
744.12/262.94	   U22(x0, active(x1))
744.12/262.94	   U23(mark(x0))
744.12/262.94	   U23(active(x0))
744.12/262.94	   U31(mark(x0), x1, x2)
744.12/262.94	   U31(x0, mark(x1), x2)
744.12/262.94	   U31(x0, x1, mark(x2))
744.12/262.94	   U31(active(x0), x1, x2)
744.12/262.94	   U31(x0, active(x1), x2)
744.12/262.94	   U31(x0, x1, active(x2))
744.12/262.94	   U32(mark(x0), x1, x2)
744.12/262.94	   U32(x0, mark(x1), x2)
744.12/262.94	   U32(x0, x1, mark(x2))
744.12/262.94	   U32(active(x0), x1, x2)
744.12/262.94	   U32(x0, active(x1), x2)
744.12/262.94	   U32(x0, x1, active(x2))
744.12/262.94	   U33(mark(x0), x1, x2)
744.12/262.94	   U33(x0, mark(x1), x2)
744.12/262.94	   U33(x0, x1, mark(x2))
744.12/262.94	   U33(active(x0), x1, x2)
744.12/262.94	   U33(x0, active(x1), x2)
744.12/262.94	   U33(x0, x1, active(x2))
744.12/262.94	   U34(mark(x0), x1, x2)
744.12/262.94	   U34(x0, mark(x1), x2)
744.12/262.94	   U34(x0, x1, mark(x2))
744.12/262.94	   U34(active(x0), x1, x2)
744.12/262.94	   U34(x0, active(x1), x2)
744.12/262.94	   U34(x0, x1, active(x2))
744.12/262.94	   U35(mark(x0), x1)
744.12/262.94	   U35(x0, mark(x1))
744.12/262.94	   U35(active(x0), x1)
744.12/262.94	   U35(x0, active(x1))
744.12/262.94	   U36(mark(x0))
744.12/262.94	   U36(active(x0))
744.12/262.94	   U41(mark(x0), x1)
744.12/262.94	   U41(x0, mark(x1))
744.12/262.94	   U41(active(x0), x1)
744.12/262.94	   U41(x0, active(x1))
744.12/262.94	   U42(mark(x0))
744.12/262.94	   U42(active(x0))
744.12/262.94	   U51(mark(x0))
744.12/262.94	   U51(active(x0))
744.12/262.94	   U61(mark(x0), x1)
744.12/262.94	   U61(x0, mark(x1))
744.12/262.94	   U61(active(x0), x1)
744.12/262.94	   U61(x0, active(x1))
744.12/262.94	   U62(mark(x0))
744.12/262.94	   U62(active(x0))
744.12/262.94	   U71(mark(x0), x1)
744.12/262.94	   U71(x0, mark(x1))
744.12/262.94	   U71(active(x0), x1)
744.12/262.94	   U71(x0, active(x1))
744.12/262.94	   U72(mark(x0), x1)
744.12/262.94	   U72(x0, mark(x1))
744.12/262.94	   U72(active(x0), x1)
744.12/262.94	   U72(x0, active(x1))
744.12/262.94	   U81(mark(x0), x1, x2)
744.12/262.94	   U81(x0, mark(x1), x2)
744.12/262.94	   U81(x0, x1, mark(x2))
744.12/262.94	   U81(active(x0), x1, x2)
744.12/262.94	   U81(x0, active(x1), x2)
744.12/262.94	   U81(x0, x1, active(x2))
744.12/262.94	   U82(mark(x0), x1, x2)
744.12/262.94	   U82(x0, mark(x1), x2)
744.12/262.94	   U82(x0, x1, mark(x2))
744.12/262.94	   U82(active(x0), x1, x2)
744.12/262.94	   U82(x0, active(x1), x2)
744.12/262.94	   U82(x0, x1, active(x2))
744.12/262.94	   U83(mark(x0), x1, x2)
744.12/262.94	   U83(x0, mark(x1), x2)
744.12/262.94	   U83(x0, x1, mark(x2))
744.12/262.94	   U83(active(x0), x1, x2)
744.12/262.94	   U83(x0, active(x1), x2)
744.12/262.94	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(218) QReductionProof (EQUIVALENT)
744.12/262.94	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.94	
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.94	   U14(x0, x1, mark(x2))
744.12/262.94	   U14(active(x0), x1, x2)
744.12/262.94	   U14(x0, active(x1), x2)
744.12/262.94	   U14(x0, x1, active(x2))
744.12/262.94	   U15(mark(x0), x1)
744.12/262.94	   U15(x0, mark(x1))
744.12/262.94	   U15(active(x0), x1)
744.12/262.94	   U15(x0, active(x1))
744.12/262.94	   U16(mark(x0))
744.12/262.94	   U16(active(x0))
744.12/262.94	   U21(mark(x0), x1)
744.12/262.94	   U21(x0, mark(x1))
744.12/262.94	   U21(active(x0), x1)
744.12/262.94	   U21(x0, active(x1))
744.12/262.94	   U22(mark(x0), x1)
744.12/262.94	   U22(x0, mark(x1))
744.12/262.94	   U22(active(x0), x1)
744.12/262.94	   U22(x0, active(x1))
744.12/262.94	   U23(mark(x0))
744.12/262.94	   U23(active(x0))
744.12/262.94	   U31(mark(x0), x1, x2)
744.12/262.94	   U31(x0, mark(x1), x2)
744.12/262.94	   U31(x0, x1, mark(x2))
744.12/262.94	   U31(active(x0), x1, x2)
744.12/262.94	   U31(x0, active(x1), x2)
744.12/262.94	   U31(x0, x1, active(x2))
744.12/262.94	   U32(mark(x0), x1, x2)
744.12/262.94	   U32(x0, mark(x1), x2)
744.12/262.94	   U32(x0, x1, mark(x2))
744.12/262.94	   U32(active(x0), x1, x2)
744.12/262.94	   U32(x0, active(x1), x2)
744.12/262.94	   U32(x0, x1, active(x2))
744.12/262.94	   U33(mark(x0), x1, x2)
744.12/262.94	   U33(x0, mark(x1), x2)
744.12/262.94	   U33(x0, x1, mark(x2))
744.12/262.94	   U33(active(x0), x1, x2)
744.12/262.94	   U33(x0, active(x1), x2)
744.12/262.94	   U33(x0, x1, active(x2))
744.12/262.94	   U34(mark(x0), x1, x2)
744.12/262.94	   U34(x0, mark(x1), x2)
744.12/262.94	   U34(x0, x1, mark(x2))
744.12/262.94	   U34(active(x0), x1, x2)
744.12/262.94	   U34(x0, active(x1), x2)
744.12/262.94	   U34(x0, x1, active(x2))
744.12/262.94	   U35(mark(x0), x1)
744.12/262.94	   U35(x0, mark(x1))
744.12/262.94	   U35(active(x0), x1)
744.12/262.94	   U35(x0, active(x1))
744.12/262.94	   U36(mark(x0))
744.12/262.94	   U36(active(x0))
744.12/262.94	   U41(mark(x0), x1)
744.12/262.94	   U41(x0, mark(x1))
744.12/262.94	   U41(active(x0), x1)
744.12/262.94	   U41(x0, active(x1))
744.12/262.94	   U42(mark(x0))
744.12/262.94	   U42(active(x0))
744.12/262.94	   U51(mark(x0))
744.12/262.94	   U51(active(x0))
744.12/262.94	   U61(mark(x0), x1)
744.12/262.94	   U61(x0, mark(x1))
744.12/262.94	   U61(active(x0), x1)
744.12/262.94	   U61(x0, active(x1))
744.12/262.94	   U62(mark(x0))
744.12/262.94	   U62(active(x0))
744.12/262.94	   U71(mark(x0), x1)
744.12/262.94	   U71(x0, mark(x1))
744.12/262.94	   U71(active(x0), x1)
744.12/262.94	   U71(x0, active(x1))
744.12/262.94	   U72(mark(x0), x1)
744.12/262.94	   U72(x0, mark(x1))
744.12/262.94	   U72(active(x0), x1)
744.12/262.94	   U72(x0, active(x1))
744.12/262.94	   U81(mark(x0), x1, x2)
744.12/262.94	   U81(x0, mark(x1), x2)
744.12/262.94	   U81(x0, x1, mark(x2))
744.12/262.94	   U81(active(x0), x1, x2)
744.12/262.94	   U81(x0, active(x1), x2)
744.12/262.94	   U81(x0, x1, active(x2))
744.12/262.94	   U82(mark(x0), x1, x2)
744.12/262.94	   U82(x0, mark(x1), x2)
744.12/262.94	   U82(x0, x1, mark(x2))
744.12/262.94	   U82(active(x0), x1, x2)
744.12/262.94	   U82(x0, active(x1), x2)
744.12/262.94	   U82(x0, x1, active(x2))
744.12/262.94	   U83(mark(x0), x1, x2)
744.12/262.94	   U83(x0, mark(x1), x2)
744.12/262.94	   U83(x0, x1, mark(x2))
744.12/262.94	   U83(active(x0), x1, x2)
744.12/262.94	   U83(x0, active(x1), x2)
744.12/262.94	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(219)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   PLUS(X1, mark(X2)) -> PLUS(X1, X2)
744.12/262.94	   PLUS(mark(X1), X2) -> PLUS(X1, X2)
744.12/262.94	   PLUS(active(X1), X2) -> PLUS(X1, X2)
744.12/262.94	   PLUS(X1, active(X2)) -> PLUS(X1, X2)
744.12/262.94	
744.12/262.94	R is empty.
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(220) QDPSizeChangeProof (EQUIVALENT)
744.12/262.94	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. 
744.12/262.94	
744.12/262.94	From the DPs we obtained the following set of size-change graphs:
744.12/262.94	*PLUS(X1, mark(X2)) -> PLUS(X1, X2)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.94	
744.12/262.94	
744.12/262.94	*PLUS(mark(X1), X2) -> PLUS(X1, X2)
744.12/262.94	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.94	
744.12/262.94	
744.12/262.94	*PLUS(active(X1), X2) -> PLUS(X1, X2)
744.12/262.94	The graph contains the following edges 1 > 1, 2 >= 2
744.12/262.94	
744.12/262.94	
744.12/262.94	*PLUS(X1, active(X2)) -> PLUS(X1, X2)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 > 2
744.12/262.94	
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(221)
744.12/262.94	YES
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(222)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   U104^1(X1, mark(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(mark(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, mark(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(active(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, active(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, active(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	
744.12/262.94	The TRS R consists of the following rules:
744.12/262.94	
744.12/262.94	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.94	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.94	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.94	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.94	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.94	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.94	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.94	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.94	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.94	   active(U16(tt)) -> mark(tt)
744.12/262.94	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.94	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.94	   active(U23(tt)) -> mark(tt)
744.12/262.94	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.94	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.94	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.94	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.94	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.94	   active(U36(tt)) -> mark(tt)
744.12/262.94	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.94	   active(U42(tt)) -> mark(tt)
744.12/262.94	   active(U51(tt)) -> mark(tt)
744.12/262.94	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.94	   active(U62(tt)) -> mark(tt)
744.12/262.94	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.94	   active(U72(tt, N)) -> mark(N)
744.12/262.94	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.94	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.94	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.94	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.94	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.94	   active(U92(tt)) -> mark(0)
744.12/262.94	   active(isNat(0)) -> mark(tt)
744.12/262.94	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.94	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.94	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.94	   active(isNatKind(0)) -> mark(tt)
744.12/262.94	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.94	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.94	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.94	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.94	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.94	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.94	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.94	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.94	   mark(tt) -> active(tt)
744.12/262.94	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.94	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.94	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.94	   mark(isNat(X)) -> active(isNat(X))
744.12/262.94	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.94	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.94	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.94	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.94	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.94	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.94	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.94	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.94	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.94	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.94	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.94	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.94	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.94	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.94	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.94	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.94	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.94	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.94	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.94	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.94	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.94	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.94	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.94	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.94	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.94	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.94	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.94	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.94	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.94	   mark(s(X)) -> active(s(mark(X)))
744.12/262.94	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.94	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.94	   mark(0) -> active(0)
744.12/262.94	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.94	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.94	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.94	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.94	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.94	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.94	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.94	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.94	   isNat(mark(X)) -> isNat(X)
744.12/262.94	   isNat(active(X)) -> isNat(X)
744.12/262.94	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.94	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.94	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.94	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.94	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.94	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.94	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.94	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.94	   x(active(X1), X2) -> x(X1, X2)
744.12/262.94	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.94	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.94	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.94	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.94	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.94	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.94	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.94	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.94	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.94	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.94	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.94	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.94	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.94	   U16(mark(X)) -> U16(X)
744.12/262.94	   U16(active(X)) -> U16(X)
744.12/262.94	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.94	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.94	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.94	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.94	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.94	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.94	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.94	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.94	   U23(mark(X)) -> U23(X)
744.12/262.94	   U23(active(X)) -> U23(X)
744.12/262.94	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.94	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.94	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.94	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.94	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.94	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.94	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.94	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.94	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.94	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.94	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.94	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.94	   U36(mark(X)) -> U36(X)
744.12/262.94	   U36(active(X)) -> U36(X)
744.12/262.94	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.94	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.94	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.94	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.94	   U42(mark(X)) -> U42(X)
744.12/262.94	   U42(active(X)) -> U42(X)
744.12/262.94	   U51(mark(X)) -> U51(X)
744.12/262.94	   U51(active(X)) -> U51(X)
744.12/262.94	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.94	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.94	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.94	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.94	   U62(mark(X)) -> U62(X)
744.12/262.94	   U62(active(X)) -> U62(X)
744.12/262.94	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.94	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.94	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.94	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.94	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.94	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.94	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.94	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.94	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.94	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.94	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.94	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.94	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.94	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.94	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.94	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.94	   s(mark(X)) -> s(X)
744.12/262.94	   s(active(X)) -> s(X)
744.12/262.94	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.94	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.94	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.94	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.94	   U92(mark(X)) -> U92(X)
744.12/262.94	   U92(active(X)) -> U92(X)
744.12/262.94	
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.94	   U14(x0, x1, mark(x2))
744.12/262.94	   U14(active(x0), x1, x2)
744.12/262.94	   U14(x0, active(x1), x2)
744.12/262.94	   U14(x0, x1, active(x2))
744.12/262.94	   U15(mark(x0), x1)
744.12/262.94	   U15(x0, mark(x1))
744.12/262.94	   U15(active(x0), x1)
744.12/262.94	   U15(x0, active(x1))
744.12/262.94	   U16(mark(x0))
744.12/262.94	   U16(active(x0))
744.12/262.94	   U21(mark(x0), x1)
744.12/262.94	   U21(x0, mark(x1))
744.12/262.94	   U21(active(x0), x1)
744.12/262.94	   U21(x0, active(x1))
744.12/262.94	   U22(mark(x0), x1)
744.12/262.94	   U22(x0, mark(x1))
744.12/262.94	   U22(active(x0), x1)
744.12/262.94	   U22(x0, active(x1))
744.12/262.94	   U23(mark(x0))
744.12/262.94	   U23(active(x0))
744.12/262.94	   U31(mark(x0), x1, x2)
744.12/262.94	   U31(x0, mark(x1), x2)
744.12/262.94	   U31(x0, x1, mark(x2))
744.12/262.94	   U31(active(x0), x1, x2)
744.12/262.94	   U31(x0, active(x1), x2)
744.12/262.94	   U31(x0, x1, active(x2))
744.12/262.94	   U32(mark(x0), x1, x2)
744.12/262.94	   U32(x0, mark(x1), x2)
744.12/262.94	   U32(x0, x1, mark(x2))
744.12/262.94	   U32(active(x0), x1, x2)
744.12/262.94	   U32(x0, active(x1), x2)
744.12/262.94	   U32(x0, x1, active(x2))
744.12/262.94	   U33(mark(x0), x1, x2)
744.12/262.94	   U33(x0, mark(x1), x2)
744.12/262.94	   U33(x0, x1, mark(x2))
744.12/262.94	   U33(active(x0), x1, x2)
744.12/262.94	   U33(x0, active(x1), x2)
744.12/262.94	   U33(x0, x1, active(x2))
744.12/262.94	   U34(mark(x0), x1, x2)
744.12/262.94	   U34(x0, mark(x1), x2)
744.12/262.94	   U34(x0, x1, mark(x2))
744.12/262.94	   U34(active(x0), x1, x2)
744.12/262.94	   U34(x0, active(x1), x2)
744.12/262.94	   U34(x0, x1, active(x2))
744.12/262.94	   U35(mark(x0), x1)
744.12/262.94	   U35(x0, mark(x1))
744.12/262.94	   U35(active(x0), x1)
744.12/262.94	   U35(x0, active(x1))
744.12/262.94	   U36(mark(x0))
744.12/262.94	   U36(active(x0))
744.12/262.94	   U41(mark(x0), x1)
744.12/262.94	   U41(x0, mark(x1))
744.12/262.94	   U41(active(x0), x1)
744.12/262.94	   U41(x0, active(x1))
744.12/262.94	   U42(mark(x0))
744.12/262.94	   U42(active(x0))
744.12/262.94	   U51(mark(x0))
744.12/262.94	   U51(active(x0))
744.12/262.94	   U61(mark(x0), x1)
744.12/262.94	   U61(x0, mark(x1))
744.12/262.94	   U61(active(x0), x1)
744.12/262.94	   U61(x0, active(x1))
744.12/262.94	   U62(mark(x0))
744.12/262.94	   U62(active(x0))
744.12/262.94	   U71(mark(x0), x1)
744.12/262.94	   U71(x0, mark(x1))
744.12/262.94	   U71(active(x0), x1)
744.12/262.94	   U71(x0, active(x1))
744.12/262.94	   U72(mark(x0), x1)
744.12/262.94	   U72(x0, mark(x1))
744.12/262.94	   U72(active(x0), x1)
744.12/262.94	   U72(x0, active(x1))
744.12/262.94	   U81(mark(x0), x1, x2)
744.12/262.94	   U81(x0, mark(x1), x2)
744.12/262.94	   U81(x0, x1, mark(x2))
744.12/262.94	   U81(active(x0), x1, x2)
744.12/262.94	   U81(x0, active(x1), x2)
744.12/262.94	   U81(x0, x1, active(x2))
744.12/262.94	   U82(mark(x0), x1, x2)
744.12/262.94	   U82(x0, mark(x1), x2)
744.12/262.94	   U82(x0, x1, mark(x2))
744.12/262.94	   U82(active(x0), x1, x2)
744.12/262.94	   U82(x0, active(x1), x2)
744.12/262.94	   U82(x0, x1, active(x2))
744.12/262.94	   U83(mark(x0), x1, x2)
744.12/262.94	   U83(x0, mark(x1), x2)
744.12/262.94	   U83(x0, x1, mark(x2))
744.12/262.94	   U83(active(x0), x1, x2)
744.12/262.94	   U83(x0, active(x1), x2)
744.12/262.94	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(223) UsableRulesProof (EQUIVALENT)
744.12/262.94	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.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(224)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   U104^1(X1, mark(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(mark(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, mark(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(active(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, active(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, active(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	
744.12/262.94	R is empty.
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.94	   U14(x0, x1, mark(x2))
744.12/262.94	   U14(active(x0), x1, x2)
744.12/262.94	   U14(x0, active(x1), x2)
744.12/262.94	   U14(x0, x1, active(x2))
744.12/262.94	   U15(mark(x0), x1)
744.12/262.94	   U15(x0, mark(x1))
744.12/262.94	   U15(active(x0), x1)
744.12/262.94	   U15(x0, active(x1))
744.12/262.94	   U16(mark(x0))
744.12/262.94	   U16(active(x0))
744.12/262.94	   U21(mark(x0), x1)
744.12/262.94	   U21(x0, mark(x1))
744.12/262.94	   U21(active(x0), x1)
744.12/262.94	   U21(x0, active(x1))
744.12/262.94	   U22(mark(x0), x1)
744.12/262.94	   U22(x0, mark(x1))
744.12/262.94	   U22(active(x0), x1)
744.12/262.94	   U22(x0, active(x1))
744.12/262.94	   U23(mark(x0))
744.12/262.94	   U23(active(x0))
744.12/262.94	   U31(mark(x0), x1, x2)
744.12/262.94	   U31(x0, mark(x1), x2)
744.12/262.94	   U31(x0, x1, mark(x2))
744.12/262.94	   U31(active(x0), x1, x2)
744.12/262.94	   U31(x0, active(x1), x2)
744.12/262.94	   U31(x0, x1, active(x2))
744.12/262.94	   U32(mark(x0), x1, x2)
744.12/262.94	   U32(x0, mark(x1), x2)
744.12/262.94	   U32(x0, x1, mark(x2))
744.12/262.94	   U32(active(x0), x1, x2)
744.12/262.94	   U32(x0, active(x1), x2)
744.12/262.94	   U32(x0, x1, active(x2))
744.12/262.94	   U33(mark(x0), x1, x2)
744.12/262.94	   U33(x0, mark(x1), x2)
744.12/262.94	   U33(x0, x1, mark(x2))
744.12/262.94	   U33(active(x0), x1, x2)
744.12/262.94	   U33(x0, active(x1), x2)
744.12/262.94	   U33(x0, x1, active(x2))
744.12/262.94	   U34(mark(x0), x1, x2)
744.12/262.94	   U34(x0, mark(x1), x2)
744.12/262.94	   U34(x0, x1, mark(x2))
744.12/262.94	   U34(active(x0), x1, x2)
744.12/262.94	   U34(x0, active(x1), x2)
744.12/262.94	   U34(x0, x1, active(x2))
744.12/262.94	   U35(mark(x0), x1)
744.12/262.94	   U35(x0, mark(x1))
744.12/262.94	   U35(active(x0), x1)
744.12/262.94	   U35(x0, active(x1))
744.12/262.94	   U36(mark(x0))
744.12/262.94	   U36(active(x0))
744.12/262.94	   U41(mark(x0), x1)
744.12/262.94	   U41(x0, mark(x1))
744.12/262.94	   U41(active(x0), x1)
744.12/262.94	   U41(x0, active(x1))
744.12/262.94	   U42(mark(x0))
744.12/262.94	   U42(active(x0))
744.12/262.94	   U51(mark(x0))
744.12/262.94	   U51(active(x0))
744.12/262.94	   U61(mark(x0), x1)
744.12/262.94	   U61(x0, mark(x1))
744.12/262.94	   U61(active(x0), x1)
744.12/262.94	   U61(x0, active(x1))
744.12/262.94	   U62(mark(x0))
744.12/262.94	   U62(active(x0))
744.12/262.94	   U71(mark(x0), x1)
744.12/262.94	   U71(x0, mark(x1))
744.12/262.94	   U71(active(x0), x1)
744.12/262.94	   U71(x0, active(x1))
744.12/262.94	   U72(mark(x0), x1)
744.12/262.94	   U72(x0, mark(x1))
744.12/262.94	   U72(active(x0), x1)
744.12/262.94	   U72(x0, active(x1))
744.12/262.94	   U81(mark(x0), x1, x2)
744.12/262.94	   U81(x0, mark(x1), x2)
744.12/262.94	   U81(x0, x1, mark(x2))
744.12/262.94	   U81(active(x0), x1, x2)
744.12/262.94	   U81(x0, active(x1), x2)
744.12/262.94	   U81(x0, x1, active(x2))
744.12/262.94	   U82(mark(x0), x1, x2)
744.12/262.94	   U82(x0, mark(x1), x2)
744.12/262.94	   U82(x0, x1, mark(x2))
744.12/262.94	   U82(active(x0), x1, x2)
744.12/262.94	   U82(x0, active(x1), x2)
744.12/262.94	   U82(x0, x1, active(x2))
744.12/262.94	   U83(mark(x0), x1, x2)
744.12/262.94	   U83(x0, mark(x1), x2)
744.12/262.94	   U83(x0, x1, mark(x2))
744.12/262.94	   U83(active(x0), x1, x2)
744.12/262.94	   U83(x0, active(x1), x2)
744.12/262.94	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(225) QReductionProof (EQUIVALENT)
744.12/262.94	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.94	
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.94	   U14(x0, x1, mark(x2))
744.12/262.94	   U14(active(x0), x1, x2)
744.12/262.94	   U14(x0, active(x1), x2)
744.12/262.94	   U14(x0, x1, active(x2))
744.12/262.94	   U15(mark(x0), x1)
744.12/262.94	   U15(x0, mark(x1))
744.12/262.94	   U15(active(x0), x1)
744.12/262.94	   U15(x0, active(x1))
744.12/262.94	   U16(mark(x0))
744.12/262.94	   U16(active(x0))
744.12/262.94	   U21(mark(x0), x1)
744.12/262.94	   U21(x0, mark(x1))
744.12/262.94	   U21(active(x0), x1)
744.12/262.94	   U21(x0, active(x1))
744.12/262.94	   U22(mark(x0), x1)
744.12/262.94	   U22(x0, mark(x1))
744.12/262.94	   U22(active(x0), x1)
744.12/262.94	   U22(x0, active(x1))
744.12/262.94	   U23(mark(x0))
744.12/262.94	   U23(active(x0))
744.12/262.94	   U31(mark(x0), x1, x2)
744.12/262.94	   U31(x0, mark(x1), x2)
744.12/262.94	   U31(x0, x1, mark(x2))
744.12/262.94	   U31(active(x0), x1, x2)
744.12/262.94	   U31(x0, active(x1), x2)
744.12/262.94	   U31(x0, x1, active(x2))
744.12/262.94	   U32(mark(x0), x1, x2)
744.12/262.94	   U32(x0, mark(x1), x2)
744.12/262.94	   U32(x0, x1, mark(x2))
744.12/262.94	   U32(active(x0), x1, x2)
744.12/262.94	   U32(x0, active(x1), x2)
744.12/262.94	   U32(x0, x1, active(x2))
744.12/262.94	   U33(mark(x0), x1, x2)
744.12/262.94	   U33(x0, mark(x1), x2)
744.12/262.94	   U33(x0, x1, mark(x2))
744.12/262.94	   U33(active(x0), x1, x2)
744.12/262.94	   U33(x0, active(x1), x2)
744.12/262.94	   U33(x0, x1, active(x2))
744.12/262.94	   U34(mark(x0), x1, x2)
744.12/262.94	   U34(x0, mark(x1), x2)
744.12/262.94	   U34(x0, x1, mark(x2))
744.12/262.94	   U34(active(x0), x1, x2)
744.12/262.94	   U34(x0, active(x1), x2)
744.12/262.94	   U34(x0, x1, active(x2))
744.12/262.94	   U35(mark(x0), x1)
744.12/262.94	   U35(x0, mark(x1))
744.12/262.94	   U35(active(x0), x1)
744.12/262.94	   U35(x0, active(x1))
744.12/262.94	   U36(mark(x0))
744.12/262.94	   U36(active(x0))
744.12/262.94	   U41(mark(x0), x1)
744.12/262.94	   U41(x0, mark(x1))
744.12/262.94	   U41(active(x0), x1)
744.12/262.94	   U41(x0, active(x1))
744.12/262.94	   U42(mark(x0))
744.12/262.94	   U42(active(x0))
744.12/262.94	   U51(mark(x0))
744.12/262.94	   U51(active(x0))
744.12/262.94	   U61(mark(x0), x1)
744.12/262.94	   U61(x0, mark(x1))
744.12/262.94	   U61(active(x0), x1)
744.12/262.94	   U61(x0, active(x1))
744.12/262.94	   U62(mark(x0))
744.12/262.94	   U62(active(x0))
744.12/262.94	   U71(mark(x0), x1)
744.12/262.94	   U71(x0, mark(x1))
744.12/262.94	   U71(active(x0), x1)
744.12/262.94	   U71(x0, active(x1))
744.12/262.94	   U72(mark(x0), x1)
744.12/262.94	   U72(x0, mark(x1))
744.12/262.94	   U72(active(x0), x1)
744.12/262.94	   U72(x0, active(x1))
744.12/262.94	   U81(mark(x0), x1, x2)
744.12/262.94	   U81(x0, mark(x1), x2)
744.12/262.94	   U81(x0, x1, mark(x2))
744.12/262.94	   U81(active(x0), x1, x2)
744.12/262.94	   U81(x0, active(x1), x2)
744.12/262.94	   U81(x0, x1, active(x2))
744.12/262.94	   U82(mark(x0), x1, x2)
744.12/262.94	   U82(x0, mark(x1), x2)
744.12/262.94	   U82(x0, x1, mark(x2))
744.12/262.94	   U82(active(x0), x1, x2)
744.12/262.94	   U82(x0, active(x1), x2)
744.12/262.94	   U82(x0, x1, active(x2))
744.12/262.94	   U83(mark(x0), x1, x2)
744.12/262.94	   U83(x0, mark(x1), x2)
744.12/262.94	   U83(x0, x1, mark(x2))
744.12/262.94	   U83(active(x0), x1, x2)
744.12/262.94	   U83(x0, active(x1), x2)
744.12/262.94	   U83(x0, x1, active(x2))
744.12/262.94	   U84(mark(x0), x1, x2)
744.12/262.94	   U84(x0, mark(x1), x2)
744.12/262.94	   U84(x0, x1, mark(x2))
744.12/262.94	   U84(active(x0), x1, x2)
744.12/262.94	   U84(x0, active(x1), x2)
744.12/262.94	   U84(x0, x1, active(x2))
744.12/262.94	   s(mark(x0))
744.12/262.94	   s(active(x0))
744.12/262.94	   U91(mark(x0), x1)
744.12/262.94	   U91(x0, mark(x1))
744.12/262.94	   U91(active(x0), x1)
744.12/262.94	   U91(x0, active(x1))
744.12/262.94	   U92(mark(x0))
744.12/262.94	   U92(active(x0))
744.12/262.94	
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(226)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   U104^1(X1, mark(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(mark(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, mark(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(active(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, active(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	   U104^1(X1, X2, active(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	
744.12/262.94	R is empty.
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	
744.12/262.94	We have to consider all minimal (P,Q,R)-chains.
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(227) QDPSizeChangeProof (EQUIVALENT)
744.12/262.94	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. 
744.12/262.94	
744.12/262.94	From the DPs we obtained the following set of size-change graphs:
744.12/262.94	*U104^1(X1, mark(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.94	
744.12/262.94	
744.12/262.94	*U104^1(mark(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.94	
744.12/262.94	
744.12/262.94	*U104^1(X1, X2, mark(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.94	
744.12/262.94	
744.12/262.94	*U104^1(active(X1), X2, X3) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.12/262.94	
744.12/262.94	
744.12/262.94	*U104^1(X1, active(X2), X3) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.12/262.94	
744.12/262.94	
744.12/262.94	*U104^1(X1, X2, active(X3)) -> U104^1(X1, X2, X3)
744.12/262.94	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.12/262.94	
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(228)
744.12/262.94	YES
744.12/262.94	
744.12/262.94	----------------------------------------
744.12/262.94	
744.12/262.94	(229)
744.12/262.94	Obligation:
744.12/262.94	Q DP problem:
744.12/262.94	The TRS P consists of the following rules:
744.12/262.94	
744.12/262.94	   ISNAT(active(X)) -> ISNAT(X)
744.12/262.94	   ISNAT(mark(X)) -> ISNAT(X)
744.12/262.94	
744.12/262.94	The TRS R consists of the following rules:
744.12/262.94	
744.12/262.94	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.94	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.94	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.94	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.94	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.94	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.94	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.94	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.94	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.94	   active(U16(tt)) -> mark(tt)
744.12/262.94	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.94	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.94	   active(U23(tt)) -> mark(tt)
744.12/262.94	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.94	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.94	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.94	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.94	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.94	   active(U36(tt)) -> mark(tt)
744.12/262.94	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.94	   active(U42(tt)) -> mark(tt)
744.12/262.94	   active(U51(tt)) -> mark(tt)
744.12/262.94	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.94	   active(U62(tt)) -> mark(tt)
744.12/262.94	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.94	   active(U72(tt, N)) -> mark(N)
744.12/262.94	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.94	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.94	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.94	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.94	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.94	   active(U92(tt)) -> mark(0)
744.12/262.94	   active(isNat(0)) -> mark(tt)
744.12/262.94	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.94	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.94	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.94	   active(isNatKind(0)) -> mark(tt)
744.12/262.94	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.94	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.94	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.94	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.94	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.94	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.94	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.94	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.94	   mark(tt) -> active(tt)
744.12/262.94	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.94	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.94	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.94	   mark(isNat(X)) -> active(isNat(X))
744.12/262.94	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.94	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.94	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.94	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.94	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.94	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.94	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.94	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.94	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.94	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.94	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.94	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.94	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.94	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.94	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.94	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.94	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.94	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.94	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.94	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.94	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.94	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.94	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.94	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.94	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.94	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.94	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.94	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.94	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.94	   mark(s(X)) -> active(s(mark(X)))
744.12/262.94	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.94	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.94	   mark(0) -> active(0)
744.12/262.94	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.94	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.94	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.94	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.94	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.94	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.94	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.94	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.94	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.94	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.94	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.94	   isNat(mark(X)) -> isNat(X)
744.12/262.94	   isNat(active(X)) -> isNat(X)
744.12/262.94	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.94	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.94	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.94	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.94	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.94	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.94	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.94	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.94	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.94	   x(active(X1), X2) -> x(X1, X2)
744.12/262.94	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.94	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.94	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.94	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.94	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.94	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.94	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.94	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.94	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.94	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.94	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.94	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.94	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.94	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.94	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.94	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.94	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.94	   U16(mark(X)) -> U16(X)
744.12/262.94	   U16(active(X)) -> U16(X)
744.12/262.94	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.94	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.94	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.94	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.94	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.94	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.94	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.94	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.94	   U23(mark(X)) -> U23(X)
744.12/262.94	   U23(active(X)) -> U23(X)
744.12/262.94	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.94	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.94	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.94	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.94	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.94	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.94	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.94	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.94	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.94	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.94	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.94	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.94	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.94	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.94	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.94	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.94	   U36(mark(X)) -> U36(X)
744.12/262.94	   U36(active(X)) -> U36(X)
744.12/262.94	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.94	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.94	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.94	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.94	   U42(mark(X)) -> U42(X)
744.12/262.94	   U42(active(X)) -> U42(X)
744.12/262.94	   U51(mark(X)) -> U51(X)
744.12/262.94	   U51(active(X)) -> U51(X)
744.12/262.94	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.94	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.94	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.94	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.94	   U62(mark(X)) -> U62(X)
744.12/262.94	   U62(active(X)) -> U62(X)
744.12/262.94	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.94	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.94	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.94	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.94	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.94	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.94	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.94	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.94	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.94	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.94	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.94	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.94	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.94	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.94	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.94	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.94	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.94	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.94	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.94	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.94	   s(mark(X)) -> s(X)
744.12/262.94	   s(active(X)) -> s(X)
744.12/262.94	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.94	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.94	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.94	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.94	   U92(mark(X)) -> U92(X)
744.12/262.94	   U92(active(X)) -> U92(X)
744.12/262.94	
744.12/262.94	The set Q consists of the following terms:
744.12/262.94	
744.12/262.94	   active(U101(tt, x0, x1))
744.12/262.94	   active(U102(tt, x0, x1))
744.12/262.94	   active(U103(tt, x0, x1))
744.12/262.94	   active(U104(tt, x0, x1))
744.12/262.94	   active(U11(tt, x0, x1))
744.12/262.94	   active(U12(tt, x0, x1))
744.12/262.94	   active(U13(tt, x0, x1))
744.12/262.94	   active(U14(tt, x0, x1))
744.12/262.94	   active(U15(tt, x0))
744.12/262.94	   active(U16(tt))
744.12/262.94	   active(U21(tt, x0))
744.12/262.94	   active(U22(tt, x0))
744.12/262.94	   active(U23(tt))
744.12/262.94	   active(U31(tt, x0, x1))
744.12/262.94	   active(U32(tt, x0, x1))
744.12/262.94	   active(U33(tt, x0, x1))
744.12/262.94	   active(U34(tt, x0, x1))
744.12/262.94	   active(U35(tt, x0))
744.12/262.94	   active(U36(tt))
744.12/262.94	   active(U41(tt, x0))
744.12/262.94	   active(U42(tt))
744.12/262.94	   active(U51(tt))
744.12/262.94	   active(U61(tt, x0))
744.12/262.94	   active(U62(tt))
744.12/262.94	   active(U71(tt, x0))
744.12/262.94	   active(U72(tt, x0))
744.12/262.94	   active(U81(tt, x0, x1))
744.12/262.94	   active(U82(tt, x0, x1))
744.12/262.94	   active(U83(tt, x0, x1))
744.12/262.94	   active(U84(tt, x0, x1))
744.12/262.94	   active(U91(tt, x0))
744.12/262.94	   active(U92(tt))
744.12/262.94	   active(isNat(0))
744.12/262.94	   active(isNat(plus(x0, x1)))
744.12/262.94	   active(isNat(s(x0)))
744.12/262.94	   active(isNat(x(x0, x1)))
744.12/262.94	   active(isNatKind(0))
744.12/262.94	   active(isNatKind(plus(x0, x1)))
744.12/262.94	   active(isNatKind(s(x0)))
744.12/262.94	   active(isNatKind(x(x0, x1)))
744.12/262.94	   active(plus(x0, 0))
744.12/262.94	   active(plus(x0, s(x1)))
744.12/262.94	   active(x(x0, 0))
744.12/262.94	   active(x(x0, s(x1)))
744.12/262.94	   mark(U101(x0, x1, x2))
744.12/262.94	   mark(tt)
744.12/262.94	   mark(U102(x0, x1, x2))
744.12/262.94	   mark(isNatKind(x0))
744.12/262.94	   mark(U103(x0, x1, x2))
744.12/262.94	   mark(isNat(x0))
744.12/262.94	   mark(U104(x0, x1, x2))
744.12/262.94	   mark(plus(x0, x1))
744.12/262.94	   mark(x(x0, x1))
744.12/262.94	   mark(U11(x0, x1, x2))
744.12/262.94	   mark(U12(x0, x1, x2))
744.12/262.94	   mark(U13(x0, x1, x2))
744.12/262.94	   mark(U14(x0, x1, x2))
744.12/262.94	   mark(U15(x0, x1))
744.12/262.94	   mark(U16(x0))
744.12/262.94	   mark(U21(x0, x1))
744.12/262.94	   mark(U22(x0, x1))
744.12/262.94	   mark(U23(x0))
744.12/262.94	   mark(U31(x0, x1, x2))
744.12/262.94	   mark(U32(x0, x1, x2))
744.12/262.94	   mark(U33(x0, x1, x2))
744.12/262.94	   mark(U34(x0, x1, x2))
744.12/262.94	   mark(U35(x0, x1))
744.12/262.94	   mark(U36(x0))
744.12/262.94	   mark(U41(x0, x1))
744.12/262.94	   mark(U42(x0))
744.12/262.94	   mark(U51(x0))
744.12/262.94	   mark(U61(x0, x1))
744.12/262.94	   mark(U62(x0))
744.12/262.94	   mark(U71(x0, x1))
744.12/262.94	   mark(U72(x0, x1))
744.12/262.94	   mark(U81(x0, x1, x2))
744.12/262.94	   mark(U82(x0, x1, x2))
744.12/262.94	   mark(U83(x0, x1, x2))
744.12/262.94	   mark(U84(x0, x1, x2))
744.12/262.94	   mark(s(x0))
744.12/262.94	   mark(U91(x0, x1))
744.12/262.94	   mark(U92(x0))
744.12/262.94	   mark(0)
744.12/262.94	   U101(mark(x0), x1, x2)
744.12/262.94	   U101(x0, mark(x1), x2)
744.12/262.94	   U101(x0, x1, mark(x2))
744.12/262.94	   U101(active(x0), x1, x2)
744.12/262.94	   U101(x0, active(x1), x2)
744.12/262.94	   U101(x0, x1, active(x2))
744.12/262.94	   U102(mark(x0), x1, x2)
744.12/262.94	   U102(x0, mark(x1), x2)
744.12/262.94	   U102(x0, x1, mark(x2))
744.12/262.94	   U102(active(x0), x1, x2)
744.12/262.94	   U102(x0, active(x1), x2)
744.12/262.94	   U102(x0, x1, active(x2))
744.12/262.94	   isNatKind(mark(x0))
744.12/262.94	   isNatKind(active(x0))
744.12/262.94	   U103(mark(x0), x1, x2)
744.12/262.94	   U103(x0, mark(x1), x2)
744.12/262.94	   U103(x0, x1, mark(x2))
744.12/262.94	   U103(active(x0), x1, x2)
744.12/262.94	   U103(x0, active(x1), x2)
744.12/262.94	   U103(x0, x1, active(x2))
744.12/262.94	   isNat(mark(x0))
744.12/262.94	   isNat(active(x0))
744.12/262.94	   U104(mark(x0), x1, x2)
744.12/262.94	   U104(x0, mark(x1), x2)
744.12/262.94	   U104(x0, x1, mark(x2))
744.12/262.94	   U104(active(x0), x1, x2)
744.12/262.94	   U104(x0, active(x1), x2)
744.12/262.94	   U104(x0, x1, active(x2))
744.12/262.94	   plus(mark(x0), x1)
744.12/262.94	   plus(x0, mark(x1))
744.12/262.94	   plus(active(x0), x1)
744.12/262.94	   plus(x0, active(x1))
744.12/262.94	   x(mark(x0), x1)
744.12/262.94	   x(x0, mark(x1))
744.12/262.94	   x(active(x0), x1)
744.12/262.94	   x(x0, active(x1))
744.12/262.94	   U11(mark(x0), x1, x2)
744.12/262.94	   U11(x0, mark(x1), x2)
744.12/262.94	   U11(x0, x1, mark(x2))
744.12/262.94	   U11(active(x0), x1, x2)
744.12/262.94	   U11(x0, active(x1), x2)
744.12/262.94	   U11(x0, x1, active(x2))
744.12/262.94	   U12(mark(x0), x1, x2)
744.12/262.94	   U12(x0, mark(x1), x2)
744.12/262.94	   U12(x0, x1, mark(x2))
744.12/262.94	   U12(active(x0), x1, x2)
744.12/262.94	   U12(x0, active(x1), x2)
744.12/262.94	   U12(x0, x1, active(x2))
744.12/262.94	   U13(mark(x0), x1, x2)
744.12/262.94	   U13(x0, mark(x1), x2)
744.12/262.94	   U13(x0, x1, mark(x2))
744.12/262.94	   U13(active(x0), x1, x2)
744.12/262.94	   U13(x0, active(x1), x2)
744.12/262.94	   U13(x0, x1, active(x2))
744.12/262.94	   U14(mark(x0), x1, x2)
744.12/262.94	   U14(x0, mark(x1), x2)
744.12/262.95	   U14(x0, x1, mark(x2))
744.12/262.95	   U14(active(x0), x1, x2)
744.12/262.95	   U14(x0, active(x1), x2)
744.12/262.95	   U14(x0, x1, active(x2))
744.12/262.95	   U15(mark(x0), x1)
744.12/262.95	   U15(x0, mark(x1))
744.12/262.95	   U15(active(x0), x1)
744.12/262.95	   U15(x0, active(x1))
744.12/262.95	   U16(mark(x0))
744.12/262.95	   U16(active(x0))
744.12/262.95	   U21(mark(x0), x1)
744.12/262.95	   U21(x0, mark(x1))
744.12/262.95	   U21(active(x0), x1)
744.12/262.95	   U21(x0, active(x1))
744.12/262.95	   U22(mark(x0), x1)
744.12/262.95	   U22(x0, mark(x1))
744.12/262.95	   U22(active(x0), x1)
744.12/262.95	   U22(x0, active(x1))
744.12/262.95	   U23(mark(x0))
744.12/262.95	   U23(active(x0))
744.12/262.95	   U31(mark(x0), x1, x2)
744.12/262.95	   U31(x0, mark(x1), x2)
744.12/262.95	   U31(x0, x1, mark(x2))
744.12/262.95	   U31(active(x0), x1, x2)
744.12/262.95	   U31(x0, active(x1), x2)
744.12/262.95	   U31(x0, x1, active(x2))
744.12/262.95	   U32(mark(x0), x1, x2)
744.12/262.95	   U32(x0, mark(x1), x2)
744.12/262.95	   U32(x0, x1, mark(x2))
744.12/262.95	   U32(active(x0), x1, x2)
744.12/262.95	   U32(x0, active(x1), x2)
744.12/262.95	   U32(x0, x1, active(x2))
744.12/262.95	   U33(mark(x0), x1, x2)
744.12/262.95	   U33(x0, mark(x1), x2)
744.12/262.95	   U33(x0, x1, mark(x2))
744.12/262.95	   U33(active(x0), x1, x2)
744.12/262.95	   U33(x0, active(x1), x2)
744.12/262.95	   U33(x0, x1, active(x2))
744.12/262.95	   U34(mark(x0), x1, x2)
744.12/262.95	   U34(x0, mark(x1), x2)
744.12/262.95	   U34(x0, x1, mark(x2))
744.12/262.95	   U34(active(x0), x1, x2)
744.12/262.95	   U34(x0, active(x1), x2)
744.12/262.95	   U34(x0, x1, active(x2))
744.12/262.95	   U35(mark(x0), x1)
744.12/262.95	   U35(x0, mark(x1))
744.12/262.95	   U35(active(x0), x1)
744.12/262.95	   U35(x0, active(x1))
744.12/262.95	   U36(mark(x0))
744.12/262.95	   U36(active(x0))
744.12/262.95	   U41(mark(x0), x1)
744.12/262.95	   U41(x0, mark(x1))
744.12/262.95	   U41(active(x0), x1)
744.12/262.95	   U41(x0, active(x1))
744.12/262.95	   U42(mark(x0))
744.12/262.95	   U42(active(x0))
744.12/262.95	   U51(mark(x0))
744.12/262.95	   U51(active(x0))
744.12/262.95	   U61(mark(x0), x1)
744.12/262.95	   U61(x0, mark(x1))
744.12/262.95	   U61(active(x0), x1)
744.12/262.95	   U61(x0, active(x1))
744.12/262.95	   U62(mark(x0))
744.12/262.95	   U62(active(x0))
744.12/262.95	   U71(mark(x0), x1)
744.12/262.95	   U71(x0, mark(x1))
744.12/262.95	   U71(active(x0), x1)
744.12/262.95	   U71(x0, active(x1))
744.12/262.95	   U72(mark(x0), x1)
744.12/262.95	   U72(x0, mark(x1))
744.12/262.95	   U72(active(x0), x1)
744.12/262.95	   U72(x0, active(x1))
744.12/262.95	   U81(mark(x0), x1, x2)
744.12/262.95	   U81(x0, mark(x1), x2)
744.12/262.95	   U81(x0, x1, mark(x2))
744.12/262.95	   U81(active(x0), x1, x2)
744.12/262.95	   U81(x0, active(x1), x2)
744.12/262.95	   U81(x0, x1, active(x2))
744.12/262.95	   U82(mark(x0), x1, x2)
744.12/262.95	   U82(x0, mark(x1), x2)
744.12/262.95	   U82(x0, x1, mark(x2))
744.12/262.95	   U82(active(x0), x1, x2)
744.12/262.95	   U82(x0, active(x1), x2)
744.12/262.95	   U82(x0, x1, active(x2))
744.12/262.95	   U83(mark(x0), x1, x2)
744.12/262.95	   U83(x0, mark(x1), x2)
744.12/262.95	   U83(x0, x1, mark(x2))
744.12/262.95	   U83(active(x0), x1, x2)
744.12/262.95	   U83(x0, active(x1), x2)
744.12/262.95	   U83(x0, x1, active(x2))
744.12/262.95	   U84(mark(x0), x1, x2)
744.12/262.95	   U84(x0, mark(x1), x2)
744.12/262.95	   U84(x0, x1, mark(x2))
744.12/262.95	   U84(active(x0), x1, x2)
744.12/262.95	   U84(x0, active(x1), x2)
744.12/262.95	   U84(x0, x1, active(x2))
744.12/262.95	   s(mark(x0))
744.12/262.95	   s(active(x0))
744.12/262.95	   U91(mark(x0), x1)
744.12/262.95	   U91(x0, mark(x1))
744.12/262.95	   U91(active(x0), x1)
744.12/262.95	   U91(x0, active(x1))
744.12/262.95	   U92(mark(x0))
744.12/262.95	   U92(active(x0))
744.12/262.95	
744.12/262.95	We have to consider all minimal (P,Q,R)-chains.
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(230) UsableRulesProof (EQUIVALENT)
744.12/262.95	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.
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(231)
744.12/262.95	Obligation:
744.12/262.95	Q DP problem:
744.12/262.95	The TRS P consists of the following rules:
744.12/262.95	
744.12/262.95	   ISNAT(active(X)) -> ISNAT(X)
744.12/262.95	   ISNAT(mark(X)) -> ISNAT(X)
744.12/262.95	
744.12/262.95	R is empty.
744.12/262.95	The set Q consists of the following terms:
744.12/262.95	
744.12/262.95	   active(U101(tt, x0, x1))
744.12/262.95	   active(U102(tt, x0, x1))
744.12/262.95	   active(U103(tt, x0, x1))
744.12/262.95	   active(U104(tt, x0, x1))
744.12/262.95	   active(U11(tt, x0, x1))
744.12/262.95	   active(U12(tt, x0, x1))
744.12/262.95	   active(U13(tt, x0, x1))
744.12/262.95	   active(U14(tt, x0, x1))
744.12/262.95	   active(U15(tt, x0))
744.12/262.95	   active(U16(tt))
744.12/262.95	   active(U21(tt, x0))
744.12/262.95	   active(U22(tt, x0))
744.12/262.95	   active(U23(tt))
744.12/262.95	   active(U31(tt, x0, x1))
744.12/262.95	   active(U32(tt, x0, x1))
744.12/262.95	   active(U33(tt, x0, x1))
744.12/262.95	   active(U34(tt, x0, x1))
744.12/262.95	   active(U35(tt, x0))
744.12/262.95	   active(U36(tt))
744.12/262.95	   active(U41(tt, x0))
744.12/262.95	   active(U42(tt))
744.12/262.95	   active(U51(tt))
744.12/262.95	   active(U61(tt, x0))
744.12/262.95	   active(U62(tt))
744.12/262.95	   active(U71(tt, x0))
744.12/262.95	   active(U72(tt, x0))
744.12/262.95	   active(U81(tt, x0, x1))
744.12/262.95	   active(U82(tt, x0, x1))
744.12/262.95	   active(U83(tt, x0, x1))
744.12/262.95	   active(U84(tt, x0, x1))
744.12/262.95	   active(U91(tt, x0))
744.12/262.95	   active(U92(tt))
744.12/262.95	   active(isNat(0))
744.12/262.95	   active(isNat(plus(x0, x1)))
744.12/262.95	   active(isNat(s(x0)))
744.12/262.95	   active(isNat(x(x0, x1)))
744.12/262.95	   active(isNatKind(0))
744.12/262.95	   active(isNatKind(plus(x0, x1)))
744.12/262.95	   active(isNatKind(s(x0)))
744.12/262.95	   active(isNatKind(x(x0, x1)))
744.12/262.95	   active(plus(x0, 0))
744.12/262.95	   active(plus(x0, s(x1)))
744.12/262.95	   active(x(x0, 0))
744.12/262.95	   active(x(x0, s(x1)))
744.12/262.95	   mark(U101(x0, x1, x2))
744.12/262.95	   mark(tt)
744.12/262.95	   mark(U102(x0, x1, x2))
744.12/262.95	   mark(isNatKind(x0))
744.12/262.95	   mark(U103(x0, x1, x2))
744.12/262.95	   mark(isNat(x0))
744.12/262.95	   mark(U104(x0, x1, x2))
744.12/262.95	   mark(plus(x0, x1))
744.12/262.95	   mark(x(x0, x1))
744.12/262.95	   mark(U11(x0, x1, x2))
744.12/262.95	   mark(U12(x0, x1, x2))
744.12/262.95	   mark(U13(x0, x1, x2))
744.12/262.95	   mark(U14(x0, x1, x2))
744.12/262.95	   mark(U15(x0, x1))
744.12/262.95	   mark(U16(x0))
744.12/262.95	   mark(U21(x0, x1))
744.12/262.95	   mark(U22(x0, x1))
744.12/262.95	   mark(U23(x0))
744.12/262.95	   mark(U31(x0, x1, x2))
744.12/262.95	   mark(U32(x0, x1, x2))
744.12/262.95	   mark(U33(x0, x1, x2))
744.12/262.95	   mark(U34(x0, x1, x2))
744.12/262.95	   mark(U35(x0, x1))
744.12/262.95	   mark(U36(x0))
744.12/262.95	   mark(U41(x0, x1))
744.12/262.95	   mark(U42(x0))
744.12/262.95	   mark(U51(x0))
744.12/262.95	   mark(U61(x0, x1))
744.12/262.95	   mark(U62(x0))
744.12/262.95	   mark(U71(x0, x1))
744.12/262.95	   mark(U72(x0, x1))
744.12/262.95	   mark(U81(x0, x1, x2))
744.12/262.95	   mark(U82(x0, x1, x2))
744.12/262.95	   mark(U83(x0, x1, x2))
744.12/262.95	   mark(U84(x0, x1, x2))
744.12/262.95	   mark(s(x0))
744.12/262.95	   mark(U91(x0, x1))
744.12/262.95	   mark(U92(x0))
744.12/262.95	   mark(0)
744.12/262.95	   U101(mark(x0), x1, x2)
744.12/262.95	   U101(x0, mark(x1), x2)
744.12/262.95	   U101(x0, x1, mark(x2))
744.12/262.95	   U101(active(x0), x1, x2)
744.12/262.95	   U101(x0, active(x1), x2)
744.12/262.95	   U101(x0, x1, active(x2))
744.12/262.95	   U102(mark(x0), x1, x2)
744.12/262.95	   U102(x0, mark(x1), x2)
744.12/262.95	   U102(x0, x1, mark(x2))
744.12/262.95	   U102(active(x0), x1, x2)
744.12/262.95	   U102(x0, active(x1), x2)
744.12/262.95	   U102(x0, x1, active(x2))
744.12/262.95	   isNatKind(mark(x0))
744.12/262.95	   isNatKind(active(x0))
744.12/262.95	   U103(mark(x0), x1, x2)
744.12/262.95	   U103(x0, mark(x1), x2)
744.12/262.95	   U103(x0, x1, mark(x2))
744.12/262.95	   U103(active(x0), x1, x2)
744.12/262.95	   U103(x0, active(x1), x2)
744.12/262.95	   U103(x0, x1, active(x2))
744.12/262.95	   isNat(mark(x0))
744.12/262.95	   isNat(active(x0))
744.12/262.95	   U104(mark(x0), x1, x2)
744.12/262.95	   U104(x0, mark(x1), x2)
744.12/262.95	   U104(x0, x1, mark(x2))
744.12/262.95	   U104(active(x0), x1, x2)
744.12/262.95	   U104(x0, active(x1), x2)
744.12/262.95	   U104(x0, x1, active(x2))
744.12/262.95	   plus(mark(x0), x1)
744.12/262.95	   plus(x0, mark(x1))
744.12/262.95	   plus(active(x0), x1)
744.12/262.95	   plus(x0, active(x1))
744.12/262.95	   x(mark(x0), x1)
744.12/262.95	   x(x0, mark(x1))
744.12/262.95	   x(active(x0), x1)
744.12/262.95	   x(x0, active(x1))
744.12/262.95	   U11(mark(x0), x1, x2)
744.12/262.95	   U11(x0, mark(x1), x2)
744.12/262.95	   U11(x0, x1, mark(x2))
744.12/262.95	   U11(active(x0), x1, x2)
744.12/262.95	   U11(x0, active(x1), x2)
744.12/262.95	   U11(x0, x1, active(x2))
744.12/262.95	   U12(mark(x0), x1, x2)
744.12/262.95	   U12(x0, mark(x1), x2)
744.12/262.95	   U12(x0, x1, mark(x2))
744.12/262.95	   U12(active(x0), x1, x2)
744.12/262.95	   U12(x0, active(x1), x2)
744.12/262.95	   U12(x0, x1, active(x2))
744.12/262.95	   U13(mark(x0), x1, x2)
744.12/262.95	   U13(x0, mark(x1), x2)
744.12/262.95	   U13(x0, x1, mark(x2))
744.12/262.95	   U13(active(x0), x1, x2)
744.12/262.95	   U13(x0, active(x1), x2)
744.12/262.95	   U13(x0, x1, active(x2))
744.12/262.95	   U14(mark(x0), x1, x2)
744.12/262.95	   U14(x0, mark(x1), x2)
744.12/262.95	   U14(x0, x1, mark(x2))
744.12/262.95	   U14(active(x0), x1, x2)
744.12/262.95	   U14(x0, active(x1), x2)
744.12/262.95	   U14(x0, x1, active(x2))
744.12/262.95	   U15(mark(x0), x1)
744.12/262.95	   U15(x0, mark(x1))
744.12/262.95	   U15(active(x0), x1)
744.12/262.95	   U15(x0, active(x1))
744.12/262.95	   U16(mark(x0))
744.12/262.95	   U16(active(x0))
744.12/262.95	   U21(mark(x0), x1)
744.12/262.95	   U21(x0, mark(x1))
744.12/262.95	   U21(active(x0), x1)
744.12/262.95	   U21(x0, active(x1))
744.12/262.95	   U22(mark(x0), x1)
744.12/262.95	   U22(x0, mark(x1))
744.12/262.95	   U22(active(x0), x1)
744.12/262.95	   U22(x0, active(x1))
744.12/262.95	   U23(mark(x0))
744.12/262.95	   U23(active(x0))
744.12/262.95	   U31(mark(x0), x1, x2)
744.12/262.95	   U31(x0, mark(x1), x2)
744.12/262.95	   U31(x0, x1, mark(x2))
744.12/262.95	   U31(active(x0), x1, x2)
744.12/262.95	   U31(x0, active(x1), x2)
744.12/262.95	   U31(x0, x1, active(x2))
744.12/262.95	   U32(mark(x0), x1, x2)
744.12/262.95	   U32(x0, mark(x1), x2)
744.12/262.95	   U32(x0, x1, mark(x2))
744.12/262.95	   U32(active(x0), x1, x2)
744.12/262.95	   U32(x0, active(x1), x2)
744.12/262.95	   U32(x0, x1, active(x2))
744.12/262.95	   U33(mark(x0), x1, x2)
744.12/262.95	   U33(x0, mark(x1), x2)
744.12/262.95	   U33(x0, x1, mark(x2))
744.12/262.95	   U33(active(x0), x1, x2)
744.12/262.95	   U33(x0, active(x1), x2)
744.12/262.95	   U33(x0, x1, active(x2))
744.12/262.95	   U34(mark(x0), x1, x2)
744.12/262.95	   U34(x0, mark(x1), x2)
744.12/262.95	   U34(x0, x1, mark(x2))
744.12/262.95	   U34(active(x0), x1, x2)
744.12/262.95	   U34(x0, active(x1), x2)
744.12/262.95	   U34(x0, x1, active(x2))
744.12/262.95	   U35(mark(x0), x1)
744.12/262.95	   U35(x0, mark(x1))
744.12/262.95	   U35(active(x0), x1)
744.12/262.95	   U35(x0, active(x1))
744.12/262.95	   U36(mark(x0))
744.12/262.95	   U36(active(x0))
744.12/262.95	   U41(mark(x0), x1)
744.12/262.95	   U41(x0, mark(x1))
744.12/262.95	   U41(active(x0), x1)
744.12/262.95	   U41(x0, active(x1))
744.12/262.95	   U42(mark(x0))
744.12/262.95	   U42(active(x0))
744.12/262.95	   U51(mark(x0))
744.12/262.95	   U51(active(x0))
744.12/262.95	   U61(mark(x0), x1)
744.12/262.95	   U61(x0, mark(x1))
744.12/262.95	   U61(active(x0), x1)
744.12/262.95	   U61(x0, active(x1))
744.12/262.95	   U62(mark(x0))
744.12/262.95	   U62(active(x0))
744.12/262.95	   U71(mark(x0), x1)
744.12/262.95	   U71(x0, mark(x1))
744.12/262.95	   U71(active(x0), x1)
744.12/262.95	   U71(x0, active(x1))
744.12/262.95	   U72(mark(x0), x1)
744.12/262.95	   U72(x0, mark(x1))
744.12/262.95	   U72(active(x0), x1)
744.12/262.95	   U72(x0, active(x1))
744.12/262.95	   U81(mark(x0), x1, x2)
744.12/262.95	   U81(x0, mark(x1), x2)
744.12/262.95	   U81(x0, x1, mark(x2))
744.12/262.95	   U81(active(x0), x1, x2)
744.12/262.95	   U81(x0, active(x1), x2)
744.12/262.95	   U81(x0, x1, active(x2))
744.12/262.95	   U82(mark(x0), x1, x2)
744.12/262.95	   U82(x0, mark(x1), x2)
744.12/262.95	   U82(x0, x1, mark(x2))
744.12/262.95	   U82(active(x0), x1, x2)
744.12/262.95	   U82(x0, active(x1), x2)
744.12/262.95	   U82(x0, x1, active(x2))
744.12/262.95	   U83(mark(x0), x1, x2)
744.12/262.95	   U83(x0, mark(x1), x2)
744.12/262.95	   U83(x0, x1, mark(x2))
744.12/262.95	   U83(active(x0), x1, x2)
744.12/262.95	   U83(x0, active(x1), x2)
744.12/262.95	   U83(x0, x1, active(x2))
744.12/262.95	   U84(mark(x0), x1, x2)
744.12/262.95	   U84(x0, mark(x1), x2)
744.12/262.95	   U84(x0, x1, mark(x2))
744.12/262.95	   U84(active(x0), x1, x2)
744.12/262.95	   U84(x0, active(x1), x2)
744.12/262.95	   U84(x0, x1, active(x2))
744.12/262.95	   s(mark(x0))
744.12/262.95	   s(active(x0))
744.12/262.95	   U91(mark(x0), x1)
744.12/262.95	   U91(x0, mark(x1))
744.12/262.95	   U91(active(x0), x1)
744.12/262.95	   U91(x0, active(x1))
744.12/262.95	   U92(mark(x0))
744.12/262.95	   U92(active(x0))
744.12/262.95	
744.12/262.95	We have to consider all minimal (P,Q,R)-chains.
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(232) QReductionProof (EQUIVALENT)
744.12/262.95	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.12/262.95	
744.12/262.95	   U101(mark(x0), x1, x2)
744.12/262.95	   U101(x0, mark(x1), x2)
744.12/262.95	   U101(x0, x1, mark(x2))
744.12/262.95	   U101(active(x0), x1, x2)
744.12/262.95	   U101(x0, active(x1), x2)
744.12/262.95	   U101(x0, x1, active(x2))
744.12/262.95	   U102(mark(x0), x1, x2)
744.12/262.95	   U102(x0, mark(x1), x2)
744.12/262.95	   U102(x0, x1, mark(x2))
744.12/262.95	   U102(active(x0), x1, x2)
744.12/262.95	   U102(x0, active(x1), x2)
744.12/262.95	   U102(x0, x1, active(x2))
744.12/262.95	   isNatKind(mark(x0))
744.12/262.95	   isNatKind(active(x0))
744.12/262.95	   U103(mark(x0), x1, x2)
744.12/262.95	   U103(x0, mark(x1), x2)
744.12/262.95	   U103(x0, x1, mark(x2))
744.12/262.95	   U103(active(x0), x1, x2)
744.12/262.95	   U103(x0, active(x1), x2)
744.12/262.95	   U103(x0, x1, active(x2))
744.12/262.95	   isNat(mark(x0))
744.12/262.95	   isNat(active(x0))
744.12/262.95	   U104(mark(x0), x1, x2)
744.12/262.95	   U104(x0, mark(x1), x2)
744.12/262.95	   U104(x0, x1, mark(x2))
744.12/262.95	   U104(active(x0), x1, x2)
744.12/262.95	   U104(x0, active(x1), x2)
744.12/262.95	   U104(x0, x1, active(x2))
744.12/262.95	   plus(mark(x0), x1)
744.12/262.95	   plus(x0, mark(x1))
744.12/262.95	   plus(active(x0), x1)
744.12/262.95	   plus(x0, active(x1))
744.12/262.95	   x(mark(x0), x1)
744.12/262.95	   x(x0, mark(x1))
744.12/262.95	   x(active(x0), x1)
744.12/262.95	   x(x0, active(x1))
744.12/262.95	   U11(mark(x0), x1, x2)
744.12/262.95	   U11(x0, mark(x1), x2)
744.12/262.95	   U11(x0, x1, mark(x2))
744.12/262.95	   U11(active(x0), x1, x2)
744.12/262.95	   U11(x0, active(x1), x2)
744.12/262.95	   U11(x0, x1, active(x2))
744.12/262.95	   U12(mark(x0), x1, x2)
744.12/262.95	   U12(x0, mark(x1), x2)
744.12/262.95	   U12(x0, x1, mark(x2))
744.12/262.95	   U12(active(x0), x1, x2)
744.12/262.95	   U12(x0, active(x1), x2)
744.12/262.95	   U12(x0, x1, active(x2))
744.12/262.95	   U13(mark(x0), x1, x2)
744.12/262.95	   U13(x0, mark(x1), x2)
744.12/262.95	   U13(x0, x1, mark(x2))
744.12/262.95	   U13(active(x0), x1, x2)
744.12/262.95	   U13(x0, active(x1), x2)
744.12/262.95	   U13(x0, x1, active(x2))
744.12/262.95	   U14(mark(x0), x1, x2)
744.12/262.95	   U14(x0, mark(x1), x2)
744.12/262.95	   U14(x0, x1, mark(x2))
744.12/262.95	   U14(active(x0), x1, x2)
744.12/262.95	   U14(x0, active(x1), x2)
744.12/262.95	   U14(x0, x1, active(x2))
744.12/262.95	   U15(mark(x0), x1)
744.12/262.95	   U15(x0, mark(x1))
744.12/262.95	   U15(active(x0), x1)
744.12/262.95	   U15(x0, active(x1))
744.12/262.95	   U16(mark(x0))
744.12/262.95	   U16(active(x0))
744.12/262.95	   U21(mark(x0), x1)
744.12/262.95	   U21(x0, mark(x1))
744.12/262.95	   U21(active(x0), x1)
744.12/262.95	   U21(x0, active(x1))
744.12/262.95	   U22(mark(x0), x1)
744.12/262.95	   U22(x0, mark(x1))
744.12/262.95	   U22(active(x0), x1)
744.12/262.95	   U22(x0, active(x1))
744.12/262.95	   U23(mark(x0))
744.12/262.95	   U23(active(x0))
744.12/262.95	   U31(mark(x0), x1, x2)
744.12/262.95	   U31(x0, mark(x1), x2)
744.12/262.95	   U31(x0, x1, mark(x2))
744.12/262.95	   U31(active(x0), x1, x2)
744.12/262.95	   U31(x0, active(x1), x2)
744.12/262.95	   U31(x0, x1, active(x2))
744.12/262.95	   U32(mark(x0), x1, x2)
744.12/262.95	   U32(x0, mark(x1), x2)
744.12/262.95	   U32(x0, x1, mark(x2))
744.12/262.95	   U32(active(x0), x1, x2)
744.12/262.95	   U32(x0, active(x1), x2)
744.12/262.95	   U32(x0, x1, active(x2))
744.12/262.95	   U33(mark(x0), x1, x2)
744.12/262.95	   U33(x0, mark(x1), x2)
744.12/262.95	   U33(x0, x1, mark(x2))
744.12/262.95	   U33(active(x0), x1, x2)
744.12/262.95	   U33(x0, active(x1), x2)
744.12/262.95	   U33(x0, x1, active(x2))
744.12/262.95	   U34(mark(x0), x1, x2)
744.12/262.95	   U34(x0, mark(x1), x2)
744.12/262.95	   U34(x0, x1, mark(x2))
744.12/262.95	   U34(active(x0), x1, x2)
744.12/262.95	   U34(x0, active(x1), x2)
744.12/262.95	   U34(x0, x1, active(x2))
744.12/262.95	   U35(mark(x0), x1)
744.12/262.95	   U35(x0, mark(x1))
744.12/262.95	   U35(active(x0), x1)
744.12/262.95	   U35(x0, active(x1))
744.12/262.95	   U36(mark(x0))
744.12/262.95	   U36(active(x0))
744.12/262.95	   U41(mark(x0), x1)
744.12/262.95	   U41(x0, mark(x1))
744.12/262.95	   U41(active(x0), x1)
744.12/262.95	   U41(x0, active(x1))
744.12/262.95	   U42(mark(x0))
744.12/262.95	   U42(active(x0))
744.12/262.95	   U51(mark(x0))
744.12/262.95	   U51(active(x0))
744.12/262.95	   U61(mark(x0), x1)
744.12/262.95	   U61(x0, mark(x1))
744.12/262.95	   U61(active(x0), x1)
744.12/262.95	   U61(x0, active(x1))
744.12/262.95	   U62(mark(x0))
744.12/262.95	   U62(active(x0))
744.12/262.95	   U71(mark(x0), x1)
744.12/262.95	   U71(x0, mark(x1))
744.12/262.95	   U71(active(x0), x1)
744.12/262.95	   U71(x0, active(x1))
744.12/262.95	   U72(mark(x0), x1)
744.12/262.95	   U72(x0, mark(x1))
744.12/262.95	   U72(active(x0), x1)
744.12/262.95	   U72(x0, active(x1))
744.12/262.95	   U81(mark(x0), x1, x2)
744.12/262.95	   U81(x0, mark(x1), x2)
744.12/262.95	   U81(x0, x1, mark(x2))
744.12/262.95	   U81(active(x0), x1, x2)
744.12/262.95	   U81(x0, active(x1), x2)
744.12/262.95	   U81(x0, x1, active(x2))
744.12/262.95	   U82(mark(x0), x1, x2)
744.12/262.95	   U82(x0, mark(x1), x2)
744.12/262.95	   U82(x0, x1, mark(x2))
744.12/262.95	   U82(active(x0), x1, x2)
744.12/262.95	   U82(x0, active(x1), x2)
744.12/262.95	   U82(x0, x1, active(x2))
744.12/262.95	   U83(mark(x0), x1, x2)
744.12/262.95	   U83(x0, mark(x1), x2)
744.12/262.95	   U83(x0, x1, mark(x2))
744.12/262.95	   U83(active(x0), x1, x2)
744.12/262.95	   U83(x0, active(x1), x2)
744.12/262.95	   U83(x0, x1, active(x2))
744.12/262.95	   U84(mark(x0), x1, x2)
744.12/262.95	   U84(x0, mark(x1), x2)
744.12/262.95	   U84(x0, x1, mark(x2))
744.12/262.95	   U84(active(x0), x1, x2)
744.12/262.95	   U84(x0, active(x1), x2)
744.12/262.95	   U84(x0, x1, active(x2))
744.12/262.95	   s(mark(x0))
744.12/262.95	   s(active(x0))
744.12/262.95	   U91(mark(x0), x1)
744.12/262.95	   U91(x0, mark(x1))
744.12/262.95	   U91(active(x0), x1)
744.12/262.95	   U91(x0, active(x1))
744.12/262.95	   U92(mark(x0))
744.12/262.95	   U92(active(x0))
744.12/262.95	
744.12/262.95	
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(233)
744.12/262.95	Obligation:
744.12/262.95	Q DP problem:
744.12/262.95	The TRS P consists of the following rules:
744.12/262.95	
744.12/262.95	   ISNAT(active(X)) -> ISNAT(X)
744.12/262.95	   ISNAT(mark(X)) -> ISNAT(X)
744.12/262.95	
744.12/262.95	R is empty.
744.12/262.95	The set Q consists of the following terms:
744.12/262.95	
744.12/262.95	   active(U101(tt, x0, x1))
744.12/262.95	   active(U102(tt, x0, x1))
744.12/262.95	   active(U103(tt, x0, x1))
744.12/262.95	   active(U104(tt, x0, x1))
744.12/262.95	   active(U11(tt, x0, x1))
744.12/262.95	   active(U12(tt, x0, x1))
744.12/262.95	   active(U13(tt, x0, x1))
744.12/262.95	   active(U14(tt, x0, x1))
744.12/262.95	   active(U15(tt, x0))
744.12/262.95	   active(U16(tt))
744.12/262.95	   active(U21(tt, x0))
744.12/262.95	   active(U22(tt, x0))
744.12/262.95	   active(U23(tt))
744.12/262.95	   active(U31(tt, x0, x1))
744.12/262.95	   active(U32(tt, x0, x1))
744.12/262.95	   active(U33(tt, x0, x1))
744.12/262.95	   active(U34(tt, x0, x1))
744.12/262.95	   active(U35(tt, x0))
744.12/262.95	   active(U36(tt))
744.12/262.95	   active(U41(tt, x0))
744.12/262.95	   active(U42(tt))
744.12/262.95	   active(U51(tt))
744.12/262.95	   active(U61(tt, x0))
744.12/262.95	   active(U62(tt))
744.12/262.95	   active(U71(tt, x0))
744.12/262.95	   active(U72(tt, x0))
744.12/262.95	   active(U81(tt, x0, x1))
744.12/262.95	   active(U82(tt, x0, x1))
744.12/262.95	   active(U83(tt, x0, x1))
744.12/262.95	   active(U84(tt, x0, x1))
744.12/262.95	   active(U91(tt, x0))
744.12/262.95	   active(U92(tt))
744.12/262.95	   active(isNat(0))
744.12/262.95	   active(isNat(plus(x0, x1)))
744.12/262.95	   active(isNat(s(x0)))
744.12/262.95	   active(isNat(x(x0, x1)))
744.12/262.95	   active(isNatKind(0))
744.12/262.95	   active(isNatKind(plus(x0, x1)))
744.12/262.95	   active(isNatKind(s(x0)))
744.12/262.95	   active(isNatKind(x(x0, x1)))
744.12/262.95	   active(plus(x0, 0))
744.12/262.95	   active(plus(x0, s(x1)))
744.12/262.95	   active(x(x0, 0))
744.12/262.95	   active(x(x0, s(x1)))
744.12/262.95	   mark(U101(x0, x1, x2))
744.12/262.95	   mark(tt)
744.12/262.95	   mark(U102(x0, x1, x2))
744.12/262.95	   mark(isNatKind(x0))
744.12/262.95	   mark(U103(x0, x1, x2))
744.12/262.95	   mark(isNat(x0))
744.12/262.95	   mark(U104(x0, x1, x2))
744.12/262.95	   mark(plus(x0, x1))
744.12/262.95	   mark(x(x0, x1))
744.12/262.95	   mark(U11(x0, x1, x2))
744.12/262.95	   mark(U12(x0, x1, x2))
744.12/262.95	   mark(U13(x0, x1, x2))
744.12/262.95	   mark(U14(x0, x1, x2))
744.12/262.95	   mark(U15(x0, x1))
744.12/262.95	   mark(U16(x0))
744.12/262.95	   mark(U21(x0, x1))
744.12/262.95	   mark(U22(x0, x1))
744.12/262.95	   mark(U23(x0))
744.12/262.95	   mark(U31(x0, x1, x2))
744.12/262.95	   mark(U32(x0, x1, x2))
744.12/262.95	   mark(U33(x0, x1, x2))
744.12/262.95	   mark(U34(x0, x1, x2))
744.12/262.95	   mark(U35(x0, x1))
744.12/262.95	   mark(U36(x0))
744.12/262.95	   mark(U41(x0, x1))
744.12/262.95	   mark(U42(x0))
744.12/262.95	   mark(U51(x0))
744.12/262.95	   mark(U61(x0, x1))
744.12/262.95	   mark(U62(x0))
744.12/262.95	   mark(U71(x0, x1))
744.12/262.95	   mark(U72(x0, x1))
744.12/262.95	   mark(U81(x0, x1, x2))
744.12/262.95	   mark(U82(x0, x1, x2))
744.12/262.95	   mark(U83(x0, x1, x2))
744.12/262.95	   mark(U84(x0, x1, x2))
744.12/262.95	   mark(s(x0))
744.12/262.95	   mark(U91(x0, x1))
744.12/262.95	   mark(U92(x0))
744.12/262.95	   mark(0)
744.12/262.95	
744.12/262.95	We have to consider all minimal (P,Q,R)-chains.
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(234) QDPSizeChangeProof (EQUIVALENT)
744.12/262.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
744.12/262.95	
744.12/262.95	From the DPs we obtained the following set of size-change graphs:
744.12/262.95	*ISNAT(active(X)) -> ISNAT(X)
744.12/262.95	The graph contains the following edges 1 > 1
744.12/262.95	
744.12/262.95	
744.12/262.95	*ISNAT(mark(X)) -> ISNAT(X)
744.12/262.95	The graph contains the following edges 1 > 1
744.12/262.95	
744.12/262.95	
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(235)
744.12/262.95	YES
744.12/262.95	
744.12/262.95	----------------------------------------
744.12/262.95	
744.12/262.95	(236)
744.12/262.95	Obligation:
744.12/262.95	Q DP problem:
744.12/262.95	The TRS P consists of the following rules:
744.12/262.95	
744.12/262.95	   U103^1(X1, mark(X2), X3) -> U103^1(X1, X2, X3)
744.12/262.95	   U103^1(mark(X1), X2, X3) -> U103^1(X1, X2, X3)
744.12/262.95	   U103^1(X1, X2, mark(X3)) -> U103^1(X1, X2, X3)
744.12/262.95	   U103^1(active(X1), X2, X3) -> U103^1(X1, X2, X3)
744.12/262.95	   U103^1(X1, active(X2), X3) -> U103^1(X1, X2, X3)
744.12/262.95	   U103^1(X1, X2, active(X3)) -> U103^1(X1, X2, X3)
744.12/262.95	
744.12/262.95	The TRS R consists of the following rules:
744.12/262.95	
744.12/262.95	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.12/262.95	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.12/262.95	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.12/262.95	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.12/262.95	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.12/262.95	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.12/262.95	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.12/262.95	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.12/262.95	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.12/262.95	   active(U16(tt)) -> mark(tt)
744.12/262.95	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.12/262.95	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.12/262.95	   active(U23(tt)) -> mark(tt)
744.12/262.95	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.12/262.95	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.12/262.95	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.12/262.95	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.12/262.95	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.12/262.95	   active(U36(tt)) -> mark(tt)
744.12/262.95	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.12/262.95	   active(U42(tt)) -> mark(tt)
744.12/262.95	   active(U51(tt)) -> mark(tt)
744.12/262.95	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.12/262.95	   active(U62(tt)) -> mark(tt)
744.12/262.95	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.12/262.95	   active(U72(tt, N)) -> mark(N)
744.12/262.95	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.12/262.95	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.12/262.95	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.12/262.95	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.12/262.95	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.12/262.95	   active(U92(tt)) -> mark(0)
744.12/262.95	   active(isNat(0)) -> mark(tt)
744.12/262.95	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.12/262.95	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.12/262.95	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.12/262.95	   active(isNatKind(0)) -> mark(tt)
744.12/262.95	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.12/262.95	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.12/262.95	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.12/262.95	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.12/262.95	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.12/262.95	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.12/262.95	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.12/262.95	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.12/262.95	   mark(tt) -> active(tt)
744.12/262.95	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.12/262.95	   mark(isNatKind(X)) -> active(isNatKind(X))
744.12/262.95	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.12/262.95	   mark(isNat(X)) -> active(isNat(X))
744.12/262.95	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.12/262.95	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.12/262.95	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.12/262.95	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.12/262.95	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.12/262.95	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.12/262.95	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.12/262.95	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.12/262.95	   mark(U16(X)) -> active(U16(mark(X)))
744.12/262.95	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.12/262.95	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.12/262.95	   mark(U23(X)) -> active(U23(mark(X)))
744.12/262.95	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.12/262.95	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.12/262.95	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.12/262.95	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.12/262.95	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.12/262.95	   mark(U36(X)) -> active(U36(mark(X)))
744.12/262.95	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.12/262.95	   mark(U42(X)) -> active(U42(mark(X)))
744.12/262.95	   mark(U51(X)) -> active(U51(mark(X)))
744.12/262.95	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.12/262.95	   mark(U62(X)) -> active(U62(mark(X)))
744.12/262.95	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.12/262.95	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.12/262.95	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.12/262.95	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.12/262.95	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.12/262.95	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.12/262.95	   mark(s(X)) -> active(s(mark(X)))
744.12/262.95	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.12/262.95	   mark(U92(X)) -> active(U92(mark(X)))
744.12/262.95	   mark(0) -> active(0)
744.12/262.95	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.95	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.12/262.95	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.12/262.95	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.12/262.95	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.12/262.95	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.12/262.95	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.95	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.12/262.95	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.12/262.95	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.12/262.95	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.12/262.95	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.12/262.95	   isNatKind(mark(X)) -> isNatKind(X)
744.12/262.95	   isNatKind(active(X)) -> isNatKind(X)
744.12/262.95	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.95	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.12/262.95	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.12/262.95	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.12/262.95	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.12/262.95	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.12/262.95	   isNat(mark(X)) -> isNat(X)
744.12/262.95	   isNat(active(X)) -> isNat(X)
744.12/262.95	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.95	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.12/262.95	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.12/262.95	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.12/262.95	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.12/262.95	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.12/262.95	   plus(mark(X1), X2) -> plus(X1, X2)
744.12/262.95	   plus(X1, mark(X2)) -> plus(X1, X2)
744.12/262.95	   plus(active(X1), X2) -> plus(X1, X2)
744.12/262.95	   plus(X1, active(X2)) -> plus(X1, X2)
744.12/262.95	   x(mark(X1), X2) -> x(X1, X2)
744.12/262.95	   x(X1, mark(X2)) -> x(X1, X2)
744.12/262.95	   x(active(X1), X2) -> x(X1, X2)
744.12/262.95	   x(X1, active(X2)) -> x(X1, X2)
744.12/262.95	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.95	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.12/262.95	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.12/262.95	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.12/262.95	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.12/262.95	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.12/262.95	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.95	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.12/262.95	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.12/262.95	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.12/262.95	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.12/262.95	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.12/262.95	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.95	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.12/262.95	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.12/262.95	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.12/262.95	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.12/262.95	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.12/262.95	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.95	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.12/262.95	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.12/262.95	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.12/262.95	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.12/262.95	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.12/262.95	   U15(mark(X1), X2) -> U15(X1, X2)
744.12/262.95	   U15(X1, mark(X2)) -> U15(X1, X2)
744.12/262.95	   U15(active(X1), X2) -> U15(X1, X2)
744.12/262.95	   U15(X1, active(X2)) -> U15(X1, X2)
744.12/262.95	   U16(mark(X)) -> U16(X)
744.12/262.95	   U16(active(X)) -> U16(X)
744.12/262.95	   U21(mark(X1), X2) -> U21(X1, X2)
744.12/262.95	   U21(X1, mark(X2)) -> U21(X1, X2)
744.12/262.95	   U21(active(X1), X2) -> U21(X1, X2)
744.12/262.95	   U21(X1, active(X2)) -> U21(X1, X2)
744.12/262.95	   U22(mark(X1), X2) -> U22(X1, X2)
744.12/262.95	   U22(X1, mark(X2)) -> U22(X1, X2)
744.12/262.95	   U22(active(X1), X2) -> U22(X1, X2)
744.12/262.95	   U22(X1, active(X2)) -> U22(X1, X2)
744.12/262.95	   U23(mark(X)) -> U23(X)
744.12/262.95	   U23(active(X)) -> U23(X)
744.12/262.95	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.95	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.12/262.95	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.12/262.95	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.12/262.95	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.12/262.95	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.12/262.95	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.95	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.12/262.95	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.12/262.95	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.12/262.95	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.12/262.95	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.12/262.95	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.95	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.12/262.95	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.12/262.95	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.12/262.95	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.12/262.95	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.12/262.95	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.95	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.12/262.95	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.12/262.95	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.12/262.95	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.12/262.95	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.12/262.95	   U35(mark(X1), X2) -> U35(X1, X2)
744.12/262.95	   U35(X1, mark(X2)) -> U35(X1, X2)
744.12/262.95	   U35(active(X1), X2) -> U35(X1, X2)
744.12/262.95	   U35(X1, active(X2)) -> U35(X1, X2)
744.12/262.95	   U36(mark(X)) -> U36(X)
744.12/262.95	   U36(active(X)) -> U36(X)
744.12/262.95	   U41(mark(X1), X2) -> U41(X1, X2)
744.12/262.95	   U41(X1, mark(X2)) -> U41(X1, X2)
744.12/262.95	   U41(active(X1), X2) -> U41(X1, X2)
744.12/262.95	   U41(X1, active(X2)) -> U41(X1, X2)
744.12/262.95	   U42(mark(X)) -> U42(X)
744.12/262.95	   U42(active(X)) -> U42(X)
744.12/262.95	   U51(mark(X)) -> U51(X)
744.12/262.95	   U51(active(X)) -> U51(X)
744.12/262.95	   U61(mark(X1), X2) -> U61(X1, X2)
744.12/262.95	   U61(X1, mark(X2)) -> U61(X1, X2)
744.12/262.95	   U61(active(X1), X2) -> U61(X1, X2)
744.12/262.95	   U61(X1, active(X2)) -> U61(X1, X2)
744.12/262.95	   U62(mark(X)) -> U62(X)
744.12/262.95	   U62(active(X)) -> U62(X)
744.12/262.95	   U71(mark(X1), X2) -> U71(X1, X2)
744.12/262.95	   U71(X1, mark(X2)) -> U71(X1, X2)
744.12/262.95	   U71(active(X1), X2) -> U71(X1, X2)
744.12/262.95	   U71(X1, active(X2)) -> U71(X1, X2)
744.12/262.95	   U72(mark(X1), X2) -> U72(X1, X2)
744.12/262.95	   U72(X1, mark(X2)) -> U72(X1, X2)
744.12/262.95	   U72(active(X1), X2) -> U72(X1, X2)
744.12/262.95	   U72(X1, active(X2)) -> U72(X1, X2)
744.12/262.95	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.95	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.12/262.95	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.12/262.95	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.12/262.95	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.12/262.95	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.12/262.95	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.95	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.12/262.95	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.12/262.95	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.12/262.95	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.12/262.95	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.12/262.95	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.95	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.12/262.95	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.12/262.95	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.12/262.95	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.12/262.95	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.12/262.95	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.95	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.12/262.95	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.12/262.95	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.12/262.95	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.12/262.95	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.12/262.95	   s(mark(X)) -> s(X)
744.12/262.95	   s(active(X)) -> s(X)
744.12/262.95	   U91(mark(X1), X2) -> U91(X1, X2)
744.12/262.95	   U91(X1, mark(X2)) -> U91(X1, X2)
744.12/262.95	   U91(active(X1), X2) -> U91(X1, X2)
744.12/262.95	   U91(X1, active(X2)) -> U91(X1, X2)
744.12/262.95	   U92(mark(X)) -> U92(X)
744.12/262.95	   U92(active(X)) -> U92(X)
744.12/262.95	
744.12/262.95	The set Q consists of the following terms:
744.12/262.95	
744.12/262.95	   active(U101(tt, x0, x1))
744.12/262.95	   active(U102(tt, x0, x1))
744.12/262.95	   active(U103(tt, x0, x1))
744.12/262.95	   active(U104(tt, x0, x1))
744.12/262.95	   active(U11(tt, x0, x1))
744.12/262.95	   active(U12(tt, x0, x1))
744.12/262.95	   active(U13(tt, x0, x1))
744.12/262.95	   active(U14(tt, x0, x1))
744.12/262.95	   active(U15(tt, x0))
744.12/262.95	   active(U16(tt))
744.12/262.95	   active(U21(tt, x0))
744.12/262.95	   active(U22(tt, x0))
744.12/262.95	   active(U23(tt))
744.12/262.95	   active(U31(tt, x0, x1))
744.12/262.95	   active(U32(tt, x0, x1))
744.12/262.95	   active(U33(tt, x0, x1))
744.12/262.95	   active(U34(tt, x0, x1))
744.12/262.95	   active(U35(tt, x0))
744.12/262.95	   active(U36(tt))
744.12/262.95	   active(U41(tt, x0))
744.12/262.95	   active(U42(tt))
744.12/262.95	   active(U51(tt))
744.12/262.95	   active(U61(tt, x0))
744.12/262.95	   active(U62(tt))
744.12/262.95	   active(U71(tt, x0))
744.12/262.95	   active(U72(tt, x0))
744.12/262.95	   active(U81(tt, x0, x1))
744.12/262.95	   active(U82(tt, x0, x1))
744.12/262.95	   active(U83(tt, x0, x1))
744.12/262.95	   active(U84(tt, x0, x1))
744.12/262.95	   active(U91(tt, x0))
744.12/262.95	   active(U92(tt))
744.12/262.95	   active(isNat(0))
744.12/262.95	   active(isNat(plus(x0, x1)))
744.12/262.95	   active(isNat(s(x0)))
744.12/262.95	   active(isNat(x(x0, x1)))
744.12/262.95	   active(isNatKind(0))
744.12/262.95	   active(isNatKind(plus(x0, x1)))
744.12/262.95	   active(isNatKind(s(x0)))
744.12/262.95	   active(isNatKind(x(x0, x1)))
744.12/262.95	   active(plus(x0, 0))
744.12/262.95	   active(plus(x0, s(x1)))
744.12/262.95	   active(x(x0, 0))
744.12/262.95	   active(x(x0, s(x1)))
744.12/262.95	   mark(U101(x0, x1, x2))
744.12/262.95	   mark(tt)
744.12/262.95	   mark(U102(x0, x1, x2))
744.12/262.95	   mark(isNatKind(x0))
744.12/262.95	   mark(U103(x0, x1, x2))
744.12/262.95	   mark(isNat(x0))
744.12/262.95	   mark(U104(x0, x1, x2))
744.12/262.95	   mark(plus(x0, x1))
744.12/262.95	   mark(x(x0, x1))
744.12/262.95	   mark(U11(x0, x1, x2))
744.12/262.95	   mark(U12(x0, x1, x2))
744.12/262.95	   mark(U13(x0, x1, x2))
744.12/262.95	   mark(U14(x0, x1, x2))
744.12/262.95	   mark(U15(x0, x1))
744.12/262.95	   mark(U16(x0))
744.12/262.95	   mark(U21(x0, x1))
744.12/262.95	   mark(U22(x0, x1))
744.12/262.95	   mark(U23(x0))
744.12/262.95	   mark(U31(x0, x1, x2))
744.12/262.95	   mark(U32(x0, x1, x2))
744.12/262.95	   mark(U33(x0, x1, x2))
744.12/262.95	   mark(U34(x0, x1, x2))
744.12/262.95	   mark(U35(x0, x1))
744.12/262.95	   mark(U36(x0))
744.12/262.95	   mark(U41(x0, x1))
744.12/262.95	   mark(U42(x0))
744.12/262.95	   mark(U51(x0))
744.12/262.95	   mark(U61(x0, x1))
744.12/262.95	   mark(U62(x0))
744.12/262.95	   mark(U71(x0, x1))
744.12/262.95	   mark(U72(x0, x1))
744.12/262.95	   mark(U81(x0, x1, x2))
744.12/262.95	   mark(U82(x0, x1, x2))
744.12/262.95	   mark(U83(x0, x1, x2))
744.12/262.95	   mark(U84(x0, x1, x2))
744.12/262.95	   mark(s(x0))
744.12/262.95	   mark(U91(x0, x1))
744.12/262.95	   mark(U92(x0))
744.12/262.95	   mark(0)
744.12/262.95	   U101(mark(x0), x1, x2)
744.12/262.95	   U101(x0, mark(x1), x2)
744.12/262.95	   U101(x0, x1, mark(x2))
744.12/262.95	   U101(active(x0), x1, x2)
744.12/262.95	   U101(x0, active(x1), x2)
744.12/262.95	   U101(x0, x1, active(x2))
744.12/262.95	   U102(mark(x0), x1, x2)
744.12/262.95	   U102(x0, mark(x1), x2)
744.12/262.95	   U102(x0, x1, mark(x2))
744.12/262.95	   U102(active(x0), x1, x2)
744.12/262.95	   U102(x0, active(x1), x2)
744.12/262.95	   U102(x0, x1, active(x2))
744.12/262.95	   isNatKind(mark(x0))
744.12/262.95	   isNatKind(active(x0))
744.12/262.95	   U103(mark(x0), x1, x2)
744.12/262.95	   U103(x0, mark(x1), x2)
744.12/262.95	   U103(x0, x1, mark(x2))
744.12/262.95	   U103(active(x0), x1, x2)
744.12/262.95	   U103(x0, active(x1), x2)
744.12/262.95	   U103(x0, x1, active(x2))
744.12/262.95	   isNat(mark(x0))
744.12/262.95	   isNat(active(x0))
744.12/262.95	   U104(mark(x0), x1, x2)
744.12/262.95	   U104(x0, mark(x1), x2)
744.12/262.95	   U104(x0, x1, mark(x2))
744.12/262.95	   U104(active(x0), x1, x2)
744.12/262.95	   U104(x0, active(x1), x2)
744.12/262.95	   U104(x0, x1, active(x2))
744.12/262.95	   plus(mark(x0), x1)
744.12/262.95	   plus(x0, mark(x1))
744.12/262.95	   plus(active(x0), x1)
744.12/262.95	   plus(x0, active(x1))
744.12/262.95	   x(mark(x0), x1)
744.12/262.95	   x(x0, mark(x1))
744.12/262.95	   x(active(x0), x1)
744.12/262.95	   x(x0, active(x1))
744.12/262.95	   U11(mark(x0), x1, x2)
744.12/262.95	   U11(x0, mark(x1), x2)
744.20/262.95	   U11(x0, x1, mark(x2))
744.20/262.95	   U11(active(x0), x1, x2)
744.20/262.95	   U11(x0, active(x1), x2)
744.20/262.95	   U11(x0, x1, active(x2))
744.20/262.95	   U12(mark(x0), x1, x2)
744.20/262.95	   U12(x0, mark(x1), x2)
744.20/262.95	   U12(x0, x1, mark(x2))
744.20/262.95	   U12(active(x0), x1, x2)
744.20/262.95	   U12(x0, active(x1), x2)
744.20/262.95	   U12(x0, x1, active(x2))
744.20/262.95	   U13(mark(x0), x1, x2)
744.20/262.95	   U13(x0, mark(x1), x2)
744.20/262.95	   U13(x0, x1, mark(x2))
744.20/262.95	   U13(active(x0), x1, x2)
744.20/262.95	   U13(x0, active(x1), x2)
744.20/262.95	   U13(x0, x1, active(x2))
744.20/262.95	   U14(mark(x0), x1, x2)
744.20/262.95	   U14(x0, mark(x1), x2)
744.20/262.95	   U14(x0, x1, mark(x2))
744.20/262.95	   U14(active(x0), x1, x2)
744.20/262.95	   U14(x0, active(x1), x2)
744.20/262.95	   U14(x0, x1, active(x2))
744.20/262.95	   U15(mark(x0), x1)
744.20/262.95	   U15(x0, mark(x1))
744.20/262.95	   U15(active(x0), x1)
744.20/262.95	   U15(x0, active(x1))
744.20/262.95	   U16(mark(x0))
744.20/262.95	   U16(active(x0))
744.20/262.95	   U21(mark(x0), x1)
744.20/262.95	   U21(x0, mark(x1))
744.20/262.95	   U21(active(x0), x1)
744.20/262.95	   U21(x0, active(x1))
744.20/262.95	   U22(mark(x0), x1)
744.20/262.95	   U22(x0, mark(x1))
744.20/262.95	   U22(active(x0), x1)
744.20/262.95	   U22(x0, active(x1))
744.20/262.95	   U23(mark(x0))
744.20/262.95	   U23(active(x0))
744.20/262.95	   U31(mark(x0), x1, x2)
744.20/262.95	   U31(x0, mark(x1), x2)
744.20/262.95	   U31(x0, x1, mark(x2))
744.20/262.95	   U31(active(x0), x1, x2)
744.20/262.95	   U31(x0, active(x1), x2)
744.20/262.95	   U31(x0, x1, active(x2))
744.20/262.95	   U32(mark(x0), x1, x2)
744.20/262.95	   U32(x0, mark(x1), x2)
744.20/262.95	   U32(x0, x1, mark(x2))
744.20/262.95	   U32(active(x0), x1, x2)
744.20/262.95	   U32(x0, active(x1), x2)
744.20/262.95	   U32(x0, x1, active(x2))
744.20/262.95	   U33(mark(x0), x1, x2)
744.20/262.95	   U33(x0, mark(x1), x2)
744.20/262.95	   U33(x0, x1, mark(x2))
744.20/262.95	   U33(active(x0), x1, x2)
744.20/262.95	   U33(x0, active(x1), x2)
744.20/262.95	   U33(x0, x1, active(x2))
744.20/262.95	   U34(mark(x0), x1, x2)
744.20/262.95	   U34(x0, mark(x1), x2)
744.20/262.95	   U34(x0, x1, mark(x2))
744.20/262.95	   U34(active(x0), x1, x2)
744.20/262.95	   U34(x0, active(x1), x2)
744.20/262.95	   U34(x0, x1, active(x2))
744.20/262.95	   U35(mark(x0), x1)
744.20/262.95	   U35(x0, mark(x1))
744.20/262.95	   U35(active(x0), x1)
744.20/262.95	   U35(x0, active(x1))
744.20/262.95	   U36(mark(x0))
744.20/262.95	   U36(active(x0))
744.20/262.95	   U41(mark(x0), x1)
744.20/262.95	   U41(x0, mark(x1))
744.20/262.95	   U41(active(x0), x1)
744.20/262.95	   U41(x0, active(x1))
744.20/262.95	   U42(mark(x0))
744.20/262.95	   U42(active(x0))
744.20/262.95	   U51(mark(x0))
744.20/262.95	   U51(active(x0))
744.20/262.95	   U61(mark(x0), x1)
744.20/262.95	   U61(x0, mark(x1))
744.20/262.95	   U61(active(x0), x1)
744.20/262.95	   U61(x0, active(x1))
744.20/262.95	   U62(mark(x0))
744.20/262.95	   U62(active(x0))
744.20/262.95	   U71(mark(x0), x1)
744.20/262.95	   U71(x0, mark(x1))
744.20/262.95	   U71(active(x0), x1)
744.20/262.95	   U71(x0, active(x1))
744.20/262.95	   U72(mark(x0), x1)
744.20/262.95	   U72(x0, mark(x1))
744.20/262.95	   U72(active(x0), x1)
744.20/262.95	   U72(x0, active(x1))
744.20/262.95	   U81(mark(x0), x1, x2)
744.20/262.95	   U81(x0, mark(x1), x2)
744.20/262.95	   U81(x0, x1, mark(x2))
744.20/262.95	   U81(active(x0), x1, x2)
744.20/262.95	   U81(x0, active(x1), x2)
744.20/262.95	   U81(x0, x1, active(x2))
744.20/262.95	   U82(mark(x0), x1, x2)
744.20/262.95	   U82(x0, mark(x1), x2)
744.20/262.95	   U82(x0, x1, mark(x2))
744.20/262.95	   U82(active(x0), x1, x2)
744.20/262.95	   U82(x0, active(x1), x2)
744.20/262.95	   U82(x0, x1, active(x2))
744.20/262.95	   U83(mark(x0), x1, x2)
744.20/262.95	   U83(x0, mark(x1), x2)
744.20/262.95	   U83(x0, x1, mark(x2))
744.20/262.95	   U83(active(x0), x1, x2)
744.20/262.95	   U83(x0, active(x1), x2)
744.20/262.95	   U83(x0, x1, active(x2))
744.20/262.95	   U84(mark(x0), x1, x2)
744.20/262.95	   U84(x0, mark(x1), x2)
744.20/262.95	   U84(x0, x1, mark(x2))
744.20/262.95	   U84(active(x0), x1, x2)
744.20/262.95	   U84(x0, active(x1), x2)
744.20/262.95	   U84(x0, x1, active(x2))
744.20/262.95	   s(mark(x0))
744.20/262.95	   s(active(x0))
744.20/262.95	   U91(mark(x0), x1)
744.20/262.95	   U91(x0, mark(x1))
744.20/262.95	   U91(active(x0), x1)
744.20/262.95	   U91(x0, active(x1))
744.20/262.95	   U92(mark(x0))
744.20/262.95	   U92(active(x0))
744.20/262.95	
744.20/262.95	We have to consider all minimal (P,Q,R)-chains.
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(237) UsableRulesProof (EQUIVALENT)
744.20/262.95	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.
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(238)
744.20/262.95	Obligation:
744.20/262.95	Q DP problem:
744.20/262.95	The TRS P consists of the following rules:
744.20/262.95	
744.20/262.95	   U103^1(X1, mark(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(mark(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, X2, mark(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(active(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, active(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, X2, active(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	
744.20/262.95	R is empty.
744.20/262.95	The set Q consists of the following terms:
744.20/262.95	
744.20/262.95	   active(U101(tt, x0, x1))
744.20/262.95	   active(U102(tt, x0, x1))
744.20/262.95	   active(U103(tt, x0, x1))
744.20/262.95	   active(U104(tt, x0, x1))
744.20/262.95	   active(U11(tt, x0, x1))
744.20/262.95	   active(U12(tt, x0, x1))
744.20/262.95	   active(U13(tt, x0, x1))
744.20/262.95	   active(U14(tt, x0, x1))
744.20/262.95	   active(U15(tt, x0))
744.20/262.95	   active(U16(tt))
744.20/262.95	   active(U21(tt, x0))
744.20/262.95	   active(U22(tt, x0))
744.20/262.95	   active(U23(tt))
744.20/262.95	   active(U31(tt, x0, x1))
744.20/262.95	   active(U32(tt, x0, x1))
744.20/262.95	   active(U33(tt, x0, x1))
744.20/262.95	   active(U34(tt, x0, x1))
744.20/262.95	   active(U35(tt, x0))
744.20/262.95	   active(U36(tt))
744.20/262.95	   active(U41(tt, x0))
744.20/262.95	   active(U42(tt))
744.20/262.95	   active(U51(tt))
744.20/262.95	   active(U61(tt, x0))
744.20/262.95	   active(U62(tt))
744.20/262.95	   active(U71(tt, x0))
744.20/262.95	   active(U72(tt, x0))
744.20/262.95	   active(U81(tt, x0, x1))
744.20/262.95	   active(U82(tt, x0, x1))
744.20/262.95	   active(U83(tt, x0, x1))
744.20/262.95	   active(U84(tt, x0, x1))
744.20/262.95	   active(U91(tt, x0))
744.20/262.95	   active(U92(tt))
744.20/262.95	   active(isNat(0))
744.20/262.95	   active(isNat(plus(x0, x1)))
744.20/262.95	   active(isNat(s(x0)))
744.20/262.95	   active(isNat(x(x0, x1)))
744.20/262.95	   active(isNatKind(0))
744.20/262.95	   active(isNatKind(plus(x0, x1)))
744.20/262.95	   active(isNatKind(s(x0)))
744.20/262.95	   active(isNatKind(x(x0, x1)))
744.20/262.95	   active(plus(x0, 0))
744.20/262.95	   active(plus(x0, s(x1)))
744.20/262.95	   active(x(x0, 0))
744.20/262.95	   active(x(x0, s(x1)))
744.20/262.95	   mark(U101(x0, x1, x2))
744.20/262.95	   mark(tt)
744.20/262.95	   mark(U102(x0, x1, x2))
744.20/262.95	   mark(isNatKind(x0))
744.20/262.95	   mark(U103(x0, x1, x2))
744.20/262.95	   mark(isNat(x0))
744.20/262.95	   mark(U104(x0, x1, x2))
744.20/262.95	   mark(plus(x0, x1))
744.20/262.95	   mark(x(x0, x1))
744.20/262.95	   mark(U11(x0, x1, x2))
744.20/262.95	   mark(U12(x0, x1, x2))
744.20/262.95	   mark(U13(x0, x1, x2))
744.20/262.95	   mark(U14(x0, x1, x2))
744.20/262.95	   mark(U15(x0, x1))
744.20/262.95	   mark(U16(x0))
744.20/262.95	   mark(U21(x0, x1))
744.20/262.95	   mark(U22(x0, x1))
744.20/262.95	   mark(U23(x0))
744.20/262.95	   mark(U31(x0, x1, x2))
744.20/262.95	   mark(U32(x0, x1, x2))
744.20/262.95	   mark(U33(x0, x1, x2))
744.20/262.95	   mark(U34(x0, x1, x2))
744.20/262.95	   mark(U35(x0, x1))
744.20/262.95	   mark(U36(x0))
744.20/262.95	   mark(U41(x0, x1))
744.20/262.95	   mark(U42(x0))
744.20/262.95	   mark(U51(x0))
744.20/262.95	   mark(U61(x0, x1))
744.20/262.95	   mark(U62(x0))
744.20/262.95	   mark(U71(x0, x1))
744.20/262.95	   mark(U72(x0, x1))
744.20/262.95	   mark(U81(x0, x1, x2))
744.20/262.95	   mark(U82(x0, x1, x2))
744.20/262.95	   mark(U83(x0, x1, x2))
744.20/262.95	   mark(U84(x0, x1, x2))
744.20/262.95	   mark(s(x0))
744.20/262.95	   mark(U91(x0, x1))
744.20/262.95	   mark(U92(x0))
744.20/262.95	   mark(0)
744.20/262.95	   U101(mark(x0), x1, x2)
744.20/262.95	   U101(x0, mark(x1), x2)
744.20/262.95	   U101(x0, x1, mark(x2))
744.20/262.95	   U101(active(x0), x1, x2)
744.20/262.95	   U101(x0, active(x1), x2)
744.20/262.95	   U101(x0, x1, active(x2))
744.20/262.95	   U102(mark(x0), x1, x2)
744.20/262.95	   U102(x0, mark(x1), x2)
744.20/262.95	   U102(x0, x1, mark(x2))
744.20/262.95	   U102(active(x0), x1, x2)
744.20/262.95	   U102(x0, active(x1), x2)
744.20/262.95	   U102(x0, x1, active(x2))
744.20/262.95	   isNatKind(mark(x0))
744.20/262.95	   isNatKind(active(x0))
744.20/262.95	   U103(mark(x0), x1, x2)
744.20/262.95	   U103(x0, mark(x1), x2)
744.20/262.95	   U103(x0, x1, mark(x2))
744.20/262.95	   U103(active(x0), x1, x2)
744.20/262.95	   U103(x0, active(x1), x2)
744.20/262.95	   U103(x0, x1, active(x2))
744.20/262.95	   isNat(mark(x0))
744.20/262.95	   isNat(active(x0))
744.20/262.95	   U104(mark(x0), x1, x2)
744.20/262.95	   U104(x0, mark(x1), x2)
744.20/262.95	   U104(x0, x1, mark(x2))
744.20/262.95	   U104(active(x0), x1, x2)
744.20/262.95	   U104(x0, active(x1), x2)
744.20/262.95	   U104(x0, x1, active(x2))
744.20/262.95	   plus(mark(x0), x1)
744.20/262.95	   plus(x0, mark(x1))
744.20/262.95	   plus(active(x0), x1)
744.20/262.95	   plus(x0, active(x1))
744.20/262.95	   x(mark(x0), x1)
744.20/262.95	   x(x0, mark(x1))
744.20/262.95	   x(active(x0), x1)
744.20/262.95	   x(x0, active(x1))
744.20/262.95	   U11(mark(x0), x1, x2)
744.20/262.95	   U11(x0, mark(x1), x2)
744.20/262.95	   U11(x0, x1, mark(x2))
744.20/262.95	   U11(active(x0), x1, x2)
744.20/262.95	   U11(x0, active(x1), x2)
744.20/262.95	   U11(x0, x1, active(x2))
744.20/262.95	   U12(mark(x0), x1, x2)
744.20/262.95	   U12(x0, mark(x1), x2)
744.20/262.95	   U12(x0, x1, mark(x2))
744.20/262.95	   U12(active(x0), x1, x2)
744.20/262.95	   U12(x0, active(x1), x2)
744.20/262.95	   U12(x0, x1, active(x2))
744.20/262.95	   U13(mark(x0), x1, x2)
744.20/262.95	   U13(x0, mark(x1), x2)
744.20/262.95	   U13(x0, x1, mark(x2))
744.20/262.95	   U13(active(x0), x1, x2)
744.20/262.95	   U13(x0, active(x1), x2)
744.20/262.95	   U13(x0, x1, active(x2))
744.20/262.95	   U14(mark(x0), x1, x2)
744.20/262.95	   U14(x0, mark(x1), x2)
744.20/262.95	   U14(x0, x1, mark(x2))
744.20/262.95	   U14(active(x0), x1, x2)
744.20/262.95	   U14(x0, active(x1), x2)
744.20/262.95	   U14(x0, x1, active(x2))
744.20/262.95	   U15(mark(x0), x1)
744.20/262.95	   U15(x0, mark(x1))
744.20/262.95	   U15(active(x0), x1)
744.20/262.95	   U15(x0, active(x1))
744.20/262.95	   U16(mark(x0))
744.20/262.95	   U16(active(x0))
744.20/262.95	   U21(mark(x0), x1)
744.20/262.95	   U21(x0, mark(x1))
744.20/262.95	   U21(active(x0), x1)
744.20/262.95	   U21(x0, active(x1))
744.20/262.95	   U22(mark(x0), x1)
744.20/262.95	   U22(x0, mark(x1))
744.20/262.95	   U22(active(x0), x1)
744.20/262.95	   U22(x0, active(x1))
744.20/262.95	   U23(mark(x0))
744.20/262.95	   U23(active(x0))
744.20/262.95	   U31(mark(x0), x1, x2)
744.20/262.95	   U31(x0, mark(x1), x2)
744.20/262.95	   U31(x0, x1, mark(x2))
744.20/262.95	   U31(active(x0), x1, x2)
744.20/262.95	   U31(x0, active(x1), x2)
744.20/262.95	   U31(x0, x1, active(x2))
744.20/262.95	   U32(mark(x0), x1, x2)
744.20/262.95	   U32(x0, mark(x1), x2)
744.20/262.95	   U32(x0, x1, mark(x2))
744.20/262.95	   U32(active(x0), x1, x2)
744.20/262.95	   U32(x0, active(x1), x2)
744.20/262.95	   U32(x0, x1, active(x2))
744.20/262.95	   U33(mark(x0), x1, x2)
744.20/262.95	   U33(x0, mark(x1), x2)
744.20/262.95	   U33(x0, x1, mark(x2))
744.20/262.95	   U33(active(x0), x1, x2)
744.20/262.95	   U33(x0, active(x1), x2)
744.20/262.95	   U33(x0, x1, active(x2))
744.20/262.95	   U34(mark(x0), x1, x2)
744.20/262.95	   U34(x0, mark(x1), x2)
744.20/262.95	   U34(x0, x1, mark(x2))
744.20/262.95	   U34(active(x0), x1, x2)
744.20/262.95	   U34(x0, active(x1), x2)
744.20/262.95	   U34(x0, x1, active(x2))
744.20/262.95	   U35(mark(x0), x1)
744.20/262.95	   U35(x0, mark(x1))
744.20/262.95	   U35(active(x0), x1)
744.20/262.95	   U35(x0, active(x1))
744.20/262.95	   U36(mark(x0))
744.20/262.95	   U36(active(x0))
744.20/262.95	   U41(mark(x0), x1)
744.20/262.95	   U41(x0, mark(x1))
744.20/262.95	   U41(active(x0), x1)
744.20/262.95	   U41(x0, active(x1))
744.20/262.95	   U42(mark(x0))
744.20/262.95	   U42(active(x0))
744.20/262.95	   U51(mark(x0))
744.20/262.95	   U51(active(x0))
744.20/262.95	   U61(mark(x0), x1)
744.20/262.95	   U61(x0, mark(x1))
744.20/262.95	   U61(active(x0), x1)
744.20/262.95	   U61(x0, active(x1))
744.20/262.95	   U62(mark(x0))
744.20/262.95	   U62(active(x0))
744.20/262.95	   U71(mark(x0), x1)
744.20/262.95	   U71(x0, mark(x1))
744.20/262.95	   U71(active(x0), x1)
744.20/262.95	   U71(x0, active(x1))
744.20/262.95	   U72(mark(x0), x1)
744.20/262.95	   U72(x0, mark(x1))
744.20/262.95	   U72(active(x0), x1)
744.20/262.95	   U72(x0, active(x1))
744.20/262.95	   U81(mark(x0), x1, x2)
744.20/262.95	   U81(x0, mark(x1), x2)
744.20/262.95	   U81(x0, x1, mark(x2))
744.20/262.95	   U81(active(x0), x1, x2)
744.20/262.95	   U81(x0, active(x1), x2)
744.20/262.95	   U81(x0, x1, active(x2))
744.20/262.95	   U82(mark(x0), x1, x2)
744.20/262.95	   U82(x0, mark(x1), x2)
744.20/262.95	   U82(x0, x1, mark(x2))
744.20/262.95	   U82(active(x0), x1, x2)
744.20/262.95	   U82(x0, active(x1), x2)
744.20/262.95	   U82(x0, x1, active(x2))
744.20/262.95	   U83(mark(x0), x1, x2)
744.20/262.95	   U83(x0, mark(x1), x2)
744.20/262.95	   U83(x0, x1, mark(x2))
744.20/262.95	   U83(active(x0), x1, x2)
744.20/262.95	   U83(x0, active(x1), x2)
744.20/262.95	   U83(x0, x1, active(x2))
744.20/262.95	   U84(mark(x0), x1, x2)
744.20/262.95	   U84(x0, mark(x1), x2)
744.20/262.95	   U84(x0, x1, mark(x2))
744.20/262.95	   U84(active(x0), x1, x2)
744.20/262.95	   U84(x0, active(x1), x2)
744.20/262.95	   U84(x0, x1, active(x2))
744.20/262.95	   s(mark(x0))
744.20/262.95	   s(active(x0))
744.20/262.95	   U91(mark(x0), x1)
744.20/262.95	   U91(x0, mark(x1))
744.20/262.95	   U91(active(x0), x1)
744.20/262.95	   U91(x0, active(x1))
744.20/262.95	   U92(mark(x0))
744.20/262.95	   U92(active(x0))
744.20/262.95	
744.20/262.95	We have to consider all minimal (P,Q,R)-chains.
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(239) QReductionProof (EQUIVALENT)
744.20/262.95	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.20/262.95	
744.20/262.95	   U101(mark(x0), x1, x2)
744.20/262.95	   U101(x0, mark(x1), x2)
744.20/262.95	   U101(x0, x1, mark(x2))
744.20/262.95	   U101(active(x0), x1, x2)
744.20/262.95	   U101(x0, active(x1), x2)
744.20/262.95	   U101(x0, x1, active(x2))
744.20/262.95	   U102(mark(x0), x1, x2)
744.20/262.95	   U102(x0, mark(x1), x2)
744.20/262.95	   U102(x0, x1, mark(x2))
744.20/262.95	   U102(active(x0), x1, x2)
744.20/262.95	   U102(x0, active(x1), x2)
744.20/262.95	   U102(x0, x1, active(x2))
744.20/262.95	   isNatKind(mark(x0))
744.20/262.95	   isNatKind(active(x0))
744.20/262.95	   U103(mark(x0), x1, x2)
744.20/262.95	   U103(x0, mark(x1), x2)
744.20/262.95	   U103(x0, x1, mark(x2))
744.20/262.95	   U103(active(x0), x1, x2)
744.20/262.95	   U103(x0, active(x1), x2)
744.20/262.95	   U103(x0, x1, active(x2))
744.20/262.95	   isNat(mark(x0))
744.20/262.95	   isNat(active(x0))
744.20/262.95	   U104(mark(x0), x1, x2)
744.20/262.95	   U104(x0, mark(x1), x2)
744.20/262.95	   U104(x0, x1, mark(x2))
744.20/262.95	   U104(active(x0), x1, x2)
744.20/262.95	   U104(x0, active(x1), x2)
744.20/262.95	   U104(x0, x1, active(x2))
744.20/262.95	   plus(mark(x0), x1)
744.20/262.95	   plus(x0, mark(x1))
744.20/262.95	   plus(active(x0), x1)
744.20/262.95	   plus(x0, active(x1))
744.20/262.95	   x(mark(x0), x1)
744.20/262.95	   x(x0, mark(x1))
744.20/262.95	   x(active(x0), x1)
744.20/262.95	   x(x0, active(x1))
744.20/262.95	   U11(mark(x0), x1, x2)
744.20/262.95	   U11(x0, mark(x1), x2)
744.20/262.95	   U11(x0, x1, mark(x2))
744.20/262.95	   U11(active(x0), x1, x2)
744.20/262.95	   U11(x0, active(x1), x2)
744.20/262.95	   U11(x0, x1, active(x2))
744.20/262.95	   U12(mark(x0), x1, x2)
744.20/262.95	   U12(x0, mark(x1), x2)
744.20/262.95	   U12(x0, x1, mark(x2))
744.20/262.95	   U12(active(x0), x1, x2)
744.20/262.95	   U12(x0, active(x1), x2)
744.20/262.95	   U12(x0, x1, active(x2))
744.20/262.95	   U13(mark(x0), x1, x2)
744.20/262.95	   U13(x0, mark(x1), x2)
744.20/262.95	   U13(x0, x1, mark(x2))
744.20/262.95	   U13(active(x0), x1, x2)
744.20/262.95	   U13(x0, active(x1), x2)
744.20/262.95	   U13(x0, x1, active(x2))
744.20/262.95	   U14(mark(x0), x1, x2)
744.20/262.95	   U14(x0, mark(x1), x2)
744.20/262.95	   U14(x0, x1, mark(x2))
744.20/262.95	   U14(active(x0), x1, x2)
744.20/262.95	   U14(x0, active(x1), x2)
744.20/262.95	   U14(x0, x1, active(x2))
744.20/262.95	   U15(mark(x0), x1)
744.20/262.95	   U15(x0, mark(x1))
744.20/262.95	   U15(active(x0), x1)
744.20/262.95	   U15(x0, active(x1))
744.20/262.95	   U16(mark(x0))
744.20/262.95	   U16(active(x0))
744.20/262.95	   U21(mark(x0), x1)
744.20/262.95	   U21(x0, mark(x1))
744.20/262.95	   U21(active(x0), x1)
744.20/262.95	   U21(x0, active(x1))
744.20/262.95	   U22(mark(x0), x1)
744.20/262.95	   U22(x0, mark(x1))
744.20/262.95	   U22(active(x0), x1)
744.20/262.95	   U22(x0, active(x1))
744.20/262.95	   U23(mark(x0))
744.20/262.95	   U23(active(x0))
744.20/262.95	   U31(mark(x0), x1, x2)
744.20/262.95	   U31(x0, mark(x1), x2)
744.20/262.95	   U31(x0, x1, mark(x2))
744.20/262.95	   U31(active(x0), x1, x2)
744.20/262.95	   U31(x0, active(x1), x2)
744.20/262.95	   U31(x0, x1, active(x2))
744.20/262.95	   U32(mark(x0), x1, x2)
744.20/262.95	   U32(x0, mark(x1), x2)
744.20/262.95	   U32(x0, x1, mark(x2))
744.20/262.95	   U32(active(x0), x1, x2)
744.20/262.95	   U32(x0, active(x1), x2)
744.20/262.95	   U32(x0, x1, active(x2))
744.20/262.95	   U33(mark(x0), x1, x2)
744.20/262.95	   U33(x0, mark(x1), x2)
744.20/262.95	   U33(x0, x1, mark(x2))
744.20/262.95	   U33(active(x0), x1, x2)
744.20/262.95	   U33(x0, active(x1), x2)
744.20/262.95	   U33(x0, x1, active(x2))
744.20/262.95	   U34(mark(x0), x1, x2)
744.20/262.95	   U34(x0, mark(x1), x2)
744.20/262.95	   U34(x0, x1, mark(x2))
744.20/262.95	   U34(active(x0), x1, x2)
744.20/262.95	   U34(x0, active(x1), x2)
744.20/262.95	   U34(x0, x1, active(x2))
744.20/262.95	   U35(mark(x0), x1)
744.20/262.95	   U35(x0, mark(x1))
744.20/262.95	   U35(active(x0), x1)
744.20/262.95	   U35(x0, active(x1))
744.20/262.95	   U36(mark(x0))
744.20/262.95	   U36(active(x0))
744.20/262.95	   U41(mark(x0), x1)
744.20/262.95	   U41(x0, mark(x1))
744.20/262.95	   U41(active(x0), x1)
744.20/262.95	   U41(x0, active(x1))
744.20/262.95	   U42(mark(x0))
744.20/262.95	   U42(active(x0))
744.20/262.95	   U51(mark(x0))
744.20/262.95	   U51(active(x0))
744.20/262.95	   U61(mark(x0), x1)
744.20/262.95	   U61(x0, mark(x1))
744.20/262.95	   U61(active(x0), x1)
744.20/262.95	   U61(x0, active(x1))
744.20/262.95	   U62(mark(x0))
744.20/262.95	   U62(active(x0))
744.20/262.95	   U71(mark(x0), x1)
744.20/262.95	   U71(x0, mark(x1))
744.20/262.95	   U71(active(x0), x1)
744.20/262.95	   U71(x0, active(x1))
744.20/262.95	   U72(mark(x0), x1)
744.20/262.95	   U72(x0, mark(x1))
744.20/262.95	   U72(active(x0), x1)
744.20/262.95	   U72(x0, active(x1))
744.20/262.95	   U81(mark(x0), x1, x2)
744.20/262.95	   U81(x0, mark(x1), x2)
744.20/262.95	   U81(x0, x1, mark(x2))
744.20/262.95	   U81(active(x0), x1, x2)
744.20/262.95	   U81(x0, active(x1), x2)
744.20/262.95	   U81(x0, x1, active(x2))
744.20/262.95	   U82(mark(x0), x1, x2)
744.20/262.95	   U82(x0, mark(x1), x2)
744.20/262.95	   U82(x0, x1, mark(x2))
744.20/262.95	   U82(active(x0), x1, x2)
744.20/262.95	   U82(x0, active(x1), x2)
744.20/262.95	   U82(x0, x1, active(x2))
744.20/262.95	   U83(mark(x0), x1, x2)
744.20/262.95	   U83(x0, mark(x1), x2)
744.20/262.95	   U83(x0, x1, mark(x2))
744.20/262.95	   U83(active(x0), x1, x2)
744.20/262.95	   U83(x0, active(x1), x2)
744.20/262.95	   U83(x0, x1, active(x2))
744.20/262.95	   U84(mark(x0), x1, x2)
744.20/262.95	   U84(x0, mark(x1), x2)
744.20/262.95	   U84(x0, x1, mark(x2))
744.20/262.95	   U84(active(x0), x1, x2)
744.20/262.95	   U84(x0, active(x1), x2)
744.20/262.95	   U84(x0, x1, active(x2))
744.20/262.95	   s(mark(x0))
744.20/262.95	   s(active(x0))
744.20/262.95	   U91(mark(x0), x1)
744.20/262.95	   U91(x0, mark(x1))
744.20/262.95	   U91(active(x0), x1)
744.20/262.95	   U91(x0, active(x1))
744.20/262.95	   U92(mark(x0))
744.20/262.95	   U92(active(x0))
744.20/262.95	
744.20/262.95	
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(240)
744.20/262.95	Obligation:
744.20/262.95	Q DP problem:
744.20/262.95	The TRS P consists of the following rules:
744.20/262.95	
744.20/262.95	   U103^1(X1, mark(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(mark(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, X2, mark(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(active(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, active(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	   U103^1(X1, X2, active(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	
744.20/262.95	R is empty.
744.20/262.95	The set Q consists of the following terms:
744.20/262.95	
744.20/262.95	   active(U101(tt, x0, x1))
744.20/262.95	   active(U102(tt, x0, x1))
744.20/262.95	   active(U103(tt, x0, x1))
744.20/262.95	   active(U104(tt, x0, x1))
744.20/262.95	   active(U11(tt, x0, x1))
744.20/262.95	   active(U12(tt, x0, x1))
744.20/262.95	   active(U13(tt, x0, x1))
744.20/262.95	   active(U14(tt, x0, x1))
744.20/262.95	   active(U15(tt, x0))
744.20/262.95	   active(U16(tt))
744.20/262.95	   active(U21(tt, x0))
744.20/262.95	   active(U22(tt, x0))
744.20/262.95	   active(U23(tt))
744.20/262.95	   active(U31(tt, x0, x1))
744.20/262.95	   active(U32(tt, x0, x1))
744.20/262.95	   active(U33(tt, x0, x1))
744.20/262.95	   active(U34(tt, x0, x1))
744.20/262.95	   active(U35(tt, x0))
744.20/262.95	   active(U36(tt))
744.20/262.95	   active(U41(tt, x0))
744.20/262.95	   active(U42(tt))
744.20/262.95	   active(U51(tt))
744.20/262.95	   active(U61(tt, x0))
744.20/262.95	   active(U62(tt))
744.20/262.95	   active(U71(tt, x0))
744.20/262.95	   active(U72(tt, x0))
744.20/262.95	   active(U81(tt, x0, x1))
744.20/262.95	   active(U82(tt, x0, x1))
744.20/262.95	   active(U83(tt, x0, x1))
744.20/262.95	   active(U84(tt, x0, x1))
744.20/262.95	   active(U91(tt, x0))
744.20/262.95	   active(U92(tt))
744.20/262.95	   active(isNat(0))
744.20/262.95	   active(isNat(plus(x0, x1)))
744.20/262.95	   active(isNat(s(x0)))
744.20/262.95	   active(isNat(x(x0, x1)))
744.20/262.95	   active(isNatKind(0))
744.20/262.95	   active(isNatKind(plus(x0, x1)))
744.20/262.95	   active(isNatKind(s(x0)))
744.20/262.95	   active(isNatKind(x(x0, x1)))
744.20/262.95	   active(plus(x0, 0))
744.20/262.95	   active(plus(x0, s(x1)))
744.20/262.95	   active(x(x0, 0))
744.20/262.95	   active(x(x0, s(x1)))
744.20/262.95	   mark(U101(x0, x1, x2))
744.20/262.95	   mark(tt)
744.20/262.95	   mark(U102(x0, x1, x2))
744.20/262.95	   mark(isNatKind(x0))
744.20/262.95	   mark(U103(x0, x1, x2))
744.20/262.95	   mark(isNat(x0))
744.20/262.95	   mark(U104(x0, x1, x2))
744.20/262.95	   mark(plus(x0, x1))
744.20/262.95	   mark(x(x0, x1))
744.20/262.95	   mark(U11(x0, x1, x2))
744.20/262.95	   mark(U12(x0, x1, x2))
744.20/262.95	   mark(U13(x0, x1, x2))
744.20/262.95	   mark(U14(x0, x1, x2))
744.20/262.95	   mark(U15(x0, x1))
744.20/262.95	   mark(U16(x0))
744.20/262.95	   mark(U21(x0, x1))
744.20/262.95	   mark(U22(x0, x1))
744.20/262.95	   mark(U23(x0))
744.20/262.95	   mark(U31(x0, x1, x2))
744.20/262.95	   mark(U32(x0, x1, x2))
744.20/262.95	   mark(U33(x0, x1, x2))
744.20/262.95	   mark(U34(x0, x1, x2))
744.20/262.95	   mark(U35(x0, x1))
744.20/262.95	   mark(U36(x0))
744.20/262.95	   mark(U41(x0, x1))
744.20/262.95	   mark(U42(x0))
744.20/262.95	   mark(U51(x0))
744.20/262.95	   mark(U61(x0, x1))
744.20/262.95	   mark(U62(x0))
744.20/262.95	   mark(U71(x0, x1))
744.20/262.95	   mark(U72(x0, x1))
744.20/262.95	   mark(U81(x0, x1, x2))
744.20/262.95	   mark(U82(x0, x1, x2))
744.20/262.95	   mark(U83(x0, x1, x2))
744.20/262.95	   mark(U84(x0, x1, x2))
744.20/262.95	   mark(s(x0))
744.20/262.95	   mark(U91(x0, x1))
744.20/262.95	   mark(U92(x0))
744.20/262.95	   mark(0)
744.20/262.95	
744.20/262.95	We have to consider all minimal (P,Q,R)-chains.
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(241) QDPSizeChangeProof (EQUIVALENT)
744.20/262.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
744.20/262.95	
744.20/262.95	From the DPs we obtained the following set of size-change graphs:
744.20/262.95	*U103^1(X1, mark(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.95	
744.20/262.95	
744.20/262.95	*U103^1(mark(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.95	
744.20/262.95	
744.20/262.95	*U103^1(X1, X2, mark(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.95	
744.20/262.95	
744.20/262.95	*U103^1(active(X1), X2, X3) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.95	
744.20/262.95	
744.20/262.95	*U103^1(X1, active(X2), X3) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.95	
744.20/262.95	
744.20/262.95	*U103^1(X1, X2, active(X3)) -> U103^1(X1, X2, X3)
744.20/262.95	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.95	
744.20/262.95	
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(242)
744.20/262.95	YES
744.20/262.95	
744.20/262.95	----------------------------------------
744.20/262.95	
744.20/262.95	(243)
744.20/262.95	Obligation:
744.20/262.95	Q DP problem:
744.20/262.95	The TRS P consists of the following rules:
744.20/262.95	
744.20/262.95	   ISNATKIND(active(X)) -> ISNATKIND(X)
744.20/262.95	   ISNATKIND(mark(X)) -> ISNATKIND(X)
744.20/262.95	
744.20/262.95	The TRS R consists of the following rules:
744.20/262.95	
744.20/262.95	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.95	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.95	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.95	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.95	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.95	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.95	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.95	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.95	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.95	   active(U16(tt)) -> mark(tt)
744.20/262.95	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.95	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.95	   active(U23(tt)) -> mark(tt)
744.20/262.95	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.95	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.95	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.95	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.95	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.95	   active(U36(tt)) -> mark(tt)
744.20/262.95	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.95	   active(U42(tt)) -> mark(tt)
744.20/262.95	   active(U51(tt)) -> mark(tt)
744.20/262.95	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.95	   active(U62(tt)) -> mark(tt)
744.20/262.95	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.95	   active(U72(tt, N)) -> mark(N)
744.20/262.95	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.95	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.95	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.95	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.95	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.95	   active(U92(tt)) -> mark(0)
744.20/262.95	   active(isNat(0)) -> mark(tt)
744.20/262.95	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.95	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.95	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.95	   active(isNatKind(0)) -> mark(tt)
744.20/262.95	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.95	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.95	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.95	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.95	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.95	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.95	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.95	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.95	   mark(tt) -> active(tt)
744.20/262.95	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.95	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.95	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.95	   mark(isNat(X)) -> active(isNat(X))
744.20/262.95	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.95	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.95	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.95	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.95	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.95	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.95	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.95	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.95	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.95	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.95	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.95	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.95	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.95	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.95	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.95	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.95	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.95	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.95	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.95	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.95	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.95	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.95	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.95	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.95	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.95	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.95	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.95	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.95	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.95	   mark(s(X)) -> active(s(mark(X)))
744.20/262.95	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.95	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.95	   mark(0) -> active(0)
744.20/262.95	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.95	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.95	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.95	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.95	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.95	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.95	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.95	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.95	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.95	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.95	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.95	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.95	   isNatKind(mark(X)) -> isNatKind(X)
744.20/262.95	   isNatKind(active(X)) -> isNatKind(X)
744.20/262.95	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.95	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.95	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.95	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.95	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.95	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.95	   isNat(mark(X)) -> isNat(X)
744.20/262.95	   isNat(active(X)) -> isNat(X)
744.20/262.95	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.95	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.95	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.95	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.95	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.95	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.95	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.95	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.95	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.95	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.95	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.95	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.95	   x(active(X1), X2) -> x(X1, X2)
744.20/262.95	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.95	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.95	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.95	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.95	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.95	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.95	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.95	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.95	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.95	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.95	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.95	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.95	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.95	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.95	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.95	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.95	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.95	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.95	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.95	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.95	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.95	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.95	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.95	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.95	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.95	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.95	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.95	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.95	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.95	   U16(mark(X)) -> U16(X)
744.20/262.95	   U16(active(X)) -> U16(X)
744.20/262.95	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.95	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.95	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.95	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.95	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.95	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.95	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.95	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.95	   U23(mark(X)) -> U23(X)
744.20/262.95	   U23(active(X)) -> U23(X)
744.20/262.95	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.95	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.95	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.95	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.95	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.95	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.95	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.95	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.95	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.95	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.95	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.95	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.95	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.95	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.95	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.95	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.95	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.95	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.95	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.95	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.95	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.95	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.95	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.95	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.95	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.95	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.95	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.95	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.95	   U36(mark(X)) -> U36(X)
744.20/262.95	   U36(active(X)) -> U36(X)
744.20/262.95	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.95	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.95	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.95	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.95	   U42(mark(X)) -> U42(X)
744.20/262.95	   U42(active(X)) -> U42(X)
744.20/262.95	   U51(mark(X)) -> U51(X)
744.20/262.95	   U51(active(X)) -> U51(X)
744.20/262.95	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.95	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.95	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.95	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.95	   U62(mark(X)) -> U62(X)
744.20/262.95	   U62(active(X)) -> U62(X)
744.20/262.95	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.95	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.95	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.95	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.95	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.95	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.95	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.95	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.95	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.95	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.95	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.95	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.95	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.95	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.95	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.95	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.95	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.95	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.95	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.95	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.95	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.95	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.95	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.95	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.95	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.95	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.95	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.95	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.95	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.95	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.95	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.95	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.95	   s(mark(X)) -> s(X)
744.20/262.95	   s(active(X)) -> s(X)
744.20/262.95	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.95	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.95	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.95	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.95	   U92(mark(X)) -> U92(X)
744.20/262.95	   U92(active(X)) -> U92(X)
744.20/262.95	
744.20/262.95	The set Q consists of the following terms:
744.20/262.95	
744.20/262.95	   active(U101(tt, x0, x1))
744.20/262.95	   active(U102(tt, x0, x1))
744.20/262.95	   active(U103(tt, x0, x1))
744.20/262.95	   active(U104(tt, x0, x1))
744.20/262.95	   active(U11(tt, x0, x1))
744.20/262.95	   active(U12(tt, x0, x1))
744.20/262.95	   active(U13(tt, x0, x1))
744.20/262.95	   active(U14(tt, x0, x1))
744.20/262.95	   active(U15(tt, x0))
744.20/262.95	   active(U16(tt))
744.20/262.95	   active(U21(tt, x0))
744.20/262.95	   active(U22(tt, x0))
744.20/262.95	   active(U23(tt))
744.20/262.95	   active(U31(tt, x0, x1))
744.20/262.95	   active(U32(tt, x0, x1))
744.20/262.95	   active(U33(tt, x0, x1))
744.20/262.95	   active(U34(tt, x0, x1))
744.20/262.95	   active(U35(tt, x0))
744.20/262.95	   active(U36(tt))
744.20/262.95	   active(U41(tt, x0))
744.20/262.95	   active(U42(tt))
744.20/262.95	   active(U51(tt))
744.20/262.95	   active(U61(tt, x0))
744.20/262.95	   active(U62(tt))
744.20/262.95	   active(U71(tt, x0))
744.20/262.95	   active(U72(tt, x0))
744.20/262.95	   active(U81(tt, x0, x1))
744.20/262.95	   active(U82(tt, x0, x1))
744.20/262.95	   active(U83(tt, x0, x1))
744.20/262.95	   active(U84(tt, x0, x1))
744.20/262.95	   active(U91(tt, x0))
744.20/262.95	   active(U92(tt))
744.20/262.95	   active(isNat(0))
744.20/262.95	   active(isNat(plus(x0, x1)))
744.20/262.95	   active(isNat(s(x0)))
744.20/262.95	   active(isNat(x(x0, x1)))
744.20/262.95	   active(isNatKind(0))
744.20/262.95	   active(isNatKind(plus(x0, x1)))
744.20/262.95	   active(isNatKind(s(x0)))
744.20/262.95	   active(isNatKind(x(x0, x1)))
744.20/262.95	   active(plus(x0, 0))
744.20/262.95	   active(plus(x0, s(x1)))
744.20/262.95	   active(x(x0, 0))
744.20/262.95	   active(x(x0, s(x1)))
744.20/262.95	   mark(U101(x0, x1, x2))
744.20/262.95	   mark(tt)
744.20/262.95	   mark(U102(x0, x1, x2))
744.20/262.95	   mark(isNatKind(x0))
744.20/262.95	   mark(U103(x0, x1, x2))
744.20/262.95	   mark(isNat(x0))
744.20/262.95	   mark(U104(x0, x1, x2))
744.20/262.95	   mark(plus(x0, x1))
744.20/262.95	   mark(x(x0, x1))
744.20/262.95	   mark(U11(x0, x1, x2))
744.20/262.95	   mark(U12(x0, x1, x2))
744.20/262.95	   mark(U13(x0, x1, x2))
744.20/262.95	   mark(U14(x0, x1, x2))
744.20/262.95	   mark(U15(x0, x1))
744.20/262.95	   mark(U16(x0))
744.20/262.95	   mark(U21(x0, x1))
744.20/262.95	   mark(U22(x0, x1))
744.20/262.95	   mark(U23(x0))
744.20/262.95	   mark(U31(x0, x1, x2))
744.20/262.95	   mark(U32(x0, x1, x2))
744.20/262.95	   mark(U33(x0, x1, x2))
744.20/262.95	   mark(U34(x0, x1, x2))
744.20/262.95	   mark(U35(x0, x1))
744.20/262.95	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(244) UsableRulesProof (EQUIVALENT)
744.20/262.96	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.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(245)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   ISNATKIND(active(X)) -> ISNATKIND(X)
744.20/262.96	   ISNATKIND(mark(X)) -> ISNATKIND(X)
744.20/262.96	
744.20/262.96	R is empty.
744.20/262.96	The set Q consists of the following terms:
744.20/262.96	
744.20/262.96	   active(U101(tt, x0, x1))
744.20/262.96	   active(U102(tt, x0, x1))
744.20/262.96	   active(U103(tt, x0, x1))
744.20/262.96	   active(U104(tt, x0, x1))
744.20/262.96	   active(U11(tt, x0, x1))
744.20/262.96	   active(U12(tt, x0, x1))
744.20/262.96	   active(U13(tt, x0, x1))
744.20/262.96	   active(U14(tt, x0, x1))
744.20/262.96	   active(U15(tt, x0))
744.20/262.96	   active(U16(tt))
744.20/262.96	   active(U21(tt, x0))
744.20/262.96	   active(U22(tt, x0))
744.20/262.96	   active(U23(tt))
744.20/262.96	   active(U31(tt, x0, x1))
744.20/262.96	   active(U32(tt, x0, x1))
744.20/262.96	   active(U33(tt, x0, x1))
744.20/262.96	   active(U34(tt, x0, x1))
744.20/262.96	   active(U35(tt, x0))
744.20/262.96	   active(U36(tt))
744.20/262.96	   active(U41(tt, x0))
744.20/262.96	   active(U42(tt))
744.20/262.96	   active(U51(tt))
744.20/262.96	   active(U61(tt, x0))
744.20/262.96	   active(U62(tt))
744.20/262.96	   active(U71(tt, x0))
744.20/262.96	   active(U72(tt, x0))
744.20/262.96	   active(U81(tt, x0, x1))
744.20/262.96	   active(U82(tt, x0, x1))
744.20/262.96	   active(U83(tt, x0, x1))
744.20/262.96	   active(U84(tt, x0, x1))
744.20/262.96	   active(U91(tt, x0))
744.20/262.96	   active(U92(tt))
744.20/262.96	   active(isNat(0))
744.20/262.96	   active(isNat(plus(x0, x1)))
744.20/262.96	   active(isNat(s(x0)))
744.20/262.96	   active(isNat(x(x0, x1)))
744.20/262.96	   active(isNatKind(0))
744.20/262.96	   active(isNatKind(plus(x0, x1)))
744.20/262.96	   active(isNatKind(s(x0)))
744.20/262.96	   active(isNatKind(x(x0, x1)))
744.20/262.96	   active(plus(x0, 0))
744.20/262.96	   active(plus(x0, s(x1)))
744.20/262.96	   active(x(x0, 0))
744.20/262.96	   active(x(x0, s(x1)))
744.20/262.96	   mark(U101(x0, x1, x2))
744.20/262.96	   mark(tt)
744.20/262.96	   mark(U102(x0, x1, x2))
744.20/262.96	   mark(isNatKind(x0))
744.20/262.96	   mark(U103(x0, x1, x2))
744.20/262.96	   mark(isNat(x0))
744.20/262.96	   mark(U104(x0, x1, x2))
744.20/262.96	   mark(plus(x0, x1))
744.20/262.96	   mark(x(x0, x1))
744.20/262.96	   mark(U11(x0, x1, x2))
744.20/262.96	   mark(U12(x0, x1, x2))
744.20/262.96	   mark(U13(x0, x1, x2))
744.20/262.96	   mark(U14(x0, x1, x2))
744.20/262.96	   mark(U15(x0, x1))
744.20/262.96	   mark(U16(x0))
744.20/262.96	   mark(U21(x0, x1))
744.20/262.96	   mark(U22(x0, x1))
744.20/262.96	   mark(U23(x0))
744.20/262.96	   mark(U31(x0, x1, x2))
744.20/262.96	   mark(U32(x0, x1, x2))
744.20/262.96	   mark(U33(x0, x1, x2))
744.20/262.96	   mark(U34(x0, x1, x2))
744.20/262.96	   mark(U35(x0, x1))
744.20/262.96	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(246) QReductionProof (EQUIVALENT)
744.20/262.96	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.20/262.96	
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(247)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   ISNATKIND(active(X)) -> ISNATKIND(X)
744.20/262.96	   ISNATKIND(mark(X)) -> ISNATKIND(X)
744.20/262.96	
744.20/262.96	R is empty.
744.20/262.96	The set Q consists of the following terms:
744.20/262.96	
744.20/262.96	   active(U101(tt, x0, x1))
744.20/262.96	   active(U102(tt, x0, x1))
744.20/262.96	   active(U103(tt, x0, x1))
744.20/262.96	   active(U104(tt, x0, x1))
744.20/262.96	   active(U11(tt, x0, x1))
744.20/262.96	   active(U12(tt, x0, x1))
744.20/262.96	   active(U13(tt, x0, x1))
744.20/262.96	   active(U14(tt, x0, x1))
744.20/262.96	   active(U15(tt, x0))
744.20/262.96	   active(U16(tt))
744.20/262.96	   active(U21(tt, x0))
744.20/262.96	   active(U22(tt, x0))
744.20/262.96	   active(U23(tt))
744.20/262.96	   active(U31(tt, x0, x1))
744.20/262.96	   active(U32(tt, x0, x1))
744.20/262.96	   active(U33(tt, x0, x1))
744.20/262.96	   active(U34(tt, x0, x1))
744.20/262.96	   active(U35(tt, x0))
744.20/262.96	   active(U36(tt))
744.20/262.96	   active(U41(tt, x0))
744.20/262.96	   active(U42(tt))
744.20/262.96	   active(U51(tt))
744.20/262.96	   active(U61(tt, x0))
744.20/262.96	   active(U62(tt))
744.20/262.96	   active(U71(tt, x0))
744.20/262.96	   active(U72(tt, x0))
744.20/262.96	   active(U81(tt, x0, x1))
744.20/262.96	   active(U82(tt, x0, x1))
744.20/262.96	   active(U83(tt, x0, x1))
744.20/262.96	   active(U84(tt, x0, x1))
744.20/262.96	   active(U91(tt, x0))
744.20/262.96	   active(U92(tt))
744.20/262.96	   active(isNat(0))
744.20/262.96	   active(isNat(plus(x0, x1)))
744.20/262.96	   active(isNat(s(x0)))
744.20/262.96	   active(isNat(x(x0, x1)))
744.20/262.96	   active(isNatKind(0))
744.20/262.96	   active(isNatKind(plus(x0, x1)))
744.20/262.96	   active(isNatKind(s(x0)))
744.20/262.96	   active(isNatKind(x(x0, x1)))
744.20/262.96	   active(plus(x0, 0))
744.20/262.96	   active(plus(x0, s(x1)))
744.20/262.96	   active(x(x0, 0))
744.20/262.96	   active(x(x0, s(x1)))
744.20/262.96	   mark(U101(x0, x1, x2))
744.20/262.96	   mark(tt)
744.20/262.96	   mark(U102(x0, x1, x2))
744.20/262.96	   mark(isNatKind(x0))
744.20/262.96	   mark(U103(x0, x1, x2))
744.20/262.96	   mark(isNat(x0))
744.20/262.96	   mark(U104(x0, x1, x2))
744.20/262.96	   mark(plus(x0, x1))
744.20/262.96	   mark(x(x0, x1))
744.20/262.96	   mark(U11(x0, x1, x2))
744.20/262.96	   mark(U12(x0, x1, x2))
744.20/262.96	   mark(U13(x0, x1, x2))
744.20/262.96	   mark(U14(x0, x1, x2))
744.20/262.96	   mark(U15(x0, x1))
744.20/262.96	   mark(U16(x0))
744.20/262.96	   mark(U21(x0, x1))
744.20/262.96	   mark(U22(x0, x1))
744.20/262.96	   mark(U23(x0))
744.20/262.96	   mark(U31(x0, x1, x2))
744.20/262.96	   mark(U32(x0, x1, x2))
744.20/262.96	   mark(U33(x0, x1, x2))
744.20/262.96	   mark(U34(x0, x1, x2))
744.20/262.96	   mark(U35(x0, x1))
744.20/262.96	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(248) QDPSizeChangeProof (EQUIVALENT)
744.20/262.96	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. 
744.20/262.96	
744.20/262.96	From the DPs we obtained the following set of size-change graphs:
744.20/262.96	*ISNATKIND(active(X)) -> ISNATKIND(X)
744.20/262.96	The graph contains the following edges 1 > 1
744.20/262.96	
744.20/262.96	
744.20/262.96	*ISNATKIND(mark(X)) -> ISNATKIND(X)
744.20/262.96	The graph contains the following edges 1 > 1
744.20/262.96	
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(249)
744.20/262.96	YES
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(250)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   U102^1(X1, mark(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(mark(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, mark(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(active(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, active(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, active(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	
744.20/262.96	The TRS R consists of the following rules:
744.20/262.96	
744.20/262.96	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.96	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.96	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.96	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.96	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.96	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.96	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.96	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.96	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.96	   active(U16(tt)) -> mark(tt)
744.20/262.96	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.96	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.96	   active(U23(tt)) -> mark(tt)
744.20/262.96	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.96	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.96	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.96	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.96	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.96	   active(U36(tt)) -> mark(tt)
744.20/262.96	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.96	   active(U42(tt)) -> mark(tt)
744.20/262.96	   active(U51(tt)) -> mark(tt)
744.20/262.96	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.96	   active(U62(tt)) -> mark(tt)
744.20/262.96	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.96	   active(U72(tt, N)) -> mark(N)
744.20/262.96	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.96	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.96	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.96	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.96	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.96	   active(U92(tt)) -> mark(0)
744.20/262.96	   active(isNat(0)) -> mark(tt)
744.20/262.96	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.96	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.96	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.96	   active(isNatKind(0)) -> mark(tt)
744.20/262.96	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.96	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.96	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.96	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.96	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.96	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.96	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.96	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.96	   mark(tt) -> active(tt)
744.20/262.96	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.96	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.96	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.96	   mark(isNat(X)) -> active(isNat(X))
744.20/262.96	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.96	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.96	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.96	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.96	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.96	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.96	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.96	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.96	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.96	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.96	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.96	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.96	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.96	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.96	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.96	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.96	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.96	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.96	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.96	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.96	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.96	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.96	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.96	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.96	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.96	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.96	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.96	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.96	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.96	   mark(s(X)) -> active(s(mark(X)))
744.20/262.96	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.96	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.96	   mark(0) -> active(0)
744.20/262.96	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.96	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.96	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.96	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.96	   isNatKind(mark(X)) -> isNatKind(X)
744.20/262.96	   isNatKind(active(X)) -> isNatKind(X)
744.20/262.96	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.96	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.96	   isNat(mark(X)) -> isNat(X)
744.20/262.96	   isNat(active(X)) -> isNat(X)
744.20/262.96	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.96	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.96	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.96	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.96	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.96	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.96	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.96	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.96	   x(active(X1), X2) -> x(X1, X2)
744.20/262.96	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.96	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.96	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.96	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.96	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.96	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.96	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.96	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.96	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.96	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.96	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.96	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.96	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.96	   U16(mark(X)) -> U16(X)
744.20/262.96	   U16(active(X)) -> U16(X)
744.20/262.96	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.96	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.96	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.96	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.96	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.96	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.96	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.96	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.96	   U23(mark(X)) -> U23(X)
744.20/262.96	   U23(active(X)) -> U23(X)
744.20/262.96	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.96	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.96	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.96	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.96	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.96	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.96	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.96	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.96	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.96	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.96	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.96	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.96	   U36(mark(X)) -> U36(X)
744.20/262.96	   U36(active(X)) -> U36(X)
744.20/262.96	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.96	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.96	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.96	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.96	   U42(mark(X)) -> U42(X)
744.20/262.96	   U42(active(X)) -> U42(X)
744.20/262.96	   U51(mark(X)) -> U51(X)
744.20/262.96	   U51(active(X)) -> U51(X)
744.20/262.96	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.96	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.96	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.96	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.96	   U62(mark(X)) -> U62(X)
744.20/262.96	   U62(active(X)) -> U62(X)
744.20/262.96	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.96	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.96	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.96	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.96	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.96	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.96	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.96	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.96	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.96	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.96	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.96	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.96	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.96	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.96	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.96	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.96	   s(mark(X)) -> s(X)
744.20/262.96	   s(active(X)) -> s(X)
744.20/262.96	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.96	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.96	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.96	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.96	   U92(mark(X)) -> U92(X)
744.20/262.96	   U92(active(X)) -> U92(X)
744.20/262.96	
744.20/262.96	The set Q consists of the following terms:
744.20/262.96	
744.20/262.96	   active(U101(tt, x0, x1))
744.20/262.96	   active(U102(tt, x0, x1))
744.20/262.96	   active(U103(tt, x0, x1))
744.20/262.96	   active(U104(tt, x0, x1))
744.20/262.96	   active(U11(tt, x0, x1))
744.20/262.96	   active(U12(tt, x0, x1))
744.20/262.96	   active(U13(tt, x0, x1))
744.20/262.96	   active(U14(tt, x0, x1))
744.20/262.96	   active(U15(tt, x0))
744.20/262.96	   active(U16(tt))
744.20/262.96	   active(U21(tt, x0))
744.20/262.96	   active(U22(tt, x0))
744.20/262.96	   active(U23(tt))
744.20/262.96	   active(U31(tt, x0, x1))
744.20/262.96	   active(U32(tt, x0, x1))
744.20/262.96	   active(U33(tt, x0, x1))
744.20/262.96	   active(U34(tt, x0, x1))
744.20/262.96	   active(U35(tt, x0))
744.20/262.96	   active(U36(tt))
744.20/262.96	   active(U41(tt, x0))
744.20/262.96	   active(U42(tt))
744.20/262.96	   active(U51(tt))
744.20/262.96	   active(U61(tt, x0))
744.20/262.96	   active(U62(tt))
744.20/262.96	   active(U71(tt, x0))
744.20/262.96	   active(U72(tt, x0))
744.20/262.96	   active(U81(tt, x0, x1))
744.20/262.96	   active(U82(tt, x0, x1))
744.20/262.96	   active(U83(tt, x0, x1))
744.20/262.96	   active(U84(tt, x0, x1))
744.20/262.96	   active(U91(tt, x0))
744.20/262.96	   active(U92(tt))
744.20/262.96	   active(isNat(0))
744.20/262.96	   active(isNat(plus(x0, x1)))
744.20/262.96	   active(isNat(s(x0)))
744.20/262.96	   active(isNat(x(x0, x1)))
744.20/262.96	   active(isNatKind(0))
744.20/262.96	   active(isNatKind(plus(x0, x1)))
744.20/262.96	   active(isNatKind(s(x0)))
744.20/262.96	   active(isNatKind(x(x0, x1)))
744.20/262.96	   active(plus(x0, 0))
744.20/262.96	   active(plus(x0, s(x1)))
744.20/262.96	   active(x(x0, 0))
744.20/262.96	   active(x(x0, s(x1)))
744.20/262.96	   mark(U101(x0, x1, x2))
744.20/262.96	   mark(tt)
744.20/262.96	   mark(U102(x0, x1, x2))
744.20/262.96	   mark(isNatKind(x0))
744.20/262.96	   mark(U103(x0, x1, x2))
744.20/262.96	   mark(isNat(x0))
744.20/262.96	   mark(U104(x0, x1, x2))
744.20/262.96	   mark(plus(x0, x1))
744.20/262.96	   mark(x(x0, x1))
744.20/262.96	   mark(U11(x0, x1, x2))
744.20/262.96	   mark(U12(x0, x1, x2))
744.20/262.96	   mark(U13(x0, x1, x2))
744.20/262.96	   mark(U14(x0, x1, x2))
744.20/262.96	   mark(U15(x0, x1))
744.20/262.96	   mark(U16(x0))
744.20/262.96	   mark(U21(x0, x1))
744.20/262.96	   mark(U22(x0, x1))
744.20/262.96	   mark(U23(x0))
744.20/262.96	   mark(U31(x0, x1, x2))
744.20/262.96	   mark(U32(x0, x1, x2))
744.20/262.96	   mark(U33(x0, x1, x2))
744.20/262.96	   mark(U34(x0, x1, x2))
744.20/262.96	   mark(U35(x0, x1))
744.20/262.96	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(251) UsableRulesProof (EQUIVALENT)
744.20/262.96	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.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(252)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   U102^1(X1, mark(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(mark(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, mark(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(active(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, active(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, active(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	
744.20/262.96	R is empty.
744.20/262.96	The set Q consists of the following terms:
744.20/262.96	
744.20/262.96	   active(U101(tt, x0, x1))
744.20/262.96	   active(U102(tt, x0, x1))
744.20/262.96	   active(U103(tt, x0, x1))
744.20/262.96	   active(U104(tt, x0, x1))
744.20/262.96	   active(U11(tt, x0, x1))
744.20/262.96	   active(U12(tt, x0, x1))
744.20/262.96	   active(U13(tt, x0, x1))
744.20/262.96	   active(U14(tt, x0, x1))
744.20/262.96	   active(U15(tt, x0))
744.20/262.96	   active(U16(tt))
744.20/262.96	   active(U21(tt, x0))
744.20/262.96	   active(U22(tt, x0))
744.20/262.96	   active(U23(tt))
744.20/262.96	   active(U31(tt, x0, x1))
744.20/262.96	   active(U32(tt, x0, x1))
744.20/262.96	   active(U33(tt, x0, x1))
744.20/262.96	   active(U34(tt, x0, x1))
744.20/262.96	   active(U35(tt, x0))
744.20/262.96	   active(U36(tt))
744.20/262.96	   active(U41(tt, x0))
744.20/262.96	   active(U42(tt))
744.20/262.96	   active(U51(tt))
744.20/262.96	   active(U61(tt, x0))
744.20/262.96	   active(U62(tt))
744.20/262.96	   active(U71(tt, x0))
744.20/262.96	   active(U72(tt, x0))
744.20/262.96	   active(U81(tt, x0, x1))
744.20/262.96	   active(U82(tt, x0, x1))
744.20/262.96	   active(U83(tt, x0, x1))
744.20/262.96	   active(U84(tt, x0, x1))
744.20/262.96	   active(U91(tt, x0))
744.20/262.96	   active(U92(tt))
744.20/262.96	   active(isNat(0))
744.20/262.96	   active(isNat(plus(x0, x1)))
744.20/262.96	   active(isNat(s(x0)))
744.20/262.96	   active(isNat(x(x0, x1)))
744.20/262.96	   active(isNatKind(0))
744.20/262.96	   active(isNatKind(plus(x0, x1)))
744.20/262.96	   active(isNatKind(s(x0)))
744.20/262.96	   active(isNatKind(x(x0, x1)))
744.20/262.96	   active(plus(x0, 0))
744.20/262.96	   active(plus(x0, s(x1)))
744.20/262.96	   active(x(x0, 0))
744.20/262.96	   active(x(x0, s(x1)))
744.20/262.96	   mark(U101(x0, x1, x2))
744.20/262.96	   mark(tt)
744.20/262.96	   mark(U102(x0, x1, x2))
744.20/262.96	   mark(isNatKind(x0))
744.20/262.96	   mark(U103(x0, x1, x2))
744.20/262.96	   mark(isNat(x0))
744.20/262.96	   mark(U104(x0, x1, x2))
744.20/262.96	   mark(plus(x0, x1))
744.20/262.96	   mark(x(x0, x1))
744.20/262.96	   mark(U11(x0, x1, x2))
744.20/262.96	   mark(U12(x0, x1, x2))
744.20/262.96	   mark(U13(x0, x1, x2))
744.20/262.96	   mark(U14(x0, x1, x2))
744.20/262.96	   mark(U15(x0, x1))
744.20/262.96	   mark(U16(x0))
744.20/262.96	   mark(U21(x0, x1))
744.20/262.96	   mark(U22(x0, x1))
744.20/262.96	   mark(U23(x0))
744.20/262.96	   mark(U31(x0, x1, x2))
744.20/262.96	   mark(U32(x0, x1, x2))
744.20/262.96	   mark(U33(x0, x1, x2))
744.20/262.96	   mark(U34(x0, x1, x2))
744.20/262.96	   mark(U35(x0, x1))
744.20/262.96	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(253) QReductionProof (EQUIVALENT)
744.20/262.96	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.20/262.96	
744.20/262.96	   U101(mark(x0), x1, x2)
744.20/262.96	   U101(x0, mark(x1), x2)
744.20/262.96	   U101(x0, x1, mark(x2))
744.20/262.96	   U101(active(x0), x1, x2)
744.20/262.96	   U101(x0, active(x1), x2)
744.20/262.96	   U101(x0, x1, active(x2))
744.20/262.96	   U102(mark(x0), x1, x2)
744.20/262.96	   U102(x0, mark(x1), x2)
744.20/262.96	   U102(x0, x1, mark(x2))
744.20/262.96	   U102(active(x0), x1, x2)
744.20/262.96	   U102(x0, active(x1), x2)
744.20/262.96	   U102(x0, x1, active(x2))
744.20/262.96	   isNatKind(mark(x0))
744.20/262.96	   isNatKind(active(x0))
744.20/262.96	   U103(mark(x0), x1, x2)
744.20/262.96	   U103(x0, mark(x1), x2)
744.20/262.96	   U103(x0, x1, mark(x2))
744.20/262.96	   U103(active(x0), x1, x2)
744.20/262.96	   U103(x0, active(x1), x2)
744.20/262.96	   U103(x0, x1, active(x2))
744.20/262.96	   isNat(mark(x0))
744.20/262.96	   isNat(active(x0))
744.20/262.96	   U104(mark(x0), x1, x2)
744.20/262.96	   U104(x0, mark(x1), x2)
744.20/262.96	   U104(x0, x1, mark(x2))
744.20/262.96	   U104(active(x0), x1, x2)
744.20/262.96	   U104(x0, active(x1), x2)
744.20/262.96	   U104(x0, x1, active(x2))
744.20/262.96	   plus(mark(x0), x1)
744.20/262.96	   plus(x0, mark(x1))
744.20/262.96	   plus(active(x0), x1)
744.20/262.96	   plus(x0, active(x1))
744.20/262.96	   x(mark(x0), x1)
744.20/262.96	   x(x0, mark(x1))
744.20/262.96	   x(active(x0), x1)
744.20/262.96	   x(x0, active(x1))
744.20/262.96	   U11(mark(x0), x1, x2)
744.20/262.96	   U11(x0, mark(x1), x2)
744.20/262.96	   U11(x0, x1, mark(x2))
744.20/262.96	   U11(active(x0), x1, x2)
744.20/262.96	   U11(x0, active(x1), x2)
744.20/262.96	   U11(x0, x1, active(x2))
744.20/262.96	   U12(mark(x0), x1, x2)
744.20/262.96	   U12(x0, mark(x1), x2)
744.20/262.96	   U12(x0, x1, mark(x2))
744.20/262.96	   U12(active(x0), x1, x2)
744.20/262.96	   U12(x0, active(x1), x2)
744.20/262.96	   U12(x0, x1, active(x2))
744.20/262.96	   U13(mark(x0), x1, x2)
744.20/262.96	   U13(x0, mark(x1), x2)
744.20/262.96	   U13(x0, x1, mark(x2))
744.20/262.96	   U13(active(x0), x1, x2)
744.20/262.96	   U13(x0, active(x1), x2)
744.20/262.96	   U13(x0, x1, active(x2))
744.20/262.96	   U14(mark(x0), x1, x2)
744.20/262.96	   U14(x0, mark(x1), x2)
744.20/262.96	   U14(x0, x1, mark(x2))
744.20/262.96	   U14(active(x0), x1, x2)
744.20/262.96	   U14(x0, active(x1), x2)
744.20/262.96	   U14(x0, x1, active(x2))
744.20/262.96	   U15(mark(x0), x1)
744.20/262.96	   U15(x0, mark(x1))
744.20/262.96	   U15(active(x0), x1)
744.20/262.96	   U15(x0, active(x1))
744.20/262.96	   U16(mark(x0))
744.20/262.96	   U16(active(x0))
744.20/262.96	   U21(mark(x0), x1)
744.20/262.96	   U21(x0, mark(x1))
744.20/262.96	   U21(active(x0), x1)
744.20/262.96	   U21(x0, active(x1))
744.20/262.96	   U22(mark(x0), x1)
744.20/262.96	   U22(x0, mark(x1))
744.20/262.96	   U22(active(x0), x1)
744.20/262.96	   U22(x0, active(x1))
744.20/262.96	   U23(mark(x0))
744.20/262.96	   U23(active(x0))
744.20/262.96	   U31(mark(x0), x1, x2)
744.20/262.96	   U31(x0, mark(x1), x2)
744.20/262.96	   U31(x0, x1, mark(x2))
744.20/262.96	   U31(active(x0), x1, x2)
744.20/262.96	   U31(x0, active(x1), x2)
744.20/262.96	   U31(x0, x1, active(x2))
744.20/262.96	   U32(mark(x0), x1, x2)
744.20/262.96	   U32(x0, mark(x1), x2)
744.20/262.96	   U32(x0, x1, mark(x2))
744.20/262.96	   U32(active(x0), x1, x2)
744.20/262.96	   U32(x0, active(x1), x2)
744.20/262.96	   U32(x0, x1, active(x2))
744.20/262.96	   U33(mark(x0), x1, x2)
744.20/262.96	   U33(x0, mark(x1), x2)
744.20/262.96	   U33(x0, x1, mark(x2))
744.20/262.96	   U33(active(x0), x1, x2)
744.20/262.96	   U33(x0, active(x1), x2)
744.20/262.96	   U33(x0, x1, active(x2))
744.20/262.96	   U34(mark(x0), x1, x2)
744.20/262.96	   U34(x0, mark(x1), x2)
744.20/262.96	   U34(x0, x1, mark(x2))
744.20/262.96	   U34(active(x0), x1, x2)
744.20/262.96	   U34(x0, active(x1), x2)
744.20/262.96	   U34(x0, x1, active(x2))
744.20/262.96	   U35(mark(x0), x1)
744.20/262.96	   U35(x0, mark(x1))
744.20/262.96	   U35(active(x0), x1)
744.20/262.96	   U35(x0, active(x1))
744.20/262.96	   U36(mark(x0))
744.20/262.96	   U36(active(x0))
744.20/262.96	   U41(mark(x0), x1)
744.20/262.96	   U41(x0, mark(x1))
744.20/262.96	   U41(active(x0), x1)
744.20/262.96	   U41(x0, active(x1))
744.20/262.96	   U42(mark(x0))
744.20/262.96	   U42(active(x0))
744.20/262.96	   U51(mark(x0))
744.20/262.96	   U51(active(x0))
744.20/262.96	   U61(mark(x0), x1)
744.20/262.96	   U61(x0, mark(x1))
744.20/262.96	   U61(active(x0), x1)
744.20/262.96	   U61(x0, active(x1))
744.20/262.96	   U62(mark(x0))
744.20/262.96	   U62(active(x0))
744.20/262.96	   U71(mark(x0), x1)
744.20/262.96	   U71(x0, mark(x1))
744.20/262.96	   U71(active(x0), x1)
744.20/262.96	   U71(x0, active(x1))
744.20/262.96	   U72(mark(x0), x1)
744.20/262.96	   U72(x0, mark(x1))
744.20/262.96	   U72(active(x0), x1)
744.20/262.96	   U72(x0, active(x1))
744.20/262.96	   U81(mark(x0), x1, x2)
744.20/262.96	   U81(x0, mark(x1), x2)
744.20/262.96	   U81(x0, x1, mark(x2))
744.20/262.96	   U81(active(x0), x1, x2)
744.20/262.96	   U81(x0, active(x1), x2)
744.20/262.96	   U81(x0, x1, active(x2))
744.20/262.96	   U82(mark(x0), x1, x2)
744.20/262.96	   U82(x0, mark(x1), x2)
744.20/262.96	   U82(x0, x1, mark(x2))
744.20/262.96	   U82(active(x0), x1, x2)
744.20/262.96	   U82(x0, active(x1), x2)
744.20/262.96	   U82(x0, x1, active(x2))
744.20/262.96	   U83(mark(x0), x1, x2)
744.20/262.96	   U83(x0, mark(x1), x2)
744.20/262.96	   U83(x0, x1, mark(x2))
744.20/262.96	   U83(active(x0), x1, x2)
744.20/262.96	   U83(x0, active(x1), x2)
744.20/262.96	   U83(x0, x1, active(x2))
744.20/262.96	   U84(mark(x0), x1, x2)
744.20/262.96	   U84(x0, mark(x1), x2)
744.20/262.96	   U84(x0, x1, mark(x2))
744.20/262.96	   U84(active(x0), x1, x2)
744.20/262.96	   U84(x0, active(x1), x2)
744.20/262.96	   U84(x0, x1, active(x2))
744.20/262.96	   s(mark(x0))
744.20/262.96	   s(active(x0))
744.20/262.96	   U91(mark(x0), x1)
744.20/262.96	   U91(x0, mark(x1))
744.20/262.96	   U91(active(x0), x1)
744.20/262.96	   U91(x0, active(x1))
744.20/262.96	   U92(mark(x0))
744.20/262.96	   U92(active(x0))
744.20/262.96	
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(254)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   U102^1(X1, mark(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(mark(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, mark(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(active(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, active(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	   U102^1(X1, X2, active(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	
744.20/262.96	R is empty.
744.20/262.96	The set Q consists of the following terms:
744.20/262.96	
744.20/262.96	   active(U101(tt, x0, x1))
744.20/262.96	   active(U102(tt, x0, x1))
744.20/262.96	   active(U103(tt, x0, x1))
744.20/262.96	   active(U104(tt, x0, x1))
744.20/262.96	   active(U11(tt, x0, x1))
744.20/262.96	   active(U12(tt, x0, x1))
744.20/262.96	   active(U13(tt, x0, x1))
744.20/262.96	   active(U14(tt, x0, x1))
744.20/262.96	   active(U15(tt, x0))
744.20/262.96	   active(U16(tt))
744.20/262.96	   active(U21(tt, x0))
744.20/262.96	   active(U22(tt, x0))
744.20/262.96	   active(U23(tt))
744.20/262.96	   active(U31(tt, x0, x1))
744.20/262.96	   active(U32(tt, x0, x1))
744.20/262.96	   active(U33(tt, x0, x1))
744.20/262.96	   active(U34(tt, x0, x1))
744.20/262.96	   active(U35(tt, x0))
744.20/262.96	   active(U36(tt))
744.20/262.96	   active(U41(tt, x0))
744.20/262.96	   active(U42(tt))
744.20/262.96	   active(U51(tt))
744.20/262.96	   active(U61(tt, x0))
744.20/262.96	   active(U62(tt))
744.20/262.96	   active(U71(tt, x0))
744.20/262.96	   active(U72(tt, x0))
744.20/262.96	   active(U81(tt, x0, x1))
744.20/262.96	   active(U82(tt, x0, x1))
744.20/262.96	   active(U83(tt, x0, x1))
744.20/262.96	   active(U84(tt, x0, x1))
744.20/262.96	   active(U91(tt, x0))
744.20/262.96	   active(U92(tt))
744.20/262.96	   active(isNat(0))
744.20/262.96	   active(isNat(plus(x0, x1)))
744.20/262.96	   active(isNat(s(x0)))
744.20/262.96	   active(isNat(x(x0, x1)))
744.20/262.96	   active(isNatKind(0))
744.20/262.96	   active(isNatKind(plus(x0, x1)))
744.20/262.96	   active(isNatKind(s(x0)))
744.20/262.96	   active(isNatKind(x(x0, x1)))
744.20/262.96	   active(plus(x0, 0))
744.20/262.96	   active(plus(x0, s(x1)))
744.20/262.96	   active(x(x0, 0))
744.20/262.96	   active(x(x0, s(x1)))
744.20/262.96	   mark(U101(x0, x1, x2))
744.20/262.96	   mark(tt)
744.20/262.96	   mark(U102(x0, x1, x2))
744.20/262.96	   mark(isNatKind(x0))
744.20/262.96	   mark(U103(x0, x1, x2))
744.20/262.96	   mark(isNat(x0))
744.20/262.96	   mark(U104(x0, x1, x2))
744.20/262.96	   mark(plus(x0, x1))
744.20/262.96	   mark(x(x0, x1))
744.20/262.96	   mark(U11(x0, x1, x2))
744.20/262.96	   mark(U12(x0, x1, x2))
744.20/262.96	   mark(U13(x0, x1, x2))
744.20/262.96	   mark(U14(x0, x1, x2))
744.20/262.96	   mark(U15(x0, x1))
744.20/262.96	   mark(U16(x0))
744.20/262.96	   mark(U21(x0, x1))
744.20/262.96	   mark(U22(x0, x1))
744.20/262.96	   mark(U23(x0))
744.20/262.96	   mark(U31(x0, x1, x2))
744.20/262.96	   mark(U32(x0, x1, x2))
744.20/262.96	   mark(U33(x0, x1, x2))
744.20/262.96	   mark(U34(x0, x1, x2))
744.20/262.96	   mark(U35(x0, x1))
744.20/262.96	   mark(U36(x0))
744.20/262.96	   mark(U41(x0, x1))
744.20/262.96	   mark(U42(x0))
744.20/262.96	   mark(U51(x0))
744.20/262.96	   mark(U61(x0, x1))
744.20/262.96	   mark(U62(x0))
744.20/262.96	   mark(U71(x0, x1))
744.20/262.96	   mark(U72(x0, x1))
744.20/262.96	   mark(U81(x0, x1, x2))
744.20/262.96	   mark(U82(x0, x1, x2))
744.20/262.96	   mark(U83(x0, x1, x2))
744.20/262.96	   mark(U84(x0, x1, x2))
744.20/262.96	   mark(s(x0))
744.20/262.96	   mark(U91(x0, x1))
744.20/262.96	   mark(U92(x0))
744.20/262.96	   mark(0)
744.20/262.96	
744.20/262.96	We have to consider all minimal (P,Q,R)-chains.
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(255) QDPSizeChangeProof (EQUIVALENT)
744.20/262.96	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. 
744.20/262.96	
744.20/262.96	From the DPs we obtained the following set of size-change graphs:
744.20/262.96	*U102^1(X1, mark(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.96	
744.20/262.96	
744.20/262.96	*U102^1(mark(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.96	
744.20/262.96	
744.20/262.96	*U102^1(X1, X2, mark(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.96	
744.20/262.96	
744.20/262.96	*U102^1(active(X1), X2, X3) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.96	
744.20/262.96	
744.20/262.96	*U102^1(X1, active(X2), X3) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.96	
744.20/262.96	
744.20/262.96	*U102^1(X1, X2, active(X3)) -> U102^1(X1, X2, X3)
744.20/262.96	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.96	
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(256)
744.20/262.96	YES
744.20/262.96	
744.20/262.96	----------------------------------------
744.20/262.96	
744.20/262.96	(257)
744.20/262.96	Obligation:
744.20/262.96	Q DP problem:
744.20/262.96	The TRS P consists of the following rules:
744.20/262.96	
744.20/262.96	   U101^1(X1, mark(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.96	   U101^1(mark(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.96	   U101^1(X1, X2, mark(X3)) -> U101^1(X1, X2, X3)
744.20/262.96	   U101^1(active(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.96	   U101^1(X1, active(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.96	   U101^1(X1, X2, active(X3)) -> U101^1(X1, X2, X3)
744.20/262.96	
744.20/262.96	The TRS R consists of the following rules:
744.20/262.96	
744.20/262.96	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.96	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.96	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.96	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.96	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.96	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.96	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.96	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.96	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.96	   active(U16(tt)) -> mark(tt)
744.20/262.96	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.96	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.96	   active(U23(tt)) -> mark(tt)
744.20/262.96	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.96	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.96	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.96	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.96	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.96	   active(U36(tt)) -> mark(tt)
744.20/262.96	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.96	   active(U42(tt)) -> mark(tt)
744.20/262.96	   active(U51(tt)) -> mark(tt)
744.20/262.96	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.96	   active(U62(tt)) -> mark(tt)
744.20/262.96	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.96	   active(U72(tt, N)) -> mark(N)
744.20/262.96	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.96	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.96	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.96	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.96	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.96	   active(U92(tt)) -> mark(0)
744.20/262.96	   active(isNat(0)) -> mark(tt)
744.20/262.96	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.96	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.96	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.96	   active(isNatKind(0)) -> mark(tt)
744.20/262.96	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.96	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.96	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.96	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.96	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.96	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.96	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.96	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.96	   mark(tt) -> active(tt)
744.20/262.96	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.96	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.96	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.96	   mark(isNat(X)) -> active(isNat(X))
744.20/262.96	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.96	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.96	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.96	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.96	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.96	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.96	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.96	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.96	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.96	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.96	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.96	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.96	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.96	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.96	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.96	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.96	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.96	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.96	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.96	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.96	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.96	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.96	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.96	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.96	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.96	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.96	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.96	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.96	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.96	   mark(s(X)) -> active(s(mark(X)))
744.20/262.96	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.96	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.96	   mark(0) -> active(0)
744.20/262.96	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.96	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.96	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.96	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.96	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.96	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.96	   isNatKind(mark(X)) -> isNatKind(X)
744.20/262.96	   isNatKind(active(X)) -> isNatKind(X)
744.20/262.96	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.96	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.96	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.96	   isNat(mark(X)) -> isNat(X)
744.20/262.96	   isNat(active(X)) -> isNat(X)
744.20/262.96	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.96	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.96	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.96	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.96	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.96	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.96	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.96	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.96	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.96	   x(active(X1), X2) -> x(X1, X2)
744.20/262.96	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.96	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.96	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.96	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.96	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.96	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.96	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.96	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.96	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.96	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.96	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.96	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.96	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.96	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.96	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.96	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.96	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.96	   U16(mark(X)) -> U16(X)
744.20/262.96	   U16(active(X)) -> U16(X)
744.20/262.96	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.96	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.96	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.96	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.96	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.96	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.96	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.96	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.96	   U23(mark(X)) -> U23(X)
744.20/262.96	   U23(active(X)) -> U23(X)
744.20/262.96	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.96	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.96	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.96	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.96	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.96	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.96	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.96	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.96	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.96	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.96	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.96	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.96	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.96	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.96	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.96	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.96	   U36(mark(X)) -> U36(X)
744.20/262.96	   U36(active(X)) -> U36(X)
744.20/262.96	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.96	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.96	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.96	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.96	   U42(mark(X)) -> U42(X)
744.20/262.96	   U42(active(X)) -> U42(X)
744.20/262.96	   U51(mark(X)) -> U51(X)
744.20/262.96	   U51(active(X)) -> U51(X)
744.20/262.96	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.96	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.96	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.96	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.96	   U62(mark(X)) -> U62(X)
744.20/262.96	   U62(active(X)) -> U62(X)
744.20/262.96	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.96	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.96	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.96	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.96	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.96	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.96	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.96	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.96	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.96	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.96	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.96	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.96	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.96	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.96	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.96	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.96	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.96	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.96	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.96	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.97	   s(mark(X)) -> s(X)
744.20/262.97	   s(active(X)) -> s(X)
744.20/262.97	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.97	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.97	   U92(mark(X)) -> U92(X)
744.20/262.97	   U92(active(X)) -> U92(X)
744.20/262.97	
744.20/262.97	The set Q consists of the following terms:
744.20/262.97	
744.20/262.97	   active(U101(tt, x0, x1))
744.20/262.97	   active(U102(tt, x0, x1))
744.20/262.97	   active(U103(tt, x0, x1))
744.20/262.97	   active(U104(tt, x0, x1))
744.20/262.97	   active(U11(tt, x0, x1))
744.20/262.97	   active(U12(tt, x0, x1))
744.20/262.97	   active(U13(tt, x0, x1))
744.20/262.97	   active(U14(tt, x0, x1))
744.20/262.97	   active(U15(tt, x0))
744.20/262.97	   active(U16(tt))
744.20/262.97	   active(U21(tt, x0))
744.20/262.97	   active(U22(tt, x0))
744.20/262.97	   active(U23(tt))
744.20/262.97	   active(U31(tt, x0, x1))
744.20/262.97	   active(U32(tt, x0, x1))
744.20/262.97	   active(U33(tt, x0, x1))
744.20/262.97	   active(U34(tt, x0, x1))
744.20/262.97	   active(U35(tt, x0))
744.20/262.97	   active(U36(tt))
744.20/262.97	   active(U41(tt, x0))
744.20/262.97	   active(U42(tt))
744.20/262.97	   active(U51(tt))
744.20/262.97	   active(U61(tt, x0))
744.20/262.97	   active(U62(tt))
744.20/262.97	   active(U71(tt, x0))
744.20/262.97	   active(U72(tt, x0))
744.20/262.97	   active(U81(tt, x0, x1))
744.20/262.97	   active(U82(tt, x0, x1))
744.20/262.97	   active(U83(tt, x0, x1))
744.20/262.97	   active(U84(tt, x0, x1))
744.20/262.97	   active(U91(tt, x0))
744.20/262.97	   active(U92(tt))
744.20/262.97	   active(isNat(0))
744.20/262.97	   active(isNat(plus(x0, x1)))
744.20/262.97	   active(isNat(s(x0)))
744.20/262.97	   active(isNat(x(x0, x1)))
744.20/262.97	   active(isNatKind(0))
744.20/262.97	   active(isNatKind(plus(x0, x1)))
744.20/262.97	   active(isNatKind(s(x0)))
744.20/262.97	   active(isNatKind(x(x0, x1)))
744.20/262.97	   active(plus(x0, 0))
744.20/262.97	   active(plus(x0, s(x1)))
744.20/262.97	   active(x(x0, 0))
744.20/262.97	   active(x(x0, s(x1)))
744.20/262.97	   mark(U101(x0, x1, x2))
744.20/262.97	   mark(tt)
744.20/262.97	   mark(U102(x0, x1, x2))
744.20/262.97	   mark(isNatKind(x0))
744.20/262.97	   mark(U103(x0, x1, x2))
744.20/262.97	   mark(isNat(x0))
744.20/262.97	   mark(U104(x0, x1, x2))
744.20/262.97	   mark(plus(x0, x1))
744.20/262.97	   mark(x(x0, x1))
744.20/262.97	   mark(U11(x0, x1, x2))
744.20/262.97	   mark(U12(x0, x1, x2))
744.20/262.97	   mark(U13(x0, x1, x2))
744.20/262.97	   mark(U14(x0, x1, x2))
744.20/262.97	   mark(U15(x0, x1))
744.20/262.97	   mark(U16(x0))
744.20/262.97	   mark(U21(x0, x1))
744.20/262.97	   mark(U22(x0, x1))
744.20/262.97	   mark(U23(x0))
744.20/262.97	   mark(U31(x0, x1, x2))
744.20/262.97	   mark(U32(x0, x1, x2))
744.20/262.97	   mark(U33(x0, x1, x2))
744.20/262.97	   mark(U34(x0, x1, x2))
744.20/262.97	   mark(U35(x0, x1))
744.20/262.97	   mark(U36(x0))
744.20/262.97	   mark(U41(x0, x1))
744.20/262.97	   mark(U42(x0))
744.20/262.97	   mark(U51(x0))
744.20/262.97	   mark(U61(x0, x1))
744.20/262.97	   mark(U62(x0))
744.20/262.97	   mark(U71(x0, x1))
744.20/262.97	   mark(U72(x0, x1))
744.20/262.97	   mark(U81(x0, x1, x2))
744.20/262.97	   mark(U82(x0, x1, x2))
744.20/262.97	   mark(U83(x0, x1, x2))
744.20/262.97	   mark(U84(x0, x1, x2))
744.20/262.97	   mark(s(x0))
744.20/262.97	   mark(U91(x0, x1))
744.20/262.97	   mark(U92(x0))
744.20/262.97	   mark(0)
744.20/262.97	   U101(mark(x0), x1, x2)
744.20/262.97	   U101(x0, mark(x1), x2)
744.20/262.97	   U101(x0, x1, mark(x2))
744.20/262.97	   U101(active(x0), x1, x2)
744.20/262.97	   U101(x0, active(x1), x2)
744.20/262.97	   U101(x0, x1, active(x2))
744.20/262.97	   U102(mark(x0), x1, x2)
744.20/262.97	   U102(x0, mark(x1), x2)
744.20/262.97	   U102(x0, x1, mark(x2))
744.20/262.97	   U102(active(x0), x1, x2)
744.20/262.97	   U102(x0, active(x1), x2)
744.20/262.97	   U102(x0, x1, active(x2))
744.20/262.97	   isNatKind(mark(x0))
744.20/262.97	   isNatKind(active(x0))
744.20/262.97	   U103(mark(x0), x1, x2)
744.20/262.97	   U103(x0, mark(x1), x2)
744.20/262.97	   U103(x0, x1, mark(x2))
744.20/262.97	   U103(active(x0), x1, x2)
744.20/262.97	   U103(x0, active(x1), x2)
744.20/262.97	   U103(x0, x1, active(x2))
744.20/262.97	   isNat(mark(x0))
744.20/262.97	   isNat(active(x0))
744.20/262.97	   U104(mark(x0), x1, x2)
744.20/262.97	   U104(x0, mark(x1), x2)
744.20/262.97	   U104(x0, x1, mark(x2))
744.20/262.97	   U104(active(x0), x1, x2)
744.20/262.97	   U104(x0, active(x1), x2)
744.20/262.97	   U104(x0, x1, active(x2))
744.20/262.97	   plus(mark(x0), x1)
744.20/262.97	   plus(x0, mark(x1))
744.20/262.97	   plus(active(x0), x1)
744.20/262.97	   plus(x0, active(x1))
744.20/262.97	   x(mark(x0), x1)
744.20/262.97	   x(x0, mark(x1))
744.20/262.97	   x(active(x0), x1)
744.20/262.97	   x(x0, active(x1))
744.20/262.97	   U11(mark(x0), x1, x2)
744.20/262.97	   U11(x0, mark(x1), x2)
744.20/262.97	   U11(x0, x1, mark(x2))
744.20/262.97	   U11(active(x0), x1, x2)
744.20/262.97	   U11(x0, active(x1), x2)
744.20/262.97	   U11(x0, x1, active(x2))
744.20/262.97	   U12(mark(x0), x1, x2)
744.20/262.97	   U12(x0, mark(x1), x2)
744.20/262.97	   U12(x0, x1, mark(x2))
744.20/262.97	   U12(active(x0), x1, x2)
744.20/262.97	   U12(x0, active(x1), x2)
744.20/262.97	   U12(x0, x1, active(x2))
744.20/262.97	   U13(mark(x0), x1, x2)
744.20/262.97	   U13(x0, mark(x1), x2)
744.20/262.97	   U13(x0, x1, mark(x2))
744.20/262.97	   U13(active(x0), x1, x2)
744.20/262.97	   U13(x0, active(x1), x2)
744.20/262.97	   U13(x0, x1, active(x2))
744.20/262.97	   U14(mark(x0), x1, x2)
744.20/262.97	   U14(x0, mark(x1), x2)
744.20/262.97	   U14(x0, x1, mark(x2))
744.20/262.97	   U14(active(x0), x1, x2)
744.20/262.97	   U14(x0, active(x1), x2)
744.20/262.97	   U14(x0, x1, active(x2))
744.20/262.97	   U15(mark(x0), x1)
744.20/262.97	   U15(x0, mark(x1))
744.20/262.97	   U15(active(x0), x1)
744.20/262.97	   U15(x0, active(x1))
744.20/262.97	   U16(mark(x0))
744.20/262.97	   U16(active(x0))
744.20/262.97	   U21(mark(x0), x1)
744.20/262.97	   U21(x0, mark(x1))
744.20/262.97	   U21(active(x0), x1)
744.20/262.97	   U21(x0, active(x1))
744.20/262.97	   U22(mark(x0), x1)
744.20/262.97	   U22(x0, mark(x1))
744.20/262.97	   U22(active(x0), x1)
744.20/262.97	   U22(x0, active(x1))
744.20/262.97	   U23(mark(x0))
744.20/262.97	   U23(active(x0))
744.20/262.97	   U31(mark(x0), x1, x2)
744.20/262.97	   U31(x0, mark(x1), x2)
744.20/262.97	   U31(x0, x1, mark(x2))
744.20/262.97	   U31(active(x0), x1, x2)
744.20/262.97	   U31(x0, active(x1), x2)
744.20/262.97	   U31(x0, x1, active(x2))
744.20/262.97	   U32(mark(x0), x1, x2)
744.20/262.97	   U32(x0, mark(x1), x2)
744.20/262.97	   U32(x0, x1, mark(x2))
744.20/262.97	   U32(active(x0), x1, x2)
744.20/262.97	   U32(x0, active(x1), x2)
744.20/262.97	   U32(x0, x1, active(x2))
744.20/262.97	   U33(mark(x0), x1, x2)
744.20/262.97	   U33(x0, mark(x1), x2)
744.20/262.97	   U33(x0, x1, mark(x2))
744.20/262.97	   U33(active(x0), x1, x2)
744.20/262.97	   U33(x0, active(x1), x2)
744.20/262.97	   U33(x0, x1, active(x2))
744.20/262.97	   U34(mark(x0), x1, x2)
744.20/262.97	   U34(x0, mark(x1), x2)
744.20/262.97	   U34(x0, x1, mark(x2))
744.20/262.97	   U34(active(x0), x1, x2)
744.20/262.97	   U34(x0, active(x1), x2)
744.20/262.97	   U34(x0, x1, active(x2))
744.20/262.97	   U35(mark(x0), x1)
744.20/262.97	   U35(x0, mark(x1))
744.20/262.97	   U35(active(x0), x1)
744.20/262.97	   U35(x0, active(x1))
744.20/262.97	   U36(mark(x0))
744.20/262.97	   U36(active(x0))
744.20/262.97	   U41(mark(x0), x1)
744.20/262.97	   U41(x0, mark(x1))
744.20/262.97	   U41(active(x0), x1)
744.20/262.97	   U41(x0, active(x1))
744.20/262.97	   U42(mark(x0))
744.20/262.97	   U42(active(x0))
744.20/262.97	   U51(mark(x0))
744.20/262.97	   U51(active(x0))
744.20/262.97	   U61(mark(x0), x1)
744.20/262.97	   U61(x0, mark(x1))
744.20/262.97	   U61(active(x0), x1)
744.20/262.97	   U61(x0, active(x1))
744.20/262.97	   U62(mark(x0))
744.20/262.97	   U62(active(x0))
744.20/262.97	   U71(mark(x0), x1)
744.20/262.97	   U71(x0, mark(x1))
744.20/262.97	   U71(active(x0), x1)
744.20/262.97	   U71(x0, active(x1))
744.20/262.97	   U72(mark(x0), x1)
744.20/262.97	   U72(x0, mark(x1))
744.20/262.97	   U72(active(x0), x1)
744.20/262.97	   U72(x0, active(x1))
744.20/262.97	   U81(mark(x0), x1, x2)
744.20/262.97	   U81(x0, mark(x1), x2)
744.20/262.97	   U81(x0, x1, mark(x2))
744.20/262.97	   U81(active(x0), x1, x2)
744.20/262.97	   U81(x0, active(x1), x2)
744.20/262.97	   U81(x0, x1, active(x2))
744.20/262.97	   U82(mark(x0), x1, x2)
744.20/262.97	   U82(x0, mark(x1), x2)
744.20/262.97	   U82(x0, x1, mark(x2))
744.20/262.97	   U82(active(x0), x1, x2)
744.20/262.97	   U82(x0, active(x1), x2)
744.20/262.97	   U82(x0, x1, active(x2))
744.20/262.97	   U83(mark(x0), x1, x2)
744.20/262.97	   U83(x0, mark(x1), x2)
744.20/262.97	   U83(x0, x1, mark(x2))
744.20/262.97	   U83(active(x0), x1, x2)
744.20/262.97	   U83(x0, active(x1), x2)
744.20/262.97	   U83(x0, x1, active(x2))
744.20/262.97	   U84(mark(x0), x1, x2)
744.20/262.97	   U84(x0, mark(x1), x2)
744.20/262.97	   U84(x0, x1, mark(x2))
744.20/262.97	   U84(active(x0), x1, x2)
744.20/262.97	   U84(x0, active(x1), x2)
744.20/262.97	   U84(x0, x1, active(x2))
744.20/262.97	   s(mark(x0))
744.20/262.97	   s(active(x0))
744.20/262.97	   U91(mark(x0), x1)
744.20/262.97	   U91(x0, mark(x1))
744.20/262.97	   U91(active(x0), x1)
744.20/262.97	   U91(x0, active(x1))
744.20/262.97	   U92(mark(x0))
744.20/262.97	   U92(active(x0))
744.20/262.97	
744.20/262.97	We have to consider all minimal (P,Q,R)-chains.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(258) UsableRulesProof (EQUIVALENT)
744.20/262.97	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.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(259)
744.20/262.97	Obligation:
744.20/262.97	Q DP problem:
744.20/262.97	The TRS P consists of the following rules:
744.20/262.97	
744.20/262.97	   U101^1(X1, mark(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(mark(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, X2, mark(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(active(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, active(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, X2, active(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	
744.20/262.97	R is empty.
744.20/262.97	The set Q consists of the following terms:
744.20/262.97	
744.20/262.97	   active(U101(tt, x0, x1))
744.20/262.97	   active(U102(tt, x0, x1))
744.20/262.97	   active(U103(tt, x0, x1))
744.20/262.97	   active(U104(tt, x0, x1))
744.20/262.97	   active(U11(tt, x0, x1))
744.20/262.97	   active(U12(tt, x0, x1))
744.20/262.97	   active(U13(tt, x0, x1))
744.20/262.97	   active(U14(tt, x0, x1))
744.20/262.97	   active(U15(tt, x0))
744.20/262.97	   active(U16(tt))
744.20/262.97	   active(U21(tt, x0))
744.20/262.97	   active(U22(tt, x0))
744.20/262.97	   active(U23(tt))
744.20/262.97	   active(U31(tt, x0, x1))
744.20/262.97	   active(U32(tt, x0, x1))
744.20/262.97	   active(U33(tt, x0, x1))
744.20/262.97	   active(U34(tt, x0, x1))
744.20/262.97	   active(U35(tt, x0))
744.20/262.97	   active(U36(tt))
744.20/262.97	   active(U41(tt, x0))
744.20/262.97	   active(U42(tt))
744.20/262.97	   active(U51(tt))
744.20/262.97	   active(U61(tt, x0))
744.20/262.97	   active(U62(tt))
744.20/262.97	   active(U71(tt, x0))
744.20/262.97	   active(U72(tt, x0))
744.20/262.97	   active(U81(tt, x0, x1))
744.20/262.97	   active(U82(tt, x0, x1))
744.20/262.97	   active(U83(tt, x0, x1))
744.20/262.97	   active(U84(tt, x0, x1))
744.20/262.97	   active(U91(tt, x0))
744.20/262.97	   active(U92(tt))
744.20/262.97	   active(isNat(0))
744.20/262.97	   active(isNat(plus(x0, x1)))
744.20/262.97	   active(isNat(s(x0)))
744.20/262.97	   active(isNat(x(x0, x1)))
744.20/262.97	   active(isNatKind(0))
744.20/262.97	   active(isNatKind(plus(x0, x1)))
744.20/262.97	   active(isNatKind(s(x0)))
744.20/262.97	   active(isNatKind(x(x0, x1)))
744.20/262.97	   active(plus(x0, 0))
744.20/262.97	   active(plus(x0, s(x1)))
744.20/262.97	   active(x(x0, 0))
744.20/262.97	   active(x(x0, s(x1)))
744.20/262.97	   mark(U101(x0, x1, x2))
744.20/262.97	   mark(tt)
744.20/262.97	   mark(U102(x0, x1, x2))
744.20/262.97	   mark(isNatKind(x0))
744.20/262.97	   mark(U103(x0, x1, x2))
744.20/262.97	   mark(isNat(x0))
744.20/262.97	   mark(U104(x0, x1, x2))
744.20/262.97	   mark(plus(x0, x1))
744.20/262.97	   mark(x(x0, x1))
744.20/262.97	   mark(U11(x0, x1, x2))
744.20/262.97	   mark(U12(x0, x1, x2))
744.20/262.97	   mark(U13(x0, x1, x2))
744.20/262.97	   mark(U14(x0, x1, x2))
744.20/262.97	   mark(U15(x0, x1))
744.20/262.97	   mark(U16(x0))
744.20/262.97	   mark(U21(x0, x1))
744.20/262.97	   mark(U22(x0, x1))
744.20/262.97	   mark(U23(x0))
744.20/262.97	   mark(U31(x0, x1, x2))
744.20/262.97	   mark(U32(x0, x1, x2))
744.20/262.97	   mark(U33(x0, x1, x2))
744.20/262.97	   mark(U34(x0, x1, x2))
744.20/262.97	   mark(U35(x0, x1))
744.20/262.97	   mark(U36(x0))
744.20/262.97	   mark(U41(x0, x1))
744.20/262.97	   mark(U42(x0))
744.20/262.97	   mark(U51(x0))
744.20/262.97	   mark(U61(x0, x1))
744.20/262.97	   mark(U62(x0))
744.20/262.97	   mark(U71(x0, x1))
744.20/262.97	   mark(U72(x0, x1))
744.20/262.97	   mark(U81(x0, x1, x2))
744.20/262.97	   mark(U82(x0, x1, x2))
744.20/262.97	   mark(U83(x0, x1, x2))
744.20/262.97	   mark(U84(x0, x1, x2))
744.20/262.97	   mark(s(x0))
744.20/262.97	   mark(U91(x0, x1))
744.20/262.97	   mark(U92(x0))
744.20/262.97	   mark(0)
744.20/262.97	   U101(mark(x0), x1, x2)
744.20/262.97	   U101(x0, mark(x1), x2)
744.20/262.97	   U101(x0, x1, mark(x2))
744.20/262.97	   U101(active(x0), x1, x2)
744.20/262.97	   U101(x0, active(x1), x2)
744.20/262.97	   U101(x0, x1, active(x2))
744.20/262.97	   U102(mark(x0), x1, x2)
744.20/262.97	   U102(x0, mark(x1), x2)
744.20/262.97	   U102(x0, x1, mark(x2))
744.20/262.97	   U102(active(x0), x1, x2)
744.20/262.97	   U102(x0, active(x1), x2)
744.20/262.97	   U102(x0, x1, active(x2))
744.20/262.97	   isNatKind(mark(x0))
744.20/262.97	   isNatKind(active(x0))
744.20/262.97	   U103(mark(x0), x1, x2)
744.20/262.97	   U103(x0, mark(x1), x2)
744.20/262.97	   U103(x0, x1, mark(x2))
744.20/262.97	   U103(active(x0), x1, x2)
744.20/262.97	   U103(x0, active(x1), x2)
744.20/262.97	   U103(x0, x1, active(x2))
744.20/262.97	   isNat(mark(x0))
744.20/262.97	   isNat(active(x0))
744.20/262.97	   U104(mark(x0), x1, x2)
744.20/262.97	   U104(x0, mark(x1), x2)
744.20/262.97	   U104(x0, x1, mark(x2))
744.20/262.97	   U104(active(x0), x1, x2)
744.20/262.97	   U104(x0, active(x1), x2)
744.20/262.97	   U104(x0, x1, active(x2))
744.20/262.97	   plus(mark(x0), x1)
744.20/262.97	   plus(x0, mark(x1))
744.20/262.97	   plus(active(x0), x1)
744.20/262.97	   plus(x0, active(x1))
744.20/262.97	   x(mark(x0), x1)
744.20/262.97	   x(x0, mark(x1))
744.20/262.97	   x(active(x0), x1)
744.20/262.97	   x(x0, active(x1))
744.20/262.97	   U11(mark(x0), x1, x2)
744.20/262.97	   U11(x0, mark(x1), x2)
744.20/262.97	   U11(x0, x1, mark(x2))
744.20/262.97	   U11(active(x0), x1, x2)
744.20/262.97	   U11(x0, active(x1), x2)
744.20/262.97	   U11(x0, x1, active(x2))
744.20/262.97	   U12(mark(x0), x1, x2)
744.20/262.97	   U12(x0, mark(x1), x2)
744.20/262.97	   U12(x0, x1, mark(x2))
744.20/262.97	   U12(active(x0), x1, x2)
744.20/262.97	   U12(x0, active(x1), x2)
744.20/262.97	   U12(x0, x1, active(x2))
744.20/262.97	   U13(mark(x0), x1, x2)
744.20/262.97	   U13(x0, mark(x1), x2)
744.20/262.97	   U13(x0, x1, mark(x2))
744.20/262.97	   U13(active(x0), x1, x2)
744.20/262.97	   U13(x0, active(x1), x2)
744.20/262.97	   U13(x0, x1, active(x2))
744.20/262.97	   U14(mark(x0), x1, x2)
744.20/262.97	   U14(x0, mark(x1), x2)
744.20/262.97	   U14(x0, x1, mark(x2))
744.20/262.97	   U14(active(x0), x1, x2)
744.20/262.97	   U14(x0, active(x1), x2)
744.20/262.97	   U14(x0, x1, active(x2))
744.20/262.97	   U15(mark(x0), x1)
744.20/262.97	   U15(x0, mark(x1))
744.20/262.97	   U15(active(x0), x1)
744.20/262.97	   U15(x0, active(x1))
744.20/262.97	   U16(mark(x0))
744.20/262.97	   U16(active(x0))
744.20/262.97	   U21(mark(x0), x1)
744.20/262.97	   U21(x0, mark(x1))
744.20/262.97	   U21(active(x0), x1)
744.20/262.97	   U21(x0, active(x1))
744.20/262.97	   U22(mark(x0), x1)
744.20/262.97	   U22(x0, mark(x1))
744.20/262.97	   U22(active(x0), x1)
744.20/262.97	   U22(x0, active(x1))
744.20/262.97	   U23(mark(x0))
744.20/262.97	   U23(active(x0))
744.20/262.97	   U31(mark(x0), x1, x2)
744.20/262.97	   U31(x0, mark(x1), x2)
744.20/262.97	   U31(x0, x1, mark(x2))
744.20/262.97	   U31(active(x0), x1, x2)
744.20/262.97	   U31(x0, active(x1), x2)
744.20/262.97	   U31(x0, x1, active(x2))
744.20/262.97	   U32(mark(x0), x1, x2)
744.20/262.97	   U32(x0, mark(x1), x2)
744.20/262.97	   U32(x0, x1, mark(x2))
744.20/262.97	   U32(active(x0), x1, x2)
744.20/262.97	   U32(x0, active(x1), x2)
744.20/262.97	   U32(x0, x1, active(x2))
744.20/262.97	   U33(mark(x0), x1, x2)
744.20/262.97	   U33(x0, mark(x1), x2)
744.20/262.97	   U33(x0, x1, mark(x2))
744.20/262.97	   U33(active(x0), x1, x2)
744.20/262.97	   U33(x0, active(x1), x2)
744.20/262.97	   U33(x0, x1, active(x2))
744.20/262.97	   U34(mark(x0), x1, x2)
744.20/262.97	   U34(x0, mark(x1), x2)
744.20/262.97	   U34(x0, x1, mark(x2))
744.20/262.97	   U34(active(x0), x1, x2)
744.20/262.97	   U34(x0, active(x1), x2)
744.20/262.97	   U34(x0, x1, active(x2))
744.20/262.97	   U35(mark(x0), x1)
744.20/262.97	   U35(x0, mark(x1))
744.20/262.97	   U35(active(x0), x1)
744.20/262.97	   U35(x0, active(x1))
744.20/262.97	   U36(mark(x0))
744.20/262.97	   U36(active(x0))
744.20/262.97	   U41(mark(x0), x1)
744.20/262.97	   U41(x0, mark(x1))
744.20/262.97	   U41(active(x0), x1)
744.20/262.97	   U41(x0, active(x1))
744.20/262.97	   U42(mark(x0))
744.20/262.97	   U42(active(x0))
744.20/262.97	   U51(mark(x0))
744.20/262.97	   U51(active(x0))
744.20/262.97	   U61(mark(x0), x1)
744.20/262.97	   U61(x0, mark(x1))
744.20/262.97	   U61(active(x0), x1)
744.20/262.97	   U61(x0, active(x1))
744.20/262.97	   U62(mark(x0))
744.20/262.97	   U62(active(x0))
744.20/262.97	   U71(mark(x0), x1)
744.20/262.97	   U71(x0, mark(x1))
744.20/262.97	   U71(active(x0), x1)
744.20/262.97	   U71(x0, active(x1))
744.20/262.97	   U72(mark(x0), x1)
744.20/262.97	   U72(x0, mark(x1))
744.20/262.97	   U72(active(x0), x1)
744.20/262.97	   U72(x0, active(x1))
744.20/262.97	   U81(mark(x0), x1, x2)
744.20/262.97	   U81(x0, mark(x1), x2)
744.20/262.97	   U81(x0, x1, mark(x2))
744.20/262.97	   U81(active(x0), x1, x2)
744.20/262.97	   U81(x0, active(x1), x2)
744.20/262.97	   U81(x0, x1, active(x2))
744.20/262.97	   U82(mark(x0), x1, x2)
744.20/262.97	   U82(x0, mark(x1), x2)
744.20/262.97	   U82(x0, x1, mark(x2))
744.20/262.97	   U82(active(x0), x1, x2)
744.20/262.97	   U82(x0, active(x1), x2)
744.20/262.97	   U82(x0, x1, active(x2))
744.20/262.97	   U83(mark(x0), x1, x2)
744.20/262.97	   U83(x0, mark(x1), x2)
744.20/262.97	   U83(x0, x1, mark(x2))
744.20/262.97	   U83(active(x0), x1, x2)
744.20/262.97	   U83(x0, active(x1), x2)
744.20/262.97	   U83(x0, x1, active(x2))
744.20/262.97	   U84(mark(x0), x1, x2)
744.20/262.97	   U84(x0, mark(x1), x2)
744.20/262.97	   U84(x0, x1, mark(x2))
744.20/262.97	   U84(active(x0), x1, x2)
744.20/262.97	   U84(x0, active(x1), x2)
744.20/262.97	   U84(x0, x1, active(x2))
744.20/262.97	   s(mark(x0))
744.20/262.97	   s(active(x0))
744.20/262.97	   U91(mark(x0), x1)
744.20/262.97	   U91(x0, mark(x1))
744.20/262.97	   U91(active(x0), x1)
744.20/262.97	   U91(x0, active(x1))
744.20/262.97	   U92(mark(x0))
744.20/262.97	   U92(active(x0))
744.20/262.97	
744.20/262.97	We have to consider all minimal (P,Q,R)-chains.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(260) QReductionProof (EQUIVALENT)
744.20/262.97	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.20/262.97	
744.20/262.97	   U101(mark(x0), x1, x2)
744.20/262.97	   U101(x0, mark(x1), x2)
744.20/262.97	   U101(x0, x1, mark(x2))
744.20/262.97	   U101(active(x0), x1, x2)
744.20/262.97	   U101(x0, active(x1), x2)
744.20/262.97	   U101(x0, x1, active(x2))
744.20/262.97	   U102(mark(x0), x1, x2)
744.20/262.97	   U102(x0, mark(x1), x2)
744.20/262.97	   U102(x0, x1, mark(x2))
744.20/262.97	   U102(active(x0), x1, x2)
744.20/262.97	   U102(x0, active(x1), x2)
744.20/262.97	   U102(x0, x1, active(x2))
744.20/262.97	   isNatKind(mark(x0))
744.20/262.97	   isNatKind(active(x0))
744.20/262.97	   U103(mark(x0), x1, x2)
744.20/262.97	   U103(x0, mark(x1), x2)
744.20/262.97	   U103(x0, x1, mark(x2))
744.20/262.97	   U103(active(x0), x1, x2)
744.20/262.97	   U103(x0, active(x1), x2)
744.20/262.97	   U103(x0, x1, active(x2))
744.20/262.97	   isNat(mark(x0))
744.20/262.97	   isNat(active(x0))
744.20/262.97	   U104(mark(x0), x1, x2)
744.20/262.97	   U104(x0, mark(x1), x2)
744.20/262.97	   U104(x0, x1, mark(x2))
744.20/262.97	   U104(active(x0), x1, x2)
744.20/262.97	   U104(x0, active(x1), x2)
744.20/262.97	   U104(x0, x1, active(x2))
744.20/262.97	   plus(mark(x0), x1)
744.20/262.97	   plus(x0, mark(x1))
744.20/262.97	   plus(active(x0), x1)
744.20/262.97	   plus(x0, active(x1))
744.20/262.97	   x(mark(x0), x1)
744.20/262.97	   x(x0, mark(x1))
744.20/262.97	   x(active(x0), x1)
744.20/262.97	   x(x0, active(x1))
744.20/262.97	   U11(mark(x0), x1, x2)
744.20/262.97	   U11(x0, mark(x1), x2)
744.20/262.97	   U11(x0, x1, mark(x2))
744.20/262.97	   U11(active(x0), x1, x2)
744.20/262.97	   U11(x0, active(x1), x2)
744.20/262.97	   U11(x0, x1, active(x2))
744.20/262.97	   U12(mark(x0), x1, x2)
744.20/262.97	   U12(x0, mark(x1), x2)
744.20/262.97	   U12(x0, x1, mark(x2))
744.20/262.97	   U12(active(x0), x1, x2)
744.20/262.97	   U12(x0, active(x1), x2)
744.20/262.97	   U12(x0, x1, active(x2))
744.20/262.97	   U13(mark(x0), x1, x2)
744.20/262.97	   U13(x0, mark(x1), x2)
744.20/262.97	   U13(x0, x1, mark(x2))
744.20/262.97	   U13(active(x0), x1, x2)
744.20/262.97	   U13(x0, active(x1), x2)
744.20/262.97	   U13(x0, x1, active(x2))
744.20/262.97	   U14(mark(x0), x1, x2)
744.20/262.97	   U14(x0, mark(x1), x2)
744.20/262.97	   U14(x0, x1, mark(x2))
744.20/262.97	   U14(active(x0), x1, x2)
744.20/262.97	   U14(x0, active(x1), x2)
744.20/262.97	   U14(x0, x1, active(x2))
744.20/262.97	   U15(mark(x0), x1)
744.20/262.97	   U15(x0, mark(x1))
744.20/262.97	   U15(active(x0), x1)
744.20/262.97	   U15(x0, active(x1))
744.20/262.97	   U16(mark(x0))
744.20/262.97	   U16(active(x0))
744.20/262.97	   U21(mark(x0), x1)
744.20/262.97	   U21(x0, mark(x1))
744.20/262.97	   U21(active(x0), x1)
744.20/262.97	   U21(x0, active(x1))
744.20/262.97	   U22(mark(x0), x1)
744.20/262.97	   U22(x0, mark(x1))
744.20/262.97	   U22(active(x0), x1)
744.20/262.97	   U22(x0, active(x1))
744.20/262.97	   U23(mark(x0))
744.20/262.97	   U23(active(x0))
744.20/262.97	   U31(mark(x0), x1, x2)
744.20/262.97	   U31(x0, mark(x1), x2)
744.20/262.97	   U31(x0, x1, mark(x2))
744.20/262.97	   U31(active(x0), x1, x2)
744.20/262.97	   U31(x0, active(x1), x2)
744.20/262.97	   U31(x0, x1, active(x2))
744.20/262.97	   U32(mark(x0), x1, x2)
744.20/262.97	   U32(x0, mark(x1), x2)
744.20/262.97	   U32(x0, x1, mark(x2))
744.20/262.97	   U32(active(x0), x1, x2)
744.20/262.97	   U32(x0, active(x1), x2)
744.20/262.97	   U32(x0, x1, active(x2))
744.20/262.97	   U33(mark(x0), x1, x2)
744.20/262.97	   U33(x0, mark(x1), x2)
744.20/262.97	   U33(x0, x1, mark(x2))
744.20/262.97	   U33(active(x0), x1, x2)
744.20/262.97	   U33(x0, active(x1), x2)
744.20/262.97	   U33(x0, x1, active(x2))
744.20/262.97	   U34(mark(x0), x1, x2)
744.20/262.97	   U34(x0, mark(x1), x2)
744.20/262.97	   U34(x0, x1, mark(x2))
744.20/262.97	   U34(active(x0), x1, x2)
744.20/262.97	   U34(x0, active(x1), x2)
744.20/262.97	   U34(x0, x1, active(x2))
744.20/262.97	   U35(mark(x0), x1)
744.20/262.97	   U35(x0, mark(x1))
744.20/262.97	   U35(active(x0), x1)
744.20/262.97	   U35(x0, active(x1))
744.20/262.97	   U36(mark(x0))
744.20/262.97	   U36(active(x0))
744.20/262.97	   U41(mark(x0), x1)
744.20/262.97	   U41(x0, mark(x1))
744.20/262.97	   U41(active(x0), x1)
744.20/262.97	   U41(x0, active(x1))
744.20/262.97	   U42(mark(x0))
744.20/262.97	   U42(active(x0))
744.20/262.97	   U51(mark(x0))
744.20/262.97	   U51(active(x0))
744.20/262.97	   U61(mark(x0), x1)
744.20/262.97	   U61(x0, mark(x1))
744.20/262.97	   U61(active(x0), x1)
744.20/262.97	   U61(x0, active(x1))
744.20/262.97	   U62(mark(x0))
744.20/262.97	   U62(active(x0))
744.20/262.97	   U71(mark(x0), x1)
744.20/262.97	   U71(x0, mark(x1))
744.20/262.97	   U71(active(x0), x1)
744.20/262.97	   U71(x0, active(x1))
744.20/262.97	   U72(mark(x0), x1)
744.20/262.97	   U72(x0, mark(x1))
744.20/262.97	   U72(active(x0), x1)
744.20/262.97	   U72(x0, active(x1))
744.20/262.97	   U81(mark(x0), x1, x2)
744.20/262.97	   U81(x0, mark(x1), x2)
744.20/262.97	   U81(x0, x1, mark(x2))
744.20/262.97	   U81(active(x0), x1, x2)
744.20/262.97	   U81(x0, active(x1), x2)
744.20/262.97	   U81(x0, x1, active(x2))
744.20/262.97	   U82(mark(x0), x1, x2)
744.20/262.97	   U82(x0, mark(x1), x2)
744.20/262.97	   U82(x0, x1, mark(x2))
744.20/262.97	   U82(active(x0), x1, x2)
744.20/262.97	   U82(x0, active(x1), x2)
744.20/262.97	   U82(x0, x1, active(x2))
744.20/262.97	   U83(mark(x0), x1, x2)
744.20/262.97	   U83(x0, mark(x1), x2)
744.20/262.97	   U83(x0, x1, mark(x2))
744.20/262.97	   U83(active(x0), x1, x2)
744.20/262.97	   U83(x0, active(x1), x2)
744.20/262.97	   U83(x0, x1, active(x2))
744.20/262.97	   U84(mark(x0), x1, x2)
744.20/262.97	   U84(x0, mark(x1), x2)
744.20/262.97	   U84(x0, x1, mark(x2))
744.20/262.97	   U84(active(x0), x1, x2)
744.20/262.97	   U84(x0, active(x1), x2)
744.20/262.97	   U84(x0, x1, active(x2))
744.20/262.97	   s(mark(x0))
744.20/262.97	   s(active(x0))
744.20/262.97	   U91(mark(x0), x1)
744.20/262.97	   U91(x0, mark(x1))
744.20/262.97	   U91(active(x0), x1)
744.20/262.97	   U91(x0, active(x1))
744.20/262.97	   U92(mark(x0))
744.20/262.97	   U92(active(x0))
744.20/262.97	
744.20/262.97	
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(261)
744.20/262.97	Obligation:
744.20/262.97	Q DP problem:
744.20/262.97	The TRS P consists of the following rules:
744.20/262.97	
744.20/262.97	   U101^1(X1, mark(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(mark(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, X2, mark(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(active(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, active(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	   U101^1(X1, X2, active(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	
744.20/262.97	R is empty.
744.20/262.97	The set Q consists of the following terms:
744.20/262.97	
744.20/262.97	   active(U101(tt, x0, x1))
744.20/262.97	   active(U102(tt, x0, x1))
744.20/262.97	   active(U103(tt, x0, x1))
744.20/262.97	   active(U104(tt, x0, x1))
744.20/262.97	   active(U11(tt, x0, x1))
744.20/262.97	   active(U12(tt, x0, x1))
744.20/262.97	   active(U13(tt, x0, x1))
744.20/262.97	   active(U14(tt, x0, x1))
744.20/262.97	   active(U15(tt, x0))
744.20/262.97	   active(U16(tt))
744.20/262.97	   active(U21(tt, x0))
744.20/262.97	   active(U22(tt, x0))
744.20/262.97	   active(U23(tt))
744.20/262.97	   active(U31(tt, x0, x1))
744.20/262.97	   active(U32(tt, x0, x1))
744.20/262.97	   active(U33(tt, x0, x1))
744.20/262.97	   active(U34(tt, x0, x1))
744.20/262.97	   active(U35(tt, x0))
744.20/262.97	   active(U36(tt))
744.20/262.97	   active(U41(tt, x0))
744.20/262.97	   active(U42(tt))
744.20/262.97	   active(U51(tt))
744.20/262.97	   active(U61(tt, x0))
744.20/262.97	   active(U62(tt))
744.20/262.97	   active(U71(tt, x0))
744.20/262.97	   active(U72(tt, x0))
744.20/262.97	   active(U81(tt, x0, x1))
744.20/262.97	   active(U82(tt, x0, x1))
744.20/262.97	   active(U83(tt, x0, x1))
744.20/262.97	   active(U84(tt, x0, x1))
744.20/262.97	   active(U91(tt, x0))
744.20/262.97	   active(U92(tt))
744.20/262.97	   active(isNat(0))
744.20/262.97	   active(isNat(plus(x0, x1)))
744.20/262.97	   active(isNat(s(x0)))
744.20/262.97	   active(isNat(x(x0, x1)))
744.20/262.97	   active(isNatKind(0))
744.20/262.97	   active(isNatKind(plus(x0, x1)))
744.20/262.97	   active(isNatKind(s(x0)))
744.20/262.97	   active(isNatKind(x(x0, x1)))
744.20/262.97	   active(plus(x0, 0))
744.20/262.97	   active(plus(x0, s(x1)))
744.20/262.97	   active(x(x0, 0))
744.20/262.97	   active(x(x0, s(x1)))
744.20/262.97	   mark(U101(x0, x1, x2))
744.20/262.97	   mark(tt)
744.20/262.97	   mark(U102(x0, x1, x2))
744.20/262.97	   mark(isNatKind(x0))
744.20/262.97	   mark(U103(x0, x1, x2))
744.20/262.97	   mark(isNat(x0))
744.20/262.97	   mark(U104(x0, x1, x2))
744.20/262.97	   mark(plus(x0, x1))
744.20/262.97	   mark(x(x0, x1))
744.20/262.97	   mark(U11(x0, x1, x2))
744.20/262.97	   mark(U12(x0, x1, x2))
744.20/262.97	   mark(U13(x0, x1, x2))
744.20/262.97	   mark(U14(x0, x1, x2))
744.20/262.97	   mark(U15(x0, x1))
744.20/262.97	   mark(U16(x0))
744.20/262.97	   mark(U21(x0, x1))
744.20/262.97	   mark(U22(x0, x1))
744.20/262.97	   mark(U23(x0))
744.20/262.97	   mark(U31(x0, x1, x2))
744.20/262.97	   mark(U32(x0, x1, x2))
744.20/262.97	   mark(U33(x0, x1, x2))
744.20/262.97	   mark(U34(x0, x1, x2))
744.20/262.97	   mark(U35(x0, x1))
744.20/262.97	   mark(U36(x0))
744.20/262.97	   mark(U41(x0, x1))
744.20/262.97	   mark(U42(x0))
744.20/262.97	   mark(U51(x0))
744.20/262.97	   mark(U61(x0, x1))
744.20/262.97	   mark(U62(x0))
744.20/262.97	   mark(U71(x0, x1))
744.20/262.97	   mark(U72(x0, x1))
744.20/262.97	   mark(U81(x0, x1, x2))
744.20/262.97	   mark(U82(x0, x1, x2))
744.20/262.97	   mark(U83(x0, x1, x2))
744.20/262.97	   mark(U84(x0, x1, x2))
744.20/262.97	   mark(s(x0))
744.20/262.97	   mark(U91(x0, x1))
744.20/262.97	   mark(U92(x0))
744.20/262.97	   mark(0)
744.20/262.97	
744.20/262.97	We have to consider all minimal (P,Q,R)-chains.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(262) QDPSizeChangeProof (EQUIVALENT)
744.20/262.97	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. 
744.20/262.97	
744.20/262.97	From the DPs we obtained the following set of size-change graphs:
744.20/262.97	*U101^1(X1, mark(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.97	
744.20/262.97	
744.20/262.97	*U101^1(mark(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.97	
744.20/262.97	
744.20/262.97	*U101^1(X1, X2, mark(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.97	
744.20/262.97	
744.20/262.97	*U101^1(active(X1), X2, X3) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
744.20/262.97	
744.20/262.97	
744.20/262.97	*U101^1(X1, active(X2), X3) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
744.20/262.97	
744.20/262.97	
744.20/262.97	*U101^1(X1, X2, active(X3)) -> U101^1(X1, X2, X3)
744.20/262.97	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
744.20/262.97	
744.20/262.97	
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(263)
744.20/262.97	YES
744.20/262.97	
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(264)
744.20/262.97	Obligation:
744.20/262.97	Q DP problem:
744.20/262.97	The TRS P consists of the following rules:
744.20/262.97	
744.20/262.97	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.97	   MARK(U102(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.97	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.97	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
744.20/262.97	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.97	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.97	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.97	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.97	   MARK(U16(X)) -> ACTIVE(U16(mark(X)))
744.20/262.97	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.97	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.97	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.97	   MARK(U23(X)) -> ACTIVE(U23(mark(X)))
744.20/262.97	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.97	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.97	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.97	   MARK(U36(X)) -> ACTIVE(U36(mark(X)))
744.20/262.97	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.97	   MARK(U42(X)) -> ACTIVE(U42(mark(X)))
744.20/262.97	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.97	   MARK(U62(X)) -> ACTIVE(U62(mark(X)))
744.20/262.97	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
744.20/262.97	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.97	   ACTIVE(U72(tt, N)) -> MARK(N)
744.20/262.97	   MARK(U101(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.97	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.97	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.97	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.97	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.97	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.97	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
744.20/262.97	   MARK(s(X)) -> ACTIVE(s(mark(X)))
744.20/262.97	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
744.20/262.97	   MARK(U92(X)) -> ACTIVE(U92(mark(X)))
744.20/262.97	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
744.20/262.97	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.97	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
744.20/262.97	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
744.20/262.97	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.97	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
744.20/262.97	   MARK(U91(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U103(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.97	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.97	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U104(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(plus(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(plus(X1, X2)) -> MARK(X2)
744.20/262.97	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.97	   MARK(x(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(x(X1, X2)) -> MARK(X2)
744.20/262.97	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U16(X)) -> MARK(X)
744.20/262.97	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.97	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U23(X)) -> MARK(X)
744.20/262.97	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.97	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U36(X)) -> MARK(X)
744.20/262.97	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U42(X)) -> MARK(X)
744.20/262.97	   MARK(U51(X)) -> ACTIVE(U51(mark(X)))
744.20/262.97	   MARK(U51(X)) -> MARK(X)
744.20/262.97	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.97	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U62(X)) -> MARK(X)
744.20/262.97	   MARK(U71(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U72(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U81(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U82(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U83(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U84(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(s(X)) -> MARK(X)
744.20/262.97	   MARK(U92(X)) -> MARK(X)
744.20/262.97	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.97	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.97	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.97	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.97	
744.20/262.97	The TRS R consists of the following rules:
744.20/262.97	
744.20/262.97	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.97	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.97	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.97	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.97	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.97	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.97	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.97	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.97	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.97	   active(U16(tt)) -> mark(tt)
744.20/262.97	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.97	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.97	   active(U23(tt)) -> mark(tt)
744.20/262.97	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.97	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.97	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.97	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.97	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.97	   active(U36(tt)) -> mark(tt)
744.20/262.97	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.97	   active(U42(tt)) -> mark(tt)
744.20/262.97	   active(U51(tt)) -> mark(tt)
744.20/262.97	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.97	   active(U62(tt)) -> mark(tt)
744.20/262.97	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.97	   active(U72(tt, N)) -> mark(N)
744.20/262.97	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.97	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.97	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.97	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.97	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.97	   active(U92(tt)) -> mark(0)
744.20/262.97	   active(isNat(0)) -> mark(tt)
744.20/262.97	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.97	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.97	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.97	   active(isNatKind(0)) -> mark(tt)
744.20/262.97	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.97	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.97	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.97	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.97	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.97	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.97	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.97	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.97	   mark(tt) -> active(tt)
744.20/262.97	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.97	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.97	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.97	   mark(isNat(X)) -> active(isNat(X))
744.20/262.97	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.97	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.97	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.97	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.97	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.97	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.97	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.97	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.97	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.97	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.97	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.97	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.97	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.97	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.97	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.97	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.97	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.97	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.97	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.97	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.97	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.97	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.97	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.97	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.97	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.97	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.97	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.97	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.97	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.97	   mark(s(X)) -> active(s(mark(X)))
744.20/262.97	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.97	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.97	   mark(0) -> active(0)
744.20/262.97	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.97	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.97	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.97	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.97	   isNatKind(mark(X)) -> isNatKind(X)
744.20/262.97	   isNatKind(active(X)) -> isNatKind(X)
744.20/262.97	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.97	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.97	   isNat(mark(X)) -> isNat(X)
744.20/262.97	   isNat(active(X)) -> isNat(X)
744.20/262.97	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.97	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.97	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.97	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.97	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.97	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.97	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.97	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.97	   x(active(X1), X2) -> x(X1, X2)
744.20/262.97	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.97	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.97	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.97	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.97	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.97	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.97	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.97	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.97	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.97	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.97	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.97	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.97	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.97	   U16(mark(X)) -> U16(X)
744.20/262.97	   U16(active(X)) -> U16(X)
744.20/262.97	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.97	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.97	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.97	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.97	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.97	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.97	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.97	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.97	   U23(mark(X)) -> U23(X)
744.20/262.97	   U23(active(X)) -> U23(X)
744.20/262.97	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.97	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.97	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.97	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.97	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.97	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.97	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.97	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.97	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.97	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.97	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.97	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.97	   U36(mark(X)) -> U36(X)
744.20/262.97	   U36(active(X)) -> U36(X)
744.20/262.97	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.97	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.97	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.97	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.97	   U42(mark(X)) -> U42(X)
744.20/262.97	   U42(active(X)) -> U42(X)
744.20/262.97	   U51(mark(X)) -> U51(X)
744.20/262.97	   U51(active(X)) -> U51(X)
744.20/262.97	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.97	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.97	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.97	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.97	   U62(mark(X)) -> U62(X)
744.20/262.97	   U62(active(X)) -> U62(X)
744.20/262.97	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.97	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.97	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.97	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.97	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.97	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.97	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.97	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.97	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.97	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.97	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.97	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.97	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.97	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.97	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.97	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.97	   s(mark(X)) -> s(X)
744.20/262.97	   s(active(X)) -> s(X)
744.20/262.97	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.97	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.97	   U92(mark(X)) -> U92(X)
744.20/262.97	   U92(active(X)) -> U92(X)
744.20/262.97	
744.20/262.97	The set Q consists of the following terms:
744.20/262.97	
744.20/262.97	   active(U101(tt, x0, x1))
744.20/262.97	   active(U102(tt, x0, x1))
744.20/262.97	   active(U103(tt, x0, x1))
744.20/262.97	   active(U104(tt, x0, x1))
744.20/262.97	   active(U11(tt, x0, x1))
744.20/262.97	   active(U12(tt, x0, x1))
744.20/262.97	   active(U13(tt, x0, x1))
744.20/262.97	   active(U14(tt, x0, x1))
744.20/262.97	   active(U15(tt, x0))
744.20/262.97	   active(U16(tt))
744.20/262.97	   active(U21(tt, x0))
744.20/262.97	   active(U22(tt, x0))
744.20/262.97	   active(U23(tt))
744.20/262.97	   active(U31(tt, x0, x1))
744.20/262.97	   active(U32(tt, x0, x1))
744.20/262.97	   active(U33(tt, x0, x1))
744.20/262.97	   active(U34(tt, x0, x1))
744.20/262.97	   active(U35(tt, x0))
744.20/262.97	   active(U36(tt))
744.20/262.97	   active(U41(tt, x0))
744.20/262.97	   active(U42(tt))
744.20/262.97	   active(U51(tt))
744.20/262.97	   active(U61(tt, x0))
744.20/262.97	   active(U62(tt))
744.20/262.97	   active(U71(tt, x0))
744.20/262.97	   active(U72(tt, x0))
744.20/262.97	   active(U81(tt, x0, x1))
744.20/262.97	   active(U82(tt, x0, x1))
744.20/262.97	   active(U83(tt, x0, x1))
744.20/262.97	   active(U84(tt, x0, x1))
744.20/262.97	   active(U91(tt, x0))
744.20/262.97	   active(U92(tt))
744.20/262.97	   active(isNat(0))
744.20/262.97	   active(isNat(plus(x0, x1)))
744.20/262.97	   active(isNat(s(x0)))
744.20/262.97	   active(isNat(x(x0, x1)))
744.20/262.97	   active(isNatKind(0))
744.20/262.97	   active(isNatKind(plus(x0, x1)))
744.20/262.97	   active(isNatKind(s(x0)))
744.20/262.97	   active(isNatKind(x(x0, x1)))
744.20/262.97	   active(plus(x0, 0))
744.20/262.97	   active(plus(x0, s(x1)))
744.20/262.97	   active(x(x0, 0))
744.20/262.97	   active(x(x0, s(x1)))
744.20/262.97	   mark(U101(x0, x1, x2))
744.20/262.97	   mark(tt)
744.20/262.97	   mark(U102(x0, x1, x2))
744.20/262.97	   mark(isNatKind(x0))
744.20/262.97	   mark(U103(x0, x1, x2))
744.20/262.97	   mark(isNat(x0))
744.20/262.97	   mark(U104(x0, x1, x2))
744.20/262.97	   mark(plus(x0, x1))
744.20/262.97	   mark(x(x0, x1))
744.20/262.97	   mark(U11(x0, x1, x2))
744.20/262.97	   mark(U12(x0, x1, x2))
744.20/262.97	   mark(U13(x0, x1, x2))
744.20/262.97	   mark(U14(x0, x1, x2))
744.20/262.97	   mark(U15(x0, x1))
744.20/262.97	   mark(U16(x0))
744.20/262.97	   mark(U21(x0, x1))
744.20/262.97	   mark(U22(x0, x1))
744.20/262.97	   mark(U23(x0))
744.20/262.97	   mark(U31(x0, x1, x2))
744.20/262.97	   mark(U32(x0, x1, x2))
744.20/262.97	   mark(U33(x0, x1, x2))
744.20/262.97	   mark(U34(x0, x1, x2))
744.20/262.97	   mark(U35(x0, x1))
744.20/262.97	   mark(U36(x0))
744.20/262.97	   mark(U41(x0, x1))
744.20/262.97	   mark(U42(x0))
744.20/262.97	   mark(U51(x0))
744.20/262.97	   mark(U61(x0, x1))
744.20/262.97	   mark(U62(x0))
744.20/262.97	   mark(U71(x0, x1))
744.20/262.97	   mark(U72(x0, x1))
744.20/262.97	   mark(U81(x0, x1, x2))
744.20/262.97	   mark(U82(x0, x1, x2))
744.20/262.97	   mark(U83(x0, x1, x2))
744.20/262.97	   mark(U84(x0, x1, x2))
744.20/262.97	   mark(s(x0))
744.20/262.97	   mark(U91(x0, x1))
744.20/262.97	   mark(U92(x0))
744.20/262.97	   mark(0)
744.20/262.97	   U101(mark(x0), x1, x2)
744.20/262.97	   U101(x0, mark(x1), x2)
744.20/262.97	   U101(x0, x1, mark(x2))
744.20/262.97	   U101(active(x0), x1, x2)
744.20/262.97	   U101(x0, active(x1), x2)
744.20/262.97	   U101(x0, x1, active(x2))
744.20/262.97	   U102(mark(x0), x1, x2)
744.20/262.97	   U102(x0, mark(x1), x2)
744.20/262.97	   U102(x0, x1, mark(x2))
744.20/262.97	   U102(active(x0), x1, x2)
744.20/262.97	   U102(x0, active(x1), x2)
744.20/262.97	   U102(x0, x1, active(x2))
744.20/262.97	   isNatKind(mark(x0))
744.20/262.97	   isNatKind(active(x0))
744.20/262.97	   U103(mark(x0), x1, x2)
744.20/262.97	   U103(x0, mark(x1), x2)
744.20/262.97	   U103(x0, x1, mark(x2))
744.20/262.97	   U103(active(x0), x1, x2)
744.20/262.97	   U103(x0, active(x1), x2)
744.20/262.97	   U103(x0, x1, active(x2))
744.20/262.97	   isNat(mark(x0))
744.20/262.97	   isNat(active(x0))
744.20/262.97	   U104(mark(x0), x1, x2)
744.20/262.97	   U104(x0, mark(x1), x2)
744.20/262.97	   U104(x0, x1, mark(x2))
744.20/262.97	   U104(active(x0), x1, x2)
744.20/262.97	   U104(x0, active(x1), x2)
744.20/262.97	   U104(x0, x1, active(x2))
744.20/262.97	   plus(mark(x0), x1)
744.20/262.97	   plus(x0, mark(x1))
744.20/262.97	   plus(active(x0), x1)
744.20/262.97	   plus(x0, active(x1))
744.20/262.97	   x(mark(x0), x1)
744.20/262.97	   x(x0, mark(x1))
744.20/262.97	   x(active(x0), x1)
744.20/262.97	   x(x0, active(x1))
744.20/262.97	   U11(mark(x0), x1, x2)
744.20/262.97	   U11(x0, mark(x1), x2)
744.20/262.97	   U11(x0, x1, mark(x2))
744.20/262.97	   U11(active(x0), x1, x2)
744.20/262.97	   U11(x0, active(x1), x2)
744.20/262.97	   U11(x0, x1, active(x2))
744.20/262.97	   U12(mark(x0), x1, x2)
744.20/262.97	   U12(x0, mark(x1), x2)
744.20/262.97	   U12(x0, x1, mark(x2))
744.20/262.97	   U12(active(x0), x1, x2)
744.20/262.97	   U12(x0, active(x1), x2)
744.20/262.97	   U12(x0, x1, active(x2))
744.20/262.97	   U13(mark(x0), x1, x2)
744.20/262.97	   U13(x0, mark(x1), x2)
744.20/262.97	   U13(x0, x1, mark(x2))
744.20/262.97	   U13(active(x0), x1, x2)
744.20/262.97	   U13(x0, active(x1), x2)
744.20/262.97	   U13(x0, x1, active(x2))
744.20/262.97	   U14(mark(x0), x1, x2)
744.20/262.97	   U14(x0, mark(x1), x2)
744.20/262.97	   U14(x0, x1, mark(x2))
744.20/262.97	   U14(active(x0), x1, x2)
744.20/262.97	   U14(x0, active(x1), x2)
744.20/262.97	   U14(x0, x1, active(x2))
744.20/262.97	   U15(mark(x0), x1)
744.20/262.97	   U15(x0, mark(x1))
744.20/262.97	   U15(active(x0), x1)
744.20/262.97	   U15(x0, active(x1))
744.20/262.97	   U16(mark(x0))
744.20/262.97	   U16(active(x0))
744.20/262.97	   U21(mark(x0), x1)
744.20/262.97	   U21(x0, mark(x1))
744.20/262.97	   U21(active(x0), x1)
744.20/262.97	   U21(x0, active(x1))
744.20/262.97	   U22(mark(x0), x1)
744.20/262.97	   U22(x0, mark(x1))
744.20/262.97	   U22(active(x0), x1)
744.20/262.97	   U22(x0, active(x1))
744.20/262.97	   U23(mark(x0))
744.20/262.97	   U23(active(x0))
744.20/262.97	   U31(mark(x0), x1, x2)
744.20/262.97	   U31(x0, mark(x1), x2)
744.20/262.97	   U31(x0, x1, mark(x2))
744.20/262.97	   U31(active(x0), x1, x2)
744.20/262.97	   U31(x0, active(x1), x2)
744.20/262.97	   U31(x0, x1, active(x2))
744.20/262.97	   U32(mark(x0), x1, x2)
744.20/262.97	   U32(x0, mark(x1), x2)
744.20/262.97	   U32(x0, x1, mark(x2))
744.20/262.97	   U32(active(x0), x1, x2)
744.20/262.97	   U32(x0, active(x1), x2)
744.20/262.97	   U32(x0, x1, active(x2))
744.20/262.97	   U33(mark(x0), x1, x2)
744.20/262.97	   U33(x0, mark(x1), x2)
744.20/262.97	   U33(x0, x1, mark(x2))
744.20/262.97	   U33(active(x0), x1, x2)
744.20/262.97	   U33(x0, active(x1), x2)
744.20/262.97	   U33(x0, x1, active(x2))
744.20/262.97	   U34(mark(x0), x1, x2)
744.20/262.97	   U34(x0, mark(x1), x2)
744.20/262.97	   U34(x0, x1, mark(x2))
744.20/262.97	   U34(active(x0), x1, x2)
744.20/262.97	   U34(x0, active(x1), x2)
744.20/262.97	   U34(x0, x1, active(x2))
744.20/262.97	   U35(mark(x0), x1)
744.20/262.97	   U35(x0, mark(x1))
744.20/262.97	   U35(active(x0), x1)
744.20/262.97	   U35(x0, active(x1))
744.20/262.97	   U36(mark(x0))
744.20/262.97	   U36(active(x0))
744.20/262.97	   U41(mark(x0), x1)
744.20/262.97	   U41(x0, mark(x1))
744.20/262.97	   U41(active(x0), x1)
744.20/262.97	   U41(x0, active(x1))
744.20/262.97	   U42(mark(x0))
744.20/262.97	   U42(active(x0))
744.20/262.97	   U51(mark(x0))
744.20/262.97	   U51(active(x0))
744.20/262.97	   U61(mark(x0), x1)
744.20/262.97	   U61(x0, mark(x1))
744.20/262.97	   U61(active(x0), x1)
744.20/262.97	   U61(x0, active(x1))
744.20/262.97	   U62(mark(x0))
744.20/262.97	   U62(active(x0))
744.20/262.97	   U71(mark(x0), x1)
744.20/262.97	   U71(x0, mark(x1))
744.20/262.97	   U71(active(x0), x1)
744.20/262.97	   U71(x0, active(x1))
744.20/262.97	   U72(mark(x0), x1)
744.20/262.97	   U72(x0, mark(x1))
744.20/262.97	   U72(active(x0), x1)
744.20/262.97	   U72(x0, active(x1))
744.20/262.97	   U81(mark(x0), x1, x2)
744.20/262.97	   U81(x0, mark(x1), x2)
744.20/262.97	   U81(x0, x1, mark(x2))
744.20/262.97	   U81(active(x0), x1, x2)
744.20/262.97	   U81(x0, active(x1), x2)
744.20/262.97	   U81(x0, x1, active(x2))
744.20/262.97	   U82(mark(x0), x1, x2)
744.20/262.97	   U82(x0, mark(x1), x2)
744.20/262.97	   U82(x0, x1, mark(x2))
744.20/262.97	   U82(active(x0), x1, x2)
744.20/262.97	   U82(x0, active(x1), x2)
744.20/262.97	   U82(x0, x1, active(x2))
744.20/262.97	   U83(mark(x0), x1, x2)
744.20/262.97	   U83(x0, mark(x1), x2)
744.20/262.97	   U83(x0, x1, mark(x2))
744.20/262.97	   U83(active(x0), x1, x2)
744.20/262.97	   U83(x0, active(x1), x2)
744.20/262.97	   U83(x0, x1, active(x2))
744.20/262.97	   U84(mark(x0), x1, x2)
744.20/262.97	   U84(x0, mark(x1), x2)
744.20/262.97	   U84(x0, x1, mark(x2))
744.20/262.97	   U84(active(x0), x1, x2)
744.20/262.97	   U84(x0, active(x1), x2)
744.20/262.97	   U84(x0, x1, active(x2))
744.20/262.97	   s(mark(x0))
744.20/262.97	   s(active(x0))
744.20/262.97	   U91(mark(x0), x1)
744.20/262.97	   U91(x0, mark(x1))
744.20/262.97	   U91(active(x0), x1)
744.20/262.97	   U91(x0, active(x1))
744.20/262.97	   U92(mark(x0))
744.20/262.97	   U92(active(x0))
744.20/262.97	
744.20/262.97	We have to consider all minimal (P,Q,R)-chains.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(265) UsableRulesProof (EQUIVALENT)
744.20/262.97	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.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(266)
744.20/262.97	Obligation:
744.20/262.97	Q DP problem:
744.20/262.97	The TRS P consists of the following rules:
744.20/262.97	
744.20/262.97	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.97	   MARK(U102(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.97	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.97	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
744.20/262.97	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.97	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.97	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.97	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.97	   MARK(U16(X)) -> ACTIVE(U16(mark(X)))
744.20/262.97	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.97	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.97	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.97	   MARK(U23(X)) -> ACTIVE(U23(mark(X)))
744.20/262.97	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.97	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.97	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.97	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.97	   MARK(U36(X)) -> ACTIVE(U36(mark(X)))
744.20/262.97	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.97	   MARK(U42(X)) -> ACTIVE(U42(mark(X)))
744.20/262.97	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.97	   MARK(U62(X)) -> ACTIVE(U62(mark(X)))
744.20/262.97	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
744.20/262.97	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.97	   ACTIVE(U72(tt, N)) -> MARK(N)
744.20/262.97	   MARK(U101(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.97	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.97	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.97	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.97	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.97	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.97	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
744.20/262.97	   MARK(s(X)) -> ACTIVE(s(mark(X)))
744.20/262.97	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
744.20/262.97	   MARK(U92(X)) -> ACTIVE(U92(mark(X)))
744.20/262.97	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
744.20/262.97	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.97	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
744.20/262.97	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.97	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
744.20/262.97	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.97	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
744.20/262.97	   MARK(U91(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U103(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.97	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.97	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.97	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U104(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(plus(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(plus(X1, X2)) -> MARK(X2)
744.20/262.97	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.97	   MARK(x(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(x(X1, X2)) -> MARK(X2)
744.20/262.97	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U16(X)) -> MARK(X)
744.20/262.97	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.97	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U23(X)) -> MARK(X)
744.20/262.97	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.97	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U36(X)) -> MARK(X)
744.20/262.97	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U42(X)) -> MARK(X)
744.20/262.97	   MARK(U51(X)) -> ACTIVE(U51(mark(X)))
744.20/262.97	   MARK(U51(X)) -> MARK(X)
744.20/262.97	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.97	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U62(X)) -> MARK(X)
744.20/262.97	   MARK(U71(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U72(X1, X2)) -> MARK(X1)
744.20/262.97	   MARK(U81(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U82(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U83(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(U84(X1, X2, X3)) -> MARK(X1)
744.20/262.97	   MARK(s(X)) -> MARK(X)
744.20/262.97	   MARK(U92(X)) -> MARK(X)
744.20/262.97	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.97	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.97	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.97	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.97	
744.20/262.97	The TRS R consists of the following rules:
744.20/262.97	
744.20/262.97	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.97	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.97	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.97	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.97	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.97	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.97	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.97	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.97	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.97	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.97	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.97	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.97	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.97	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.97	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.97	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.97	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.97	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.97	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.97	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.97	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.97	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.97	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.97	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.97	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.97	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.97	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.97	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.97	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.97	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.97	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.97	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.97	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.97	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.97	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.97	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.97	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.97	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.97	   active(U72(tt, N)) -> mark(N)
744.20/262.97	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.97	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.97	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.97	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.97	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.97	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.97	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.97	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.97	   mark(s(X)) -> active(s(mark(X)))
744.20/262.97	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.97	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.97	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.97	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.97	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.97	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.97	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.97	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.97	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.97	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.97	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.97	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.97	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.97	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.97	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.97	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.97	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.97	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.97	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.97	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.97	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.97	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.97	   mark(isNat(X)) -> active(isNat(X))
744.20/262.97	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.97	   mark(tt) -> active(tt)
744.20/262.97	   mark(0) -> active(0)
744.20/262.97	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.97	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.97	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.97	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.97	   active(U16(tt)) -> mark(tt)
744.20/262.97	   active(U23(tt)) -> mark(tt)
744.20/262.97	   active(U36(tt)) -> mark(tt)
744.20/262.97	   active(U42(tt)) -> mark(tt)
744.20/262.97	   active(U51(tt)) -> mark(tt)
744.20/262.97	   active(U62(tt)) -> mark(tt)
744.20/262.97	   active(U92(tt)) -> mark(0)
744.20/262.97	   active(isNat(0)) -> mark(tt)
744.20/262.97	   active(isNatKind(0)) -> mark(tt)
744.20/262.97	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.97	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.97	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.97	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.97	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.97	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.97	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.97	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.97	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.97	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.97	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.97	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.97	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.97	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.97	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.97	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.97	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.97	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.97	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.97	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.97	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.97	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.97	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.97	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.97	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.97	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.97	   U16(active(X)) -> U16(X)
744.20/262.97	   U16(mark(X)) -> U16(X)
744.20/262.97	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.97	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.97	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.97	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.97	   U23(active(X)) -> U23(X)
744.20/262.97	   U23(mark(X)) -> U23(X)
744.20/262.97	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.97	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.97	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.97	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.97	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.97	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.97	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.97	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.97	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.97	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.97	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.97	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.97	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.97	   U36(active(X)) -> U36(X)
744.20/262.97	   U36(mark(X)) -> U36(X)
744.20/262.97	   U42(active(X)) -> U42(X)
744.20/262.97	   U42(mark(X)) -> U42(X)
744.20/262.97	   U62(active(X)) -> U62(X)
744.20/262.97	   U62(mark(X)) -> U62(X)
744.20/262.97	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.97	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.97	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.97	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.97	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.97	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.97	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.97	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.97	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.97	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.97	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.97	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.97	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.97	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.97	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.97	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.97	   s(active(X)) -> s(X)
744.20/262.97	   s(mark(X)) -> s(X)
744.20/262.97	   U92(active(X)) -> U92(X)
744.20/262.97	   U92(mark(X)) -> U92(X)
744.20/262.97	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.97	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.97	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.97	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.97	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.97	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.97	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.97	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.97	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.97	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.97	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.97	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.97	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.97	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.97	   U51(active(X)) -> U51(X)
744.20/262.97	   U51(mark(X)) -> U51(X)
744.20/262.97	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.97	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.97	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.97	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.97	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.97	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.97	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.97	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.97	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.97	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.97	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.97	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.97	   x(active(X1), X2) -> x(X1, X2)
744.20/262.97	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.97	
744.20/262.97	The set Q consists of the following terms:
744.20/262.97	
744.20/262.97	   active(U101(tt, x0, x1))
744.20/262.97	   active(U102(tt, x0, x1))
744.20/262.97	   active(U103(tt, x0, x1))
744.20/262.97	   active(U104(tt, x0, x1))
744.20/262.97	   active(U11(tt, x0, x1))
744.20/262.97	   active(U12(tt, x0, x1))
744.20/262.97	   active(U13(tt, x0, x1))
744.20/262.97	   active(U14(tt, x0, x1))
744.20/262.97	   active(U15(tt, x0))
744.20/262.97	   active(U16(tt))
744.20/262.97	   active(U21(tt, x0))
744.20/262.97	   active(U22(tt, x0))
744.20/262.97	   active(U23(tt))
744.20/262.97	   active(U31(tt, x0, x1))
744.20/262.97	   active(U32(tt, x0, x1))
744.20/262.97	   active(U33(tt, x0, x1))
744.20/262.97	   active(U34(tt, x0, x1))
744.20/262.97	   active(U35(tt, x0))
744.20/262.97	   active(U36(tt))
744.20/262.97	   active(U41(tt, x0))
744.20/262.97	   active(U42(tt))
744.20/262.97	   active(U51(tt))
744.20/262.97	   active(U61(tt, x0))
744.20/262.97	   active(U62(tt))
744.20/262.97	   active(U71(tt, x0))
744.20/262.97	   active(U72(tt, x0))
744.20/262.97	   active(U81(tt, x0, x1))
744.20/262.97	   active(U82(tt, x0, x1))
744.20/262.97	   active(U83(tt, x0, x1))
744.20/262.97	   active(U84(tt, x0, x1))
744.20/262.97	   active(U91(tt, x0))
744.20/262.97	   active(U92(tt))
744.20/262.97	   active(isNat(0))
744.20/262.97	   active(isNat(plus(x0, x1)))
744.20/262.97	   active(isNat(s(x0)))
744.20/262.97	   active(isNat(x(x0, x1)))
744.20/262.97	   active(isNatKind(0))
744.20/262.97	   active(isNatKind(plus(x0, x1)))
744.20/262.97	   active(isNatKind(s(x0)))
744.20/262.97	   active(isNatKind(x(x0, x1)))
744.20/262.97	   active(plus(x0, 0))
744.20/262.97	   active(plus(x0, s(x1)))
744.20/262.97	   active(x(x0, 0))
744.20/262.97	   active(x(x0, s(x1)))
744.20/262.97	   mark(U101(x0, x1, x2))
744.20/262.97	   mark(tt)
744.20/262.97	   mark(U102(x0, x1, x2))
744.20/262.97	   mark(isNatKind(x0))
744.20/262.97	   mark(U103(x0, x1, x2))
744.20/262.97	   mark(isNat(x0))
744.20/262.97	   mark(U104(x0, x1, x2))
744.20/262.97	   mark(plus(x0, x1))
744.20/262.97	   mark(x(x0, x1))
744.20/262.97	   mark(U11(x0, x1, x2))
744.20/262.97	   mark(U12(x0, x1, x2))
744.20/262.97	   mark(U13(x0, x1, x2))
744.20/262.97	   mark(U14(x0, x1, x2))
744.20/262.97	   mark(U15(x0, x1))
744.20/262.97	   mark(U16(x0))
744.20/262.97	   mark(U21(x0, x1))
744.20/262.97	   mark(U22(x0, x1))
744.20/262.97	   mark(U23(x0))
744.20/262.97	   mark(U31(x0, x1, x2))
744.20/262.97	   mark(U32(x0, x1, x2))
744.20/262.97	   mark(U33(x0, x1, x2))
744.20/262.97	   mark(U34(x0, x1, x2))
744.20/262.97	   mark(U35(x0, x1))
744.20/262.97	   mark(U36(x0))
744.20/262.97	   mark(U41(x0, x1))
744.20/262.97	   mark(U42(x0))
744.20/262.97	   mark(U51(x0))
744.20/262.97	   mark(U61(x0, x1))
744.20/262.97	   mark(U62(x0))
744.20/262.97	   mark(U71(x0, x1))
744.20/262.97	   mark(U72(x0, x1))
744.20/262.97	   mark(U81(x0, x1, x2))
744.20/262.97	   mark(U82(x0, x1, x2))
744.20/262.97	   mark(U83(x0, x1, x2))
744.20/262.97	   mark(U84(x0, x1, x2))
744.20/262.97	   mark(s(x0))
744.20/262.97	   mark(U91(x0, x1))
744.20/262.97	   mark(U92(x0))
744.20/262.97	   mark(0)
744.20/262.97	   U101(mark(x0), x1, x2)
744.20/262.97	   U101(x0, mark(x1), x2)
744.20/262.97	   U101(x0, x1, mark(x2))
744.20/262.97	   U101(active(x0), x1, x2)
744.20/262.97	   U101(x0, active(x1), x2)
744.20/262.97	   U101(x0, x1, active(x2))
744.20/262.97	   U102(mark(x0), x1, x2)
744.20/262.97	   U102(x0, mark(x1), x2)
744.20/262.97	   U102(x0, x1, mark(x2))
744.20/262.97	   U102(active(x0), x1, x2)
744.20/262.97	   U102(x0, active(x1), x2)
744.20/262.97	   U102(x0, x1, active(x2))
744.20/262.97	   isNatKind(mark(x0))
744.20/262.97	   isNatKind(active(x0))
744.20/262.97	   U103(mark(x0), x1, x2)
744.20/262.97	   U103(x0, mark(x1), x2)
744.20/262.97	   U103(x0, x1, mark(x2))
744.20/262.97	   U103(active(x0), x1, x2)
744.20/262.97	   U103(x0, active(x1), x2)
744.20/262.97	   U103(x0, x1, active(x2))
744.20/262.97	   isNat(mark(x0))
744.20/262.97	   isNat(active(x0))
744.20/262.97	   U104(mark(x0), x1, x2)
744.20/262.97	   U104(x0, mark(x1), x2)
744.20/262.97	   U104(x0, x1, mark(x2))
744.20/262.97	   U104(active(x0), x1, x2)
744.20/262.97	   U104(x0, active(x1), x2)
744.20/262.97	   U104(x0, x1, active(x2))
744.20/262.97	   plus(mark(x0), x1)
744.20/262.97	   plus(x0, mark(x1))
744.20/262.97	   plus(active(x0), x1)
744.20/262.97	   plus(x0, active(x1))
744.20/262.97	   x(mark(x0), x1)
744.20/262.97	   x(x0, mark(x1))
744.20/262.97	   x(active(x0), x1)
744.20/262.97	   x(x0, active(x1))
744.20/262.97	   U11(mark(x0), x1, x2)
744.20/262.97	   U11(x0, mark(x1), x2)
744.20/262.97	   U11(x0, x1, mark(x2))
744.20/262.97	   U11(active(x0), x1, x2)
744.20/262.97	   U11(x0, active(x1), x2)
744.20/262.97	   U11(x0, x1, active(x2))
744.20/262.97	   U12(mark(x0), x1, x2)
744.20/262.97	   U12(x0, mark(x1), x2)
744.20/262.97	   U12(x0, x1, mark(x2))
744.20/262.97	   U12(active(x0), x1, x2)
744.20/262.97	   U12(x0, active(x1), x2)
744.20/262.97	   U12(x0, x1, active(x2))
744.20/262.97	   U13(mark(x0), x1, x2)
744.20/262.97	   U13(x0, mark(x1), x2)
744.20/262.97	   U13(x0, x1, mark(x2))
744.20/262.97	   U13(active(x0), x1, x2)
744.20/262.97	   U13(x0, active(x1), x2)
744.20/262.97	   U13(x0, x1, active(x2))
744.20/262.97	   U14(mark(x0), x1, x2)
744.20/262.97	   U14(x0, mark(x1), x2)
744.20/262.97	   U14(x0, x1, mark(x2))
744.20/262.97	   U14(active(x0), x1, x2)
744.20/262.97	   U14(x0, active(x1), x2)
744.20/262.97	   U14(x0, x1, active(x2))
744.20/262.97	   U15(mark(x0), x1)
744.20/262.97	   U15(x0, mark(x1))
744.20/262.97	   U15(active(x0), x1)
744.20/262.97	   U15(x0, active(x1))
744.20/262.97	   U16(mark(x0))
744.20/262.97	   U16(active(x0))
744.20/262.97	   U21(mark(x0), x1)
744.20/262.97	   U21(x0, mark(x1))
744.20/262.97	   U21(active(x0), x1)
744.20/262.97	   U21(x0, active(x1))
744.20/262.97	   U22(mark(x0), x1)
744.20/262.97	   U22(x0, mark(x1))
744.20/262.97	   U22(active(x0), x1)
744.20/262.97	   U22(x0, active(x1))
744.20/262.97	   U23(mark(x0))
744.20/262.97	   U23(active(x0))
744.20/262.97	   U31(mark(x0), x1, x2)
744.20/262.97	   U31(x0, mark(x1), x2)
744.20/262.97	   U31(x0, x1, mark(x2))
744.20/262.97	   U31(active(x0), x1, x2)
744.20/262.97	   U31(x0, active(x1), x2)
744.20/262.97	   U31(x0, x1, active(x2))
744.20/262.97	   U32(mark(x0), x1, x2)
744.20/262.97	   U32(x0, mark(x1), x2)
744.20/262.97	   U32(x0, x1, mark(x2))
744.20/262.97	   U32(active(x0), x1, x2)
744.20/262.97	   U32(x0, active(x1), x2)
744.20/262.97	   U32(x0, x1, active(x2))
744.20/262.97	   U33(mark(x0), x1, x2)
744.20/262.97	   U33(x0, mark(x1), x2)
744.20/262.97	   U33(x0, x1, mark(x2))
744.20/262.97	   U33(active(x0), x1, x2)
744.20/262.97	   U33(x0, active(x1), x2)
744.20/262.97	   U33(x0, x1, active(x2))
744.20/262.97	   U34(mark(x0), x1, x2)
744.20/262.97	   U34(x0, mark(x1), x2)
744.20/262.97	   U34(x0, x1, mark(x2))
744.20/262.97	   U34(active(x0), x1, x2)
744.20/262.97	   U34(x0, active(x1), x2)
744.20/262.97	   U34(x0, x1, active(x2))
744.20/262.97	   U35(mark(x0), x1)
744.20/262.97	   U35(x0, mark(x1))
744.20/262.97	   U35(active(x0), x1)
744.20/262.97	   U35(x0, active(x1))
744.20/262.97	   U36(mark(x0))
744.20/262.97	   U36(active(x0))
744.20/262.97	   U41(mark(x0), x1)
744.20/262.97	   U41(x0, mark(x1))
744.20/262.97	   U41(active(x0), x1)
744.20/262.97	   U41(x0, active(x1))
744.20/262.97	   U42(mark(x0))
744.20/262.97	   U42(active(x0))
744.20/262.97	   U51(mark(x0))
744.20/262.97	   U51(active(x0))
744.20/262.97	   U61(mark(x0), x1)
744.20/262.97	   U61(x0, mark(x1))
744.20/262.97	   U61(active(x0), x1)
744.20/262.97	   U61(x0, active(x1))
744.20/262.97	   U62(mark(x0))
744.20/262.97	   U62(active(x0))
744.20/262.97	   U71(mark(x0), x1)
744.20/262.97	   U71(x0, mark(x1))
744.20/262.97	   U71(active(x0), x1)
744.20/262.97	   U71(x0, active(x1))
744.20/262.97	   U72(mark(x0), x1)
744.20/262.97	   U72(x0, mark(x1))
744.20/262.97	   U72(active(x0), x1)
744.20/262.97	   U72(x0, active(x1))
744.20/262.97	   U81(mark(x0), x1, x2)
744.20/262.97	   U81(x0, mark(x1), x2)
744.20/262.97	   U81(x0, x1, mark(x2))
744.20/262.97	   U81(active(x0), x1, x2)
744.20/262.97	   U81(x0, active(x1), x2)
744.20/262.97	   U81(x0, x1, active(x2))
744.20/262.97	   U82(mark(x0), x1, x2)
744.20/262.97	   U82(x0, mark(x1), x2)
744.20/262.97	   U82(x0, x1, mark(x2))
744.20/262.97	   U82(active(x0), x1, x2)
744.20/262.97	   U82(x0, active(x1), x2)
744.20/262.97	   U82(x0, x1, active(x2))
744.20/262.97	   U83(mark(x0), x1, x2)
744.20/262.97	   U83(x0, mark(x1), x2)
744.20/262.97	   U83(x0, x1, mark(x2))
744.20/262.97	   U83(active(x0), x1, x2)
744.20/262.97	   U83(x0, active(x1), x2)
744.20/262.97	   U83(x0, x1, active(x2))
744.20/262.97	   U84(mark(x0), x1, x2)
744.20/262.97	   U84(x0, mark(x1), x2)
744.20/262.97	   U84(x0, x1, mark(x2))
744.20/262.97	   U84(active(x0), x1, x2)
744.20/262.97	   U84(x0, active(x1), x2)
744.20/262.97	   U84(x0, x1, active(x2))
744.20/262.97	   s(mark(x0))
744.20/262.97	   s(active(x0))
744.20/262.97	   U91(mark(x0), x1)
744.20/262.97	   U91(x0, mark(x1))
744.20/262.97	   U91(active(x0), x1)
744.20/262.97	   U91(x0, active(x1))
744.20/262.97	   U92(mark(x0))
744.20/262.97	   U92(active(x0))
744.20/262.97	
744.20/262.97	We have to consider all minimal (P,Q,R)-chains.
744.20/262.97	----------------------------------------
744.20/262.97	
744.20/262.97	(267) QDPOrderProof (EQUIVALENT)
744.20/262.97	We use the reduction pair processor [LPAR04,JAR06].
744.20/262.97	
744.20/262.97	
744.20/262.97	The following pairs can be oriented strictly and are deleted.
744.20/262.97	
744.20/262.97	   MARK(U16(X)) -> ACTIVE(U16(mark(X)))
744.20/262.97	   MARK(U23(X)) -> ACTIVE(U23(mark(X)))
744.20/262.97	   MARK(U36(X)) -> ACTIVE(U36(mark(X)))
744.20/262.97	   MARK(s(X)) -> ACTIVE(s(mark(X)))
744.20/262.97	   MARK(U92(X)) -> ACTIVE(U92(mark(X)))
744.20/262.97	   MARK(U51(X)) -> ACTIVE(U51(mark(X)))
744.20/262.98	The remaining pairs can at least be oriented weakly.
744.20/262.98	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/262.98	
744.20/262.98	POL( ACTIVE_1(x_1) ) = x_1
744.20/262.98	POL( U101_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U102_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U103_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U104_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U11_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U12_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U13_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U14_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U15_2(x_1, x_2) ) = 2
744.20/262.98	POL( U16_1(x_1) ) = max{0, -2}
744.20/262.98	POL( U21_2(x_1, x_2) ) = 2
744.20/262.98	POL( U22_2(x_1, x_2) ) = 2
744.20/262.98	POL( U23_1(x_1) ) = 0
744.20/262.98	POL( U31_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U32_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U33_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U34_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U35_2(x_1, x_2) ) = 2
744.20/262.98	POL( U36_1(x_1) ) = 0
744.20/262.98	POL( U41_2(x_1, x_2) ) = 2
744.20/262.98	POL( U42_1(x_1) ) = 2
744.20/262.98	POL( U51_1(x_1) ) = max{0, -2}
744.20/262.98	POL( U61_2(x_1, x_2) ) = 2
744.20/262.98	POL( U62_1(x_1) ) = 2
744.20/262.98	POL( U71_2(x_1, x_2) ) = 2
744.20/262.98	POL( U72_2(x_1, x_2) ) = 2
744.20/262.98	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U82_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U83_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U84_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U91_2(x_1, x_2) ) = 2
744.20/262.98	POL( U92_1(x_1) ) = max{0, -2}
744.20/262.98	POL( plus_2(x_1, x_2) ) = 2
744.20/262.98	POL( s_1(x_1) ) = max{0, -2}
744.20/262.98	POL( x_2(x_1, x_2) ) = 2
744.20/262.98	POL( mark_1(x_1) ) = 2
744.20/262.98	POL( active_1(x_1) ) = max{0, -2}
744.20/262.98	POL( tt ) = 0
744.20/262.98	POL( isNatKind_1(x_1) ) = 2
744.20/262.98	POL( isNat_1(x_1) ) = 2
744.20/262.98	POL( 0 ) = 0
744.20/262.98	POL( MARK_1(x_1) ) = 2
744.20/262.98	
744.20/262.98	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/262.98	
744.20/262.98	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.98	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.98	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.98	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.98	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.98	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.98	   U16(active(X)) -> U16(X)
744.20/262.98	   U16(mark(X)) -> U16(X)
744.20/262.98	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.98	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.98	   U23(active(X)) -> U23(X)
744.20/262.98	   U23(mark(X)) -> U23(X)
744.20/262.98	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.98	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.98	   U36(active(X)) -> U36(X)
744.20/262.98	   U36(mark(X)) -> U36(X)
744.20/262.98	   U42(active(X)) -> U42(X)
744.20/262.98	   U42(mark(X)) -> U42(X)
744.20/262.98	   U62(active(X)) -> U62(X)
744.20/262.98	   U62(mark(X)) -> U62(X)
744.20/262.98	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.98	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.98	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.98	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.98	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.98	   s(active(X)) -> s(X)
744.20/262.98	   s(mark(X)) -> s(X)
744.20/262.98	   U92(active(X)) -> U92(X)
744.20/262.98	   U92(mark(X)) -> U92(X)
744.20/262.98	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.98	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.98	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.98	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.98	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.98	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.98	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.98	   x(active(X1), X2) -> x(X1, X2)
744.20/262.98	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.98	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.98	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.98	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U51(active(X)) -> U51(X)
744.20/262.98	   U51(mark(X)) -> U51(X)
744.20/262.98	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.98	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.98	
744.20/262.98	
744.20/262.98	----------------------------------------
744.20/262.98	
744.20/262.98	(268)
744.20/262.98	Obligation:
744.20/262.98	Q DP problem:
744.20/262.98	The TRS P consists of the following rules:
744.20/262.98	
744.20/262.98	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.98	   MARK(U102(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.98	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.98	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
744.20/262.98	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.98	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.98	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.98	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.98	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.98	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.98	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.98	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.98	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.98	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.98	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.98	   MARK(U42(X)) -> ACTIVE(U42(mark(X)))
744.20/262.98	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.98	   MARK(U62(X)) -> ACTIVE(U62(mark(X)))
744.20/262.98	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
744.20/262.98	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.98	   ACTIVE(U72(tt, N)) -> MARK(N)
744.20/262.98	   MARK(U101(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.98	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.98	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.98	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.98	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.98	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.98	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
744.20/262.98	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
744.20/262.98	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
744.20/262.98	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.98	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
744.20/262.98	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
744.20/262.98	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.98	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
744.20/262.98	   MARK(U91(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U103(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.98	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.98	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U104(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U16(X)) -> MARK(X)
744.20/262.98	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.98	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U23(X)) -> MARK(X)
744.20/262.98	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.98	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U36(X)) -> MARK(X)
744.20/262.98	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U42(X)) -> MARK(X)
744.20/262.98	   MARK(U51(X)) -> MARK(X)
744.20/262.98	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.98	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U62(X)) -> MARK(X)
744.20/262.98	   MARK(U71(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U72(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U81(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U82(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U83(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U84(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(s(X)) -> MARK(X)
744.20/262.98	   MARK(U92(X)) -> MARK(X)
744.20/262.98	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.98	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.98	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.98	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.98	
744.20/262.98	The TRS R consists of the following rules:
744.20/262.98	
744.20/262.98	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.98	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.98	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.98	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.98	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.98	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.98	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.98	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.98	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.98	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.98	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.98	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.98	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.98	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.98	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.98	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.98	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.98	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.98	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.98	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.98	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.98	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.98	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.98	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.98	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.98	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.98	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.98	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.98	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.98	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.98	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.98	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.98	   active(U72(tt, N)) -> mark(N)
744.20/262.98	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.98	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.98	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.98	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.98	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.98	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.98	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.98	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.98	   mark(s(X)) -> active(s(mark(X)))
744.20/262.98	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.98	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.98	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.98	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.98	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.98	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.98	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.98	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.98	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.98	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.98	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.98	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.98	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.98	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.98	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.98	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.98	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.98	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.98	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.98	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.98	   mark(isNat(X)) -> active(isNat(X))
744.20/262.98	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.98	   mark(tt) -> active(tt)
744.20/262.98	   mark(0) -> active(0)
744.20/262.98	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.98	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.98	   active(U16(tt)) -> mark(tt)
744.20/262.98	   active(U23(tt)) -> mark(tt)
744.20/262.98	   active(U36(tt)) -> mark(tt)
744.20/262.98	   active(U42(tt)) -> mark(tt)
744.20/262.98	   active(U51(tt)) -> mark(tt)
744.20/262.98	   active(U62(tt)) -> mark(tt)
744.20/262.98	   active(U92(tt)) -> mark(0)
744.20/262.98	   active(isNat(0)) -> mark(tt)
744.20/262.98	   active(isNatKind(0)) -> mark(tt)
744.20/262.98	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.98	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.98	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.98	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.98	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.98	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.98	   U16(active(X)) -> U16(X)
744.20/262.98	   U16(mark(X)) -> U16(X)
744.20/262.98	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.98	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.98	   U23(active(X)) -> U23(X)
744.20/262.98	   U23(mark(X)) -> U23(X)
744.20/262.98	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.98	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.98	   U36(active(X)) -> U36(X)
744.20/262.98	   U36(mark(X)) -> U36(X)
744.20/262.98	   U42(active(X)) -> U42(X)
744.20/262.98	   U42(mark(X)) -> U42(X)
744.20/262.98	   U62(active(X)) -> U62(X)
744.20/262.98	   U62(mark(X)) -> U62(X)
744.20/262.98	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.98	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.98	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.98	   s(active(X)) -> s(X)
744.20/262.98	   s(mark(X)) -> s(X)
744.20/262.98	   U92(active(X)) -> U92(X)
744.20/262.98	   U92(mark(X)) -> U92(X)
744.20/262.98	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.98	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.98	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.98	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.98	   U51(active(X)) -> U51(X)
744.20/262.98	   U51(mark(X)) -> U51(X)
744.20/262.98	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.98	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.98	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.98	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.98	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.98	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.98	   x(active(X1), X2) -> x(X1, X2)
744.20/262.98	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.98	
744.20/262.98	The set Q consists of the following terms:
744.20/262.98	
744.20/262.98	   active(U101(tt, x0, x1))
744.20/262.98	   active(U102(tt, x0, x1))
744.20/262.98	   active(U103(tt, x0, x1))
744.20/262.98	   active(U104(tt, x0, x1))
744.20/262.98	   active(U11(tt, x0, x1))
744.20/262.98	   active(U12(tt, x0, x1))
744.20/262.98	   active(U13(tt, x0, x1))
744.20/262.98	   active(U14(tt, x0, x1))
744.20/262.98	   active(U15(tt, x0))
744.20/262.98	   active(U16(tt))
744.20/262.98	   active(U21(tt, x0))
744.20/262.98	   active(U22(tt, x0))
744.20/262.98	   active(U23(tt))
744.20/262.98	   active(U31(tt, x0, x1))
744.20/262.98	   active(U32(tt, x0, x1))
744.20/262.98	   active(U33(tt, x0, x1))
744.20/262.98	   active(U34(tt, x0, x1))
744.20/262.98	   active(U35(tt, x0))
744.20/262.98	   active(U36(tt))
744.20/262.98	   active(U41(tt, x0))
744.20/262.98	   active(U42(tt))
744.20/262.98	   active(U51(tt))
744.20/262.98	   active(U61(tt, x0))
744.20/262.98	   active(U62(tt))
744.20/262.98	   active(U71(tt, x0))
744.20/262.98	   active(U72(tt, x0))
744.20/262.98	   active(U81(tt, x0, x1))
744.20/262.98	   active(U82(tt, x0, x1))
744.20/262.98	   active(U83(tt, x0, x1))
744.20/262.98	   active(U84(tt, x0, x1))
744.20/262.98	   active(U91(tt, x0))
744.20/262.98	   active(U92(tt))
744.20/262.98	   active(isNat(0))
744.20/262.98	   active(isNat(plus(x0, x1)))
744.20/262.98	   active(isNat(s(x0)))
744.20/262.98	   active(isNat(x(x0, x1)))
744.20/262.98	   active(isNatKind(0))
744.20/262.98	   active(isNatKind(plus(x0, x1)))
744.20/262.98	   active(isNatKind(s(x0)))
744.20/262.98	   active(isNatKind(x(x0, x1)))
744.20/262.98	   active(plus(x0, 0))
744.20/262.98	   active(plus(x0, s(x1)))
744.20/262.98	   active(x(x0, 0))
744.20/262.98	   active(x(x0, s(x1)))
744.20/262.98	   mark(U101(x0, x1, x2))
744.20/262.98	   mark(tt)
744.20/262.98	   mark(U102(x0, x1, x2))
744.20/262.98	   mark(isNatKind(x0))
744.20/262.98	   mark(U103(x0, x1, x2))
744.20/262.98	   mark(isNat(x0))
744.20/262.98	   mark(U104(x0, x1, x2))
744.20/262.98	   mark(plus(x0, x1))
744.20/262.98	   mark(x(x0, x1))
744.20/262.98	   mark(U11(x0, x1, x2))
744.20/262.98	   mark(U12(x0, x1, x2))
744.20/262.98	   mark(U13(x0, x1, x2))
744.20/262.98	   mark(U14(x0, x1, x2))
744.20/262.98	   mark(U15(x0, x1))
744.20/262.98	   mark(U16(x0))
744.20/262.98	   mark(U21(x0, x1))
744.20/262.98	   mark(U22(x0, x1))
744.20/262.98	   mark(U23(x0))
744.20/262.98	   mark(U31(x0, x1, x2))
744.20/262.98	   mark(U32(x0, x1, x2))
744.20/262.98	   mark(U33(x0, x1, x2))
744.20/262.98	   mark(U34(x0, x1, x2))
744.20/262.98	   mark(U35(x0, x1))
744.20/262.98	   mark(U36(x0))
744.20/262.98	   mark(U41(x0, x1))
744.20/262.98	   mark(U42(x0))
744.20/262.98	   mark(U51(x0))
744.20/262.98	   mark(U61(x0, x1))
744.20/262.98	   mark(U62(x0))
744.20/262.98	   mark(U71(x0, x1))
744.20/262.98	   mark(U72(x0, x1))
744.20/262.98	   mark(U81(x0, x1, x2))
744.20/262.98	   mark(U82(x0, x1, x2))
744.20/262.98	   mark(U83(x0, x1, x2))
744.20/262.98	   mark(U84(x0, x1, x2))
744.20/262.98	   mark(s(x0))
744.20/262.98	   mark(U91(x0, x1))
744.20/262.98	   mark(U92(x0))
744.20/262.98	   mark(0)
744.20/262.98	   U101(mark(x0), x1, x2)
744.20/262.98	   U101(x0, mark(x1), x2)
744.20/262.98	   U101(x0, x1, mark(x2))
744.20/262.98	   U101(active(x0), x1, x2)
744.20/262.98	   U101(x0, active(x1), x2)
744.20/262.98	   U101(x0, x1, active(x2))
744.20/262.98	   U102(mark(x0), x1, x2)
744.20/262.98	   U102(x0, mark(x1), x2)
744.20/262.98	   U102(x0, x1, mark(x2))
744.20/262.98	   U102(active(x0), x1, x2)
744.20/262.98	   U102(x0, active(x1), x2)
744.20/262.98	   U102(x0, x1, active(x2))
744.20/262.98	   isNatKind(mark(x0))
744.20/262.98	   isNatKind(active(x0))
744.20/262.98	   U103(mark(x0), x1, x2)
744.20/262.98	   U103(x0, mark(x1), x2)
744.20/262.98	   U103(x0, x1, mark(x2))
744.20/262.98	   U103(active(x0), x1, x2)
744.20/262.98	   U103(x0, active(x1), x2)
744.20/262.98	   U103(x0, x1, active(x2))
744.20/262.98	   isNat(mark(x0))
744.20/262.98	   isNat(active(x0))
744.20/262.98	   U104(mark(x0), x1, x2)
744.20/262.98	   U104(x0, mark(x1), x2)
744.20/262.98	   U104(x0, x1, mark(x2))
744.20/262.98	   U104(active(x0), x1, x2)
744.20/262.98	   U104(x0, active(x1), x2)
744.20/262.98	   U104(x0, x1, active(x2))
744.20/262.98	   plus(mark(x0), x1)
744.20/262.98	   plus(x0, mark(x1))
744.20/262.98	   plus(active(x0), x1)
744.20/262.98	   plus(x0, active(x1))
744.20/262.98	   x(mark(x0), x1)
744.20/262.98	   x(x0, mark(x1))
744.20/262.98	   x(active(x0), x1)
744.20/262.98	   x(x0, active(x1))
744.20/262.98	   U11(mark(x0), x1, x2)
744.20/262.98	   U11(x0, mark(x1), x2)
744.20/262.98	   U11(x0, x1, mark(x2))
744.20/262.98	   U11(active(x0), x1, x2)
744.20/262.98	   U11(x0, active(x1), x2)
744.20/262.98	   U11(x0, x1, active(x2))
744.20/262.98	   U12(mark(x0), x1, x2)
744.20/262.98	   U12(x0, mark(x1), x2)
744.20/262.98	   U12(x0, x1, mark(x2))
744.20/262.98	   U12(active(x0), x1, x2)
744.20/262.98	   U12(x0, active(x1), x2)
744.20/262.98	   U12(x0, x1, active(x2))
744.20/262.98	   U13(mark(x0), x1, x2)
744.20/262.98	   U13(x0, mark(x1), x2)
744.20/262.98	   U13(x0, x1, mark(x2))
744.20/262.98	   U13(active(x0), x1, x2)
744.20/262.98	   U13(x0, active(x1), x2)
744.20/262.98	   U13(x0, x1, active(x2))
744.20/262.98	   U14(mark(x0), x1, x2)
744.20/262.98	   U14(x0, mark(x1), x2)
744.20/262.98	   U14(x0, x1, mark(x2))
744.20/262.98	   U14(active(x0), x1, x2)
744.20/262.98	   U14(x0, active(x1), x2)
744.20/262.98	   U14(x0, x1, active(x2))
744.20/262.98	   U15(mark(x0), x1)
744.20/262.98	   U15(x0, mark(x1))
744.20/262.98	   U15(active(x0), x1)
744.20/262.98	   U15(x0, active(x1))
744.20/262.98	   U16(mark(x0))
744.20/262.98	   U16(active(x0))
744.20/262.98	   U21(mark(x0), x1)
744.20/262.98	   U21(x0, mark(x1))
744.20/262.98	   U21(active(x0), x1)
744.20/262.98	   U21(x0, active(x1))
744.20/262.98	   U22(mark(x0), x1)
744.20/262.98	   U22(x0, mark(x1))
744.20/262.98	   U22(active(x0), x1)
744.20/262.98	   U22(x0, active(x1))
744.20/262.98	   U23(mark(x0))
744.20/262.98	   U23(active(x0))
744.20/262.98	   U31(mark(x0), x1, x2)
744.20/262.98	   U31(x0, mark(x1), x2)
744.20/262.98	   U31(x0, x1, mark(x2))
744.20/262.98	   U31(active(x0), x1, x2)
744.20/262.98	   U31(x0, active(x1), x2)
744.20/262.98	   U31(x0, x1, active(x2))
744.20/262.98	   U32(mark(x0), x1, x2)
744.20/262.98	   U32(x0, mark(x1), x2)
744.20/262.98	   U32(x0, x1, mark(x2))
744.20/262.98	   U32(active(x0), x1, x2)
744.20/262.98	   U32(x0, active(x1), x2)
744.20/262.98	   U32(x0, x1, active(x2))
744.20/262.98	   U33(mark(x0), x1, x2)
744.20/262.98	   U33(x0, mark(x1), x2)
744.20/262.98	   U33(x0, x1, mark(x2))
744.20/262.98	   U33(active(x0), x1, x2)
744.20/262.98	   U33(x0, active(x1), x2)
744.20/262.98	   U33(x0, x1, active(x2))
744.20/262.98	   U34(mark(x0), x1, x2)
744.20/262.98	   U34(x0, mark(x1), x2)
744.20/262.98	   U34(x0, x1, mark(x2))
744.20/262.98	   U34(active(x0), x1, x2)
744.20/262.98	   U34(x0, active(x1), x2)
744.20/262.98	   U34(x0, x1, active(x2))
744.20/262.98	   U35(mark(x0), x1)
744.20/262.98	   U35(x0, mark(x1))
744.20/262.98	   U35(active(x0), x1)
744.20/262.98	   U35(x0, active(x1))
744.20/262.98	   U36(mark(x0))
744.20/262.98	   U36(active(x0))
744.20/262.98	   U41(mark(x0), x1)
744.20/262.98	   U41(x0, mark(x1))
744.20/262.98	   U41(active(x0), x1)
744.20/262.98	   U41(x0, active(x1))
744.20/262.98	   U42(mark(x0))
744.20/262.98	   U42(active(x0))
744.20/262.98	   U51(mark(x0))
744.20/262.98	   U51(active(x0))
744.20/262.98	   U61(mark(x0), x1)
744.20/262.98	   U61(x0, mark(x1))
744.20/262.98	   U61(active(x0), x1)
744.20/262.98	   U61(x0, active(x1))
744.20/262.98	   U62(mark(x0))
744.20/262.98	   U62(active(x0))
744.20/262.98	   U71(mark(x0), x1)
744.20/262.98	   U71(x0, mark(x1))
744.20/262.98	   U71(active(x0), x1)
744.20/262.98	   U71(x0, active(x1))
744.20/262.98	   U72(mark(x0), x1)
744.20/262.98	   U72(x0, mark(x1))
744.20/262.98	   U72(active(x0), x1)
744.20/262.98	   U72(x0, active(x1))
744.20/262.98	   U81(mark(x0), x1, x2)
744.20/262.98	   U81(x0, mark(x1), x2)
744.20/262.98	   U81(x0, x1, mark(x2))
744.20/262.98	   U81(active(x0), x1, x2)
744.20/262.98	   U81(x0, active(x1), x2)
744.20/262.98	   U81(x0, x1, active(x2))
744.20/262.98	   U82(mark(x0), x1, x2)
744.20/262.98	   U82(x0, mark(x1), x2)
744.20/262.98	   U82(x0, x1, mark(x2))
744.20/262.98	   U82(active(x0), x1, x2)
744.20/262.98	   U82(x0, active(x1), x2)
744.20/262.98	   U82(x0, x1, active(x2))
744.20/262.98	   U83(mark(x0), x1, x2)
744.20/262.98	   U83(x0, mark(x1), x2)
744.20/262.98	   U83(x0, x1, mark(x2))
744.20/262.98	   U83(active(x0), x1, x2)
744.20/262.98	   U83(x0, active(x1), x2)
744.20/262.98	   U83(x0, x1, active(x2))
744.20/262.98	   U84(mark(x0), x1, x2)
744.20/262.98	   U84(x0, mark(x1), x2)
744.20/262.98	   U84(x0, x1, mark(x2))
744.20/262.98	   U84(active(x0), x1, x2)
744.20/262.98	   U84(x0, active(x1), x2)
744.20/262.98	   U84(x0, x1, active(x2))
744.20/262.98	   s(mark(x0))
744.20/262.98	   s(active(x0))
744.20/262.98	   U91(mark(x0), x1)
744.20/262.98	   U91(x0, mark(x1))
744.20/262.98	   U91(active(x0), x1)
744.20/262.98	   U91(x0, active(x1))
744.20/262.98	   U92(mark(x0))
744.20/262.98	   U92(active(x0))
744.20/262.98	
744.20/262.98	We have to consider all minimal (P,Q,R)-chains.
744.20/262.98	----------------------------------------
744.20/262.98	
744.20/262.98	(269) QDPOrderProof (EQUIVALENT)
744.20/262.98	We use the reduction pair processor [LPAR04,JAR06].
744.20/262.98	
744.20/262.98	
744.20/262.98	The following pairs can be oriented strictly and are deleted.
744.20/262.98	
744.20/262.98	   MARK(U42(X)) -> ACTIVE(U42(mark(X)))
744.20/262.98	   MARK(U62(X)) -> ACTIVE(U62(mark(X)))
744.20/262.98	The remaining pairs can at least be oriented weakly.
744.20/262.98	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/262.98	
744.20/262.98	POL( ACTIVE_1(x_1) ) = max{0, x_1 - 1}
744.20/262.98	POL( U101_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U102_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U103_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U104_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U11_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U12_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U13_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U14_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U15_2(x_1, x_2) ) = 2
744.20/262.98	POL( U21_2(x_1, x_2) ) = 2
744.20/262.98	POL( U22_2(x_1, x_2) ) = 2
744.20/262.98	POL( U31_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U32_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U33_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U34_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U35_2(x_1, x_2) ) = 2
744.20/262.98	POL( U41_2(x_1, x_2) ) = 2
744.20/262.98	POL( U42_1(x_1) ) = max{0, -2}
744.20/262.98	POL( U61_2(x_1, x_2) ) = 2
744.20/262.98	POL( U62_1(x_1) ) = max{0, -2}
744.20/262.98	POL( U71_2(x_1, x_2) ) = 2
744.20/262.98	POL( U72_2(x_1, x_2) ) = 2
744.20/262.98	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U82_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U83_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U84_3(x_1, ..., x_3) ) = 2
744.20/262.98	POL( U91_2(x_1, x_2) ) = 2
744.20/262.98	POL( plus_2(x_1, x_2) ) = 2
744.20/262.98	POL( x_2(x_1, x_2) ) = 2
744.20/262.98	POL( mark_1(x_1) ) = max{0, -2}
744.20/262.98	POL( active_1(x_1) ) = 2x_1 + 2
744.20/262.98	POL( tt ) = 0
744.20/262.98	POL( isNatKind_1(x_1) ) = 2
744.20/262.98	POL( isNat_1(x_1) ) = 2
744.20/262.98	POL( U16_1(x_1) ) = 2
744.20/262.98	POL( U23_1(x_1) ) = 2
744.20/262.98	POL( U36_1(x_1) ) = max{0, x_1 - 2}
744.20/262.98	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.20/262.98	POL( U92_1(x_1) ) = 0
744.20/262.98	POL( U51_1(x_1) ) = max{0, -2}
744.20/262.98	POL( 0 ) = 0
744.20/262.98	POL( MARK_1(x_1) ) = 1
744.20/262.98	
744.20/262.98	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/262.98	
744.20/262.98	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.98	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.98	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.98	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.98	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.98	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.98	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.98	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.98	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.98	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.98	   U42(active(X)) -> U42(X)
744.20/262.98	   U42(mark(X)) -> U42(X)
744.20/262.98	   U62(active(X)) -> U62(X)
744.20/262.98	   U62(mark(X)) -> U62(X)
744.20/262.98	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.98	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.98	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.98	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.98	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.98	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.98	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.98	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.98	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.98	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.98	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.98	   x(active(X1), X2) -> x(X1, X2)
744.20/262.98	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.98	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.98	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.98	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.98	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.98	
744.20/262.98	
744.20/262.98	----------------------------------------
744.20/262.98	
744.20/262.98	(270)
744.20/262.98	Obligation:
744.20/262.98	Q DP problem:
744.20/262.98	The TRS P consists of the following rules:
744.20/262.98	
744.20/262.98	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.98	   MARK(U102(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.98	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.98	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
744.20/262.98	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.98	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.98	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.98	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.98	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.98	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.98	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.98	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.98	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.98	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.98	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.98	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.98	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
744.20/262.98	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.98	   ACTIVE(U72(tt, N)) -> MARK(N)
744.20/262.98	   MARK(U101(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.98	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.98	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.98	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.98	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.98	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.98	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
744.20/262.98	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
744.20/262.98	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
744.20/262.98	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.98	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
744.20/262.98	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
744.20/262.98	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.98	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
744.20/262.98	   MARK(U91(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U103(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.98	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.98	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U104(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U16(X)) -> MARK(X)
744.20/262.98	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.98	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U23(X)) -> MARK(X)
744.20/262.98	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.98	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U36(X)) -> MARK(X)
744.20/262.98	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U42(X)) -> MARK(X)
744.20/262.98	   MARK(U51(X)) -> MARK(X)
744.20/262.98	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.98	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U62(X)) -> MARK(X)
744.20/262.98	   MARK(U71(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U72(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U81(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U82(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U83(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U84(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(s(X)) -> MARK(X)
744.20/262.98	   MARK(U92(X)) -> MARK(X)
744.20/262.98	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.98	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.98	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.98	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.98	
744.20/262.98	The TRS R consists of the following rules:
744.20/262.98	
744.20/262.98	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.98	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.98	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.98	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.98	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.98	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.98	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.98	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.98	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.98	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.98	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.98	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.98	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.98	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.98	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.98	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.98	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.98	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.98	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.98	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.98	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.98	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.98	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.98	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.98	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.98	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.98	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.98	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.98	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.98	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.98	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.98	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.98	   active(U72(tt, N)) -> mark(N)
744.20/262.98	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.98	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.98	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.98	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.98	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.98	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.98	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.98	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.98	   mark(s(X)) -> active(s(mark(X)))
744.20/262.98	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.98	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.98	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.98	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.98	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.98	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.98	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.98	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.98	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.98	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.98	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.98	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.98	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.98	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.98	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.98	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.98	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.98	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.98	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.98	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.98	   mark(isNat(X)) -> active(isNat(X))
744.20/262.98	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.98	   mark(tt) -> active(tt)
744.20/262.98	   mark(0) -> active(0)
744.20/262.98	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.98	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.98	   active(U16(tt)) -> mark(tt)
744.20/262.98	   active(U23(tt)) -> mark(tt)
744.20/262.98	   active(U36(tt)) -> mark(tt)
744.20/262.98	   active(U42(tt)) -> mark(tt)
744.20/262.98	   active(U51(tt)) -> mark(tt)
744.20/262.98	   active(U62(tt)) -> mark(tt)
744.20/262.98	   active(U92(tt)) -> mark(0)
744.20/262.98	   active(isNat(0)) -> mark(tt)
744.20/262.98	   active(isNatKind(0)) -> mark(tt)
744.20/262.98	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.98	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.98	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.98	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.98	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.98	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.98	   U16(active(X)) -> U16(X)
744.20/262.98	   U16(mark(X)) -> U16(X)
744.20/262.98	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.98	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.98	   U23(active(X)) -> U23(X)
744.20/262.98	   U23(mark(X)) -> U23(X)
744.20/262.98	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.98	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.98	   U36(active(X)) -> U36(X)
744.20/262.98	   U36(mark(X)) -> U36(X)
744.20/262.98	   U42(active(X)) -> U42(X)
744.20/262.98	   U42(mark(X)) -> U42(X)
744.20/262.98	   U62(active(X)) -> U62(X)
744.20/262.98	   U62(mark(X)) -> U62(X)
744.20/262.98	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.98	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.98	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.98	   s(active(X)) -> s(X)
744.20/262.98	   s(mark(X)) -> s(X)
744.20/262.98	   U92(active(X)) -> U92(X)
744.20/262.98	   U92(mark(X)) -> U92(X)
744.20/262.98	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.98	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.98	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.98	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.98	   U51(active(X)) -> U51(X)
744.20/262.98	   U51(mark(X)) -> U51(X)
744.20/262.98	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.98	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.98	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.98	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.98	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.98	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.98	   x(active(X1), X2) -> x(X1, X2)
744.20/262.98	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.98	
744.20/262.98	The set Q consists of the following terms:
744.20/262.98	
744.20/262.98	   active(U101(tt, x0, x1))
744.20/262.98	   active(U102(tt, x0, x1))
744.20/262.98	   active(U103(tt, x0, x1))
744.20/262.98	   active(U104(tt, x0, x1))
744.20/262.98	   active(U11(tt, x0, x1))
744.20/262.98	   active(U12(tt, x0, x1))
744.20/262.98	   active(U13(tt, x0, x1))
744.20/262.98	   active(U14(tt, x0, x1))
744.20/262.98	   active(U15(tt, x0))
744.20/262.98	   active(U16(tt))
744.20/262.98	   active(U21(tt, x0))
744.20/262.98	   active(U22(tt, x0))
744.20/262.98	   active(U23(tt))
744.20/262.98	   active(U31(tt, x0, x1))
744.20/262.98	   active(U32(tt, x0, x1))
744.20/262.98	   active(U33(tt, x0, x1))
744.20/262.98	   active(U34(tt, x0, x1))
744.20/262.98	   active(U35(tt, x0))
744.20/262.98	   active(U36(tt))
744.20/262.98	   active(U41(tt, x0))
744.20/262.98	   active(U42(tt))
744.20/262.98	   active(U51(tt))
744.20/262.98	   active(U61(tt, x0))
744.20/262.98	   active(U62(tt))
744.20/262.98	   active(U71(tt, x0))
744.20/262.98	   active(U72(tt, x0))
744.20/262.98	   active(U81(tt, x0, x1))
744.20/262.98	   active(U82(tt, x0, x1))
744.20/262.98	   active(U83(tt, x0, x1))
744.20/262.98	   active(U84(tt, x0, x1))
744.20/262.98	   active(U91(tt, x0))
744.20/262.98	   active(U92(tt))
744.20/262.98	   active(isNat(0))
744.20/262.98	   active(isNat(plus(x0, x1)))
744.20/262.98	   active(isNat(s(x0)))
744.20/262.98	   active(isNat(x(x0, x1)))
744.20/262.98	   active(isNatKind(0))
744.20/262.98	   active(isNatKind(plus(x0, x1)))
744.20/262.98	   active(isNatKind(s(x0)))
744.20/262.98	   active(isNatKind(x(x0, x1)))
744.20/262.98	   active(plus(x0, 0))
744.20/262.98	   active(plus(x0, s(x1)))
744.20/262.98	   active(x(x0, 0))
744.20/262.98	   active(x(x0, s(x1)))
744.20/262.98	   mark(U101(x0, x1, x2))
744.20/262.98	   mark(tt)
744.20/262.98	   mark(U102(x0, x1, x2))
744.20/262.98	   mark(isNatKind(x0))
744.20/262.98	   mark(U103(x0, x1, x2))
744.20/262.98	   mark(isNat(x0))
744.20/262.98	   mark(U104(x0, x1, x2))
744.20/262.98	   mark(plus(x0, x1))
744.20/262.98	   mark(x(x0, x1))
744.20/262.98	   mark(U11(x0, x1, x2))
744.20/262.98	   mark(U12(x0, x1, x2))
744.20/262.98	   mark(U13(x0, x1, x2))
744.20/262.98	   mark(U14(x0, x1, x2))
744.20/262.98	   mark(U15(x0, x1))
744.20/262.98	   mark(U16(x0))
744.20/262.98	   mark(U21(x0, x1))
744.20/262.98	   mark(U22(x0, x1))
744.20/262.98	   mark(U23(x0))
744.20/262.98	   mark(U31(x0, x1, x2))
744.20/262.98	   mark(U32(x0, x1, x2))
744.20/262.98	   mark(U33(x0, x1, x2))
744.20/262.98	   mark(U34(x0, x1, x2))
744.20/262.98	   mark(U35(x0, x1))
744.20/262.98	   mark(U36(x0))
744.20/262.98	   mark(U41(x0, x1))
744.20/262.98	   mark(U42(x0))
744.20/262.98	   mark(U51(x0))
744.20/262.98	   mark(U61(x0, x1))
744.20/262.98	   mark(U62(x0))
744.20/262.98	   mark(U71(x0, x1))
744.20/262.98	   mark(U72(x0, x1))
744.20/262.98	   mark(U81(x0, x1, x2))
744.20/262.98	   mark(U82(x0, x1, x2))
744.20/262.98	   mark(U83(x0, x1, x2))
744.20/262.98	   mark(U84(x0, x1, x2))
744.20/262.98	   mark(s(x0))
744.20/262.98	   mark(U91(x0, x1))
744.20/262.98	   mark(U92(x0))
744.20/262.98	   mark(0)
744.20/262.98	   U101(mark(x0), x1, x2)
744.20/262.98	   U101(x0, mark(x1), x2)
744.20/262.98	   U101(x0, x1, mark(x2))
744.20/262.98	   U101(active(x0), x1, x2)
744.20/262.98	   U101(x0, active(x1), x2)
744.20/262.98	   U101(x0, x1, active(x2))
744.20/262.98	   U102(mark(x0), x1, x2)
744.20/262.98	   U102(x0, mark(x1), x2)
744.20/262.98	   U102(x0, x1, mark(x2))
744.20/262.98	   U102(active(x0), x1, x2)
744.20/262.98	   U102(x0, active(x1), x2)
744.20/262.98	   U102(x0, x1, active(x2))
744.20/262.98	   isNatKind(mark(x0))
744.20/262.98	   isNatKind(active(x0))
744.20/262.98	   U103(mark(x0), x1, x2)
744.20/262.98	   U103(x0, mark(x1), x2)
744.20/262.98	   U103(x0, x1, mark(x2))
744.20/262.98	   U103(active(x0), x1, x2)
744.20/262.98	   U103(x0, active(x1), x2)
744.20/262.98	   U103(x0, x1, active(x2))
744.20/262.98	   isNat(mark(x0))
744.20/262.98	   isNat(active(x0))
744.20/262.98	   U104(mark(x0), x1, x2)
744.20/262.98	   U104(x0, mark(x1), x2)
744.20/262.98	   U104(x0, x1, mark(x2))
744.20/262.98	   U104(active(x0), x1, x2)
744.20/262.98	   U104(x0, active(x1), x2)
744.20/262.98	   U104(x0, x1, active(x2))
744.20/262.98	   plus(mark(x0), x1)
744.20/262.98	   plus(x0, mark(x1))
744.20/262.98	   plus(active(x0), x1)
744.20/262.98	   plus(x0, active(x1))
744.20/262.98	   x(mark(x0), x1)
744.20/262.98	   x(x0, mark(x1))
744.20/262.98	   x(active(x0), x1)
744.20/262.98	   x(x0, active(x1))
744.20/262.98	   U11(mark(x0), x1, x2)
744.20/262.98	   U11(x0, mark(x1), x2)
744.20/262.98	   U11(x0, x1, mark(x2))
744.20/262.98	   U11(active(x0), x1, x2)
744.20/262.98	   U11(x0, active(x1), x2)
744.20/262.98	   U11(x0, x1, active(x2))
744.20/262.98	   U12(mark(x0), x1, x2)
744.20/262.98	   U12(x0, mark(x1), x2)
744.20/262.98	   U12(x0, x1, mark(x2))
744.20/262.98	   U12(active(x0), x1, x2)
744.20/262.98	   U12(x0, active(x1), x2)
744.20/262.98	   U12(x0, x1, active(x2))
744.20/262.98	   U13(mark(x0), x1, x2)
744.20/262.98	   U13(x0, mark(x1), x2)
744.20/262.98	   U13(x0, x1, mark(x2))
744.20/262.98	   U13(active(x0), x1, x2)
744.20/262.98	   U13(x0, active(x1), x2)
744.20/262.98	   U13(x0, x1, active(x2))
744.20/262.98	   U14(mark(x0), x1, x2)
744.20/262.98	   U14(x0, mark(x1), x2)
744.20/262.98	   U14(x0, x1, mark(x2))
744.20/262.98	   U14(active(x0), x1, x2)
744.20/262.98	   U14(x0, active(x1), x2)
744.20/262.98	   U14(x0, x1, active(x2))
744.20/262.98	   U15(mark(x0), x1)
744.20/262.98	   U15(x0, mark(x1))
744.20/262.98	   U15(active(x0), x1)
744.20/262.98	   U15(x0, active(x1))
744.20/262.98	   U16(mark(x0))
744.20/262.98	   U16(active(x0))
744.20/262.98	   U21(mark(x0), x1)
744.20/262.98	   U21(x0, mark(x1))
744.20/262.98	   U21(active(x0), x1)
744.20/262.98	   U21(x0, active(x1))
744.20/262.98	   U22(mark(x0), x1)
744.20/262.98	   U22(x0, mark(x1))
744.20/262.98	   U22(active(x0), x1)
744.20/262.98	   U22(x0, active(x1))
744.20/262.98	   U23(mark(x0))
744.20/262.98	   U23(active(x0))
744.20/262.98	   U31(mark(x0), x1, x2)
744.20/262.98	   U31(x0, mark(x1), x2)
744.20/262.98	   U31(x0, x1, mark(x2))
744.20/262.98	   U31(active(x0), x1, x2)
744.20/262.98	   U31(x0, active(x1), x2)
744.20/262.98	   U31(x0, x1, active(x2))
744.20/262.98	   U32(mark(x0), x1, x2)
744.20/262.98	   U32(x0, mark(x1), x2)
744.20/262.98	   U32(x0, x1, mark(x2))
744.20/262.98	   U32(active(x0), x1, x2)
744.20/262.98	   U32(x0, active(x1), x2)
744.20/262.98	   U32(x0, x1, active(x2))
744.20/262.98	   U33(mark(x0), x1, x2)
744.20/262.98	   U33(x0, mark(x1), x2)
744.20/262.98	   U33(x0, x1, mark(x2))
744.20/262.98	   U33(active(x0), x1, x2)
744.20/262.98	   U33(x0, active(x1), x2)
744.20/262.98	   U33(x0, x1, active(x2))
744.20/262.98	   U34(mark(x0), x1, x2)
744.20/262.98	   U34(x0, mark(x1), x2)
744.20/262.98	   U34(x0, x1, mark(x2))
744.20/262.98	   U34(active(x0), x1, x2)
744.20/262.98	   U34(x0, active(x1), x2)
744.20/262.98	   U34(x0, x1, active(x2))
744.20/262.98	   U35(mark(x0), x1)
744.20/262.98	   U35(x0, mark(x1))
744.20/262.98	   U35(active(x0), x1)
744.20/262.98	   U35(x0, active(x1))
744.20/262.98	   U36(mark(x0))
744.20/262.98	   U36(active(x0))
744.20/262.98	   U41(mark(x0), x1)
744.20/262.98	   U41(x0, mark(x1))
744.20/262.98	   U41(active(x0), x1)
744.20/262.98	   U41(x0, active(x1))
744.20/262.98	   U42(mark(x0))
744.20/262.98	   U42(active(x0))
744.20/262.98	   U51(mark(x0))
744.20/262.98	   U51(active(x0))
744.20/262.98	   U61(mark(x0), x1)
744.20/262.98	   U61(x0, mark(x1))
744.20/262.98	   U61(active(x0), x1)
744.20/262.98	   U61(x0, active(x1))
744.20/262.98	   U62(mark(x0))
744.20/262.98	   U62(active(x0))
744.20/262.98	   U71(mark(x0), x1)
744.20/262.98	   U71(x0, mark(x1))
744.20/262.98	   U71(active(x0), x1)
744.20/262.98	   U71(x0, active(x1))
744.20/262.98	   U72(mark(x0), x1)
744.20/262.98	   U72(x0, mark(x1))
744.20/262.98	   U72(active(x0), x1)
744.20/262.98	   U72(x0, active(x1))
744.20/262.98	   U81(mark(x0), x1, x2)
744.20/262.98	   U81(x0, mark(x1), x2)
744.20/262.98	   U81(x0, x1, mark(x2))
744.20/262.98	   U81(active(x0), x1, x2)
744.20/262.98	   U81(x0, active(x1), x2)
744.20/262.98	   U81(x0, x1, active(x2))
744.20/262.98	   U82(mark(x0), x1, x2)
744.20/262.98	   U82(x0, mark(x1), x2)
744.20/262.98	   U82(x0, x1, mark(x2))
744.20/262.98	   U82(active(x0), x1, x2)
744.20/262.98	   U82(x0, active(x1), x2)
744.20/262.98	   U82(x0, x1, active(x2))
744.20/262.98	   U83(mark(x0), x1, x2)
744.20/262.98	   U83(x0, mark(x1), x2)
744.20/262.98	   U83(x0, x1, mark(x2))
744.20/262.98	   U83(active(x0), x1, x2)
744.20/262.98	   U83(x0, active(x1), x2)
744.20/262.98	   U83(x0, x1, active(x2))
744.20/262.98	   U84(mark(x0), x1, x2)
744.20/262.98	   U84(x0, mark(x1), x2)
744.20/262.98	   U84(x0, x1, mark(x2))
744.20/262.98	   U84(active(x0), x1, x2)
744.20/262.98	   U84(x0, active(x1), x2)
744.20/262.98	   U84(x0, x1, active(x2))
744.20/262.98	   s(mark(x0))
744.20/262.98	   s(active(x0))
744.20/262.98	   U91(mark(x0), x1)
744.20/262.98	   U91(x0, mark(x1))
744.20/262.98	   U91(active(x0), x1)
744.20/262.98	   U91(x0, active(x1))
744.20/262.98	   U92(mark(x0))
744.20/262.98	   U92(active(x0))
744.20/262.98	
744.20/262.98	We have to consider all minimal (P,Q,R)-chains.
744.20/262.98	----------------------------------------
744.20/262.98	
744.20/262.98	(271) QDPOrderProof (EQUIVALENT)
744.20/262.98	We use the reduction pair processor [LPAR04,JAR06].
744.20/262.98	
744.20/262.98	
744.20/262.98	The following pairs can be oriented strictly and are deleted.
744.20/262.98	
744.20/262.98	   MARK(U102(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   ACTIVE(U104(tt, M, N)) -> MARK(plus(x(N, M), N))
744.20/262.98	   ACTIVE(U71(tt, N)) -> MARK(U72(isNatKind(N), N))
744.20/262.98	   ACTIVE(U72(tt, N)) -> MARK(N)
744.20/262.98	   MARK(U101(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   ACTIVE(U84(tt, M, N)) -> MARK(s(plus(N, M)))
744.20/262.98	   ACTIVE(plus(N, 0)) -> MARK(U71(isNat(N), N))
744.20/262.98	   ACTIVE(plus(N, s(M))) -> MARK(U81(isNat(M), M, N))
744.20/262.98	   ACTIVE(x(N, 0)) -> MARK(U91(isNat(N), N))
744.20/262.98	   ACTIVE(x(N, s(M))) -> MARK(U101(isNat(M), M, N))
744.20/262.98	   MARK(U91(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U103(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U104(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(plus(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(x(X1, X2)) -> MARK(X2)
744.20/262.98	   MARK(U71(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U72(X1, X2)) -> MARK(X1)
744.20/262.98	   MARK(U81(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U82(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U83(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(U84(X1, X2, X3)) -> MARK(X1)
744.20/262.98	   MARK(s(X)) -> MARK(X)
744.20/262.98	   MARK(U92(X)) -> MARK(X)
744.20/262.98	The remaining pairs can at least be oriented weakly.
744.20/262.98	Used ordering:  Combined order from the following AFS and order.
744.20/262.98	MARK(x1)  =  x1
744.20/262.98	
744.20/262.98	U102(x1, x2, x3)  =  U102(x1, x2, x3)
744.20/262.98	
744.20/262.98	ACTIVE(x1)  =  x1
744.20/262.98	
744.20/262.98	mark(x1)  =  x1
744.20/262.98	
744.20/262.98	U101(x1, x2, x3)  =  U101(x1, x2, x3)
744.20/262.98	
744.20/262.98	tt  =  tt
744.20/262.98	
744.20/262.98	isNatKind(x1)  =  isNatKind
744.20/262.98	
744.20/262.98	U103(x1, x2, x3)  =  U103(x1, x2, x3)
744.20/262.98	
744.20/262.98	isNat(x1)  =  isNat
744.20/262.98	
744.20/262.98	U104(x1, x2, x3)  =  U104(x1, x2, x3)
744.20/262.98	
744.20/262.98	plus(x1, x2)  =  plus(x1, x2)
744.20/262.98	
744.20/262.98	x(x1, x2)  =  x(x1, x2)
744.20/262.98	
744.20/262.98	U11(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U12(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U13(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U14(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U15(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U16(x1)  =  x1
744.20/262.98	
744.20/262.98	U21(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U22(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U23(x1)  =  x1
744.20/262.98	
744.20/262.98	U31(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U32(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U33(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U34(x1, x2, x3)  =  x1
744.20/262.98	
744.20/262.98	U35(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U36(x1)  =  x1
744.20/262.98	
744.20/262.98	U41(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U42(x1)  =  x1
744.20/262.98	
744.20/262.98	U61(x1, x2)  =  x1
744.20/262.98	
744.20/262.98	U62(x1)  =  x1
744.20/262.98	
744.20/262.98	U71(x1, x2)  =  U71(x1, x2)
744.20/262.98	
744.20/262.98	U72(x1, x2)  =  U72(x1, x2)
744.20/262.98	
744.20/262.98	U81(x1, x2, x3)  =  U81(x1, x2, x3)
744.20/262.98	
744.20/262.98	U82(x1, x2, x3)  =  U82(x1, x2, x3)
744.20/262.98	
744.20/262.98	U83(x1, x2, x3)  =  U83(x1, x2, x3)
744.20/262.98	
744.20/262.98	U84(x1, x2, x3)  =  U84(x1, x2, x3)
744.20/262.98	
744.20/262.98	s(x1)  =  s(x1)
744.20/262.98	
744.20/262.98	U91(x1, x2)  =  U91(x1)
744.20/262.98	
744.20/262.98	U92(x1)  =  U92(x1)
744.20/262.98	
744.20/262.98	0  =  0
744.20/262.98	
744.20/262.98	U51(x1)  =  x1
744.20/262.98	
744.20/262.98	active(x1)  =  x1
744.20/262.98	
744.20/262.98	
744.20/262.98	Recursive path order with status [RPO].
744.20/262.98	Quasi-Precedence: [U102_3, U101_3, U103_3, U104_3, x_2] > [tt, isNatKind, isNat, plus_2, U81_3, U82_3, U83_3, U84_3, U91_1, U92_1, 0] > U71_2 > U72_2
744.20/262.98	[U102_3, U101_3, U103_3, U104_3, x_2] > [tt, isNatKind, isNat, plus_2, U81_3, U82_3, U83_3, U84_3, U91_1, U92_1, 0] > s_1
744.20/262.98	
744.20/262.98	Status: U102_3: [2,3,1]
744.20/262.98	U101_3: [2,3,1]
744.20/262.98	tt: multiset status
744.20/262.98	isNatKind: []
744.20/262.98	U103_3: [2,3,1]
744.20/262.98	isNat: []
744.20/262.98	U104_3: [2,3,1]
744.20/262.98	plus_2: [2,1]
744.20/262.98	x_2: [2,1]
744.20/262.98	U71_2: [2,1]
744.20/262.98	U72_2: multiset status
744.20/262.98	U81_3: [2,3,1]
744.20/262.98	U82_3: [2,3,1]
744.20/262.98	U83_3: [2,3,1]
744.20/262.98	U84_3: [2,3,1]
744.20/262.98	s_1: multiset status
744.20/262.98	U91_1: multiset status
744.20/262.98	U92_1: multiset status
744.20/262.98	0: multiset status
744.20/262.98	
744.20/262.98	
744.20/262.98	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/262.98	
744.20/262.98	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.98	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.98	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.98	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.98	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.98	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.98	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.98	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.98	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.98	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.98	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.98	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.98	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.98	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.98	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.98	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.98	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.98	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.98	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.98	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.98	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.98	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.98	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.98	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.98	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.98	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.98	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.98	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.98	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.98	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.98	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.98	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.98	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.98	   active(U72(tt, N)) -> mark(N)
744.20/262.98	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.98	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.98	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.98	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.98	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.98	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.98	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.98	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.98	   mark(s(X)) -> active(s(mark(X)))
744.20/262.98	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.98	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.98	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.98	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.98	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.98	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.98	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.98	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.98	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.98	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.98	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.98	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.98	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.98	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.98	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.98	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.98	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.98	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.98	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.98	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.98	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.98	   mark(isNat(X)) -> active(isNat(X))
744.20/262.98	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.98	   mark(tt) -> active(tt)
744.20/262.98	   mark(0) -> active(0)
744.20/262.98	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.98	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.98	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.98	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.98	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.98	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.98	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.98	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.98	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.98	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.98	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.98	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.98	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.98	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.98	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.98	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.98	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.98	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.98	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.98	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.98	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.98	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.98	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.98	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.98	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.98	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.98	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.98	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.98	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.98	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.98	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.98	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.98	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.98	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.98	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.98	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.98	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.98	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.98	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.98	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.98	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.98	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.98	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.98	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.98	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.98	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.98	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.98	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.98	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.98	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.98	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.98	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.98	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.98	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.98	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.98	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.98	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.98	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.98	   x(active(X1), X2) -> x(X1, X2)
744.20/262.98	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.98	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.98	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.98	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.98	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.98	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.98	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.98	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.98	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.98	   active(U16(tt)) -> mark(tt)
744.20/262.98	   active(U23(tt)) -> mark(tt)
744.20/262.98	   active(U36(tt)) -> mark(tt)
744.20/262.98	   active(U42(tt)) -> mark(tt)
744.20/262.98	   active(U51(tt)) -> mark(tt)
744.20/262.98	   active(U62(tt)) -> mark(tt)
744.20/262.98	   active(U92(tt)) -> mark(0)
744.20/262.98	   active(isNat(0)) -> mark(tt)
744.20/262.98	   active(isNatKind(0)) -> mark(tt)
744.20/262.98	   U16(active(X)) -> U16(X)
744.20/262.98	   U16(mark(X)) -> U16(X)
744.20/262.98	   U23(active(X)) -> U23(X)
744.20/262.98	   U23(mark(X)) -> U23(X)
744.20/262.98	   U36(active(X)) -> U36(X)
744.20/262.98	   U36(mark(X)) -> U36(X)
744.20/262.98	   U42(active(X)) -> U42(X)
744.20/262.98	   U42(mark(X)) -> U42(X)
744.20/262.98	   U62(active(X)) -> U62(X)
744.20/262.98	   U62(mark(X)) -> U62(X)
744.20/262.98	   s(active(X)) -> s(X)
744.20/262.98	   s(mark(X)) -> s(X)
744.20/262.98	   U92(active(X)) -> U92(X)
744.20/262.98	   U92(mark(X)) -> U92(X)
744.20/262.98	   U51(active(X)) -> U51(X)
744.20/262.98	   U51(mark(X)) -> U51(X)
744.20/262.98	
744.20/262.98	
744.20/262.98	----------------------------------------
744.20/262.98	
744.20/262.98	(272)
744.20/262.98	Obligation:
744.20/262.98	Q DP problem:
744.20/262.98	The TRS P consists of the following rules:
744.20/262.98	
744.20/262.98	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.98	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.98	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.98	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.98	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.98	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.98	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.98	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.98	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.98	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.98	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.98	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.98	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.98	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.98	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.99	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.99	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.99	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.99	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.99	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.99	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.99	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.99	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.99	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.99	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.99	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.99	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U91(tt, N)) -> MARK(U92(isNatKind(N)))
744.20/262.99	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.99	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.99	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.99	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.99	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.99	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U16(X)) -> MARK(X)
744.20/262.99	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.99	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U23(X)) -> MARK(X)
744.20/262.99	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.99	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U36(X)) -> MARK(X)
744.20/262.99	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U42(X)) -> MARK(X)
744.20/262.99	   MARK(U51(X)) -> MARK(X)
744.20/262.99	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.99	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U62(X)) -> MARK(X)
744.20/262.99	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.99	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.99	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.99	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.99	
744.20/262.99	The TRS R consists of the following rules:
744.20/262.99	
744.20/262.99	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.99	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.99	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.99	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.99	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.99	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.99	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.99	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.99	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.99	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.99	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.99	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.99	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.99	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.99	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.99	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.99	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.99	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.99	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.99	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.99	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.99	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.99	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.99	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.99	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.99	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.99	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.99	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.99	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.99	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.99	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.99	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.99	   active(U72(tt, N)) -> mark(N)
744.20/262.99	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.99	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.99	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.99	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.99	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.99	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.99	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.99	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.99	   mark(s(X)) -> active(s(mark(X)))
744.20/262.99	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.99	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.99	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.99	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.99	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.99	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.99	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.99	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.99	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.99	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.99	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.99	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.99	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.99	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.99	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.99	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.99	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.99	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.99	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.99	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.99	   mark(isNat(X)) -> active(isNat(X))
744.20/262.99	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.99	   mark(tt) -> active(tt)
744.20/262.99	   mark(0) -> active(0)
744.20/262.99	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.99	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.99	   active(U16(tt)) -> mark(tt)
744.20/262.99	   active(U23(tt)) -> mark(tt)
744.20/262.99	   active(U36(tt)) -> mark(tt)
744.20/262.99	   active(U42(tt)) -> mark(tt)
744.20/262.99	   active(U51(tt)) -> mark(tt)
744.20/262.99	   active(U62(tt)) -> mark(tt)
744.20/262.99	   active(U92(tt)) -> mark(0)
744.20/262.99	   active(isNat(0)) -> mark(tt)
744.20/262.99	   active(isNatKind(0)) -> mark(tt)
744.20/262.99	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.99	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.99	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.99	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.99	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.99	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.99	   U16(active(X)) -> U16(X)
744.20/262.99	   U16(mark(X)) -> U16(X)
744.20/262.99	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.99	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.99	   U23(active(X)) -> U23(X)
744.20/262.99	   U23(mark(X)) -> U23(X)
744.20/262.99	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.99	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.99	   U36(active(X)) -> U36(X)
744.20/262.99	   U36(mark(X)) -> U36(X)
744.20/262.99	   U42(active(X)) -> U42(X)
744.20/262.99	   U42(mark(X)) -> U42(X)
744.20/262.99	   U62(active(X)) -> U62(X)
744.20/262.99	   U62(mark(X)) -> U62(X)
744.20/262.99	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.99	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.99	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.99	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.99	   s(active(X)) -> s(X)
744.20/262.99	   s(mark(X)) -> s(X)
744.20/262.99	   U92(active(X)) -> U92(X)
744.20/262.99	   U92(mark(X)) -> U92(X)
744.20/262.99	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.99	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.99	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.99	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.99	   U51(active(X)) -> U51(X)
744.20/262.99	   U51(mark(X)) -> U51(X)
744.20/262.99	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.99	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.99	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.99	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.99	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.99	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.99	   x(active(X1), X2) -> x(X1, X2)
744.20/262.99	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.99	
744.20/262.99	The set Q consists of the following terms:
744.20/262.99	
744.20/262.99	   active(U101(tt, x0, x1))
744.20/262.99	   active(U102(tt, x0, x1))
744.20/262.99	   active(U103(tt, x0, x1))
744.20/262.99	   active(U104(tt, x0, x1))
744.20/262.99	   active(U11(tt, x0, x1))
744.20/262.99	   active(U12(tt, x0, x1))
744.20/262.99	   active(U13(tt, x0, x1))
744.20/262.99	   active(U14(tt, x0, x1))
744.20/262.99	   active(U15(tt, x0))
744.20/262.99	   active(U16(tt))
744.20/262.99	   active(U21(tt, x0))
744.20/262.99	   active(U22(tt, x0))
744.20/262.99	   active(U23(tt))
744.20/262.99	   active(U31(tt, x0, x1))
744.20/262.99	   active(U32(tt, x0, x1))
744.20/262.99	   active(U33(tt, x0, x1))
744.20/262.99	   active(U34(tt, x0, x1))
744.20/262.99	   active(U35(tt, x0))
744.20/262.99	   active(U36(tt))
744.20/262.99	   active(U41(tt, x0))
744.20/262.99	   active(U42(tt))
744.20/262.99	   active(U51(tt))
744.20/262.99	   active(U61(tt, x0))
744.20/262.99	   active(U62(tt))
744.20/262.99	   active(U71(tt, x0))
744.20/262.99	   active(U72(tt, x0))
744.20/262.99	   active(U81(tt, x0, x1))
744.20/262.99	   active(U82(tt, x0, x1))
744.20/262.99	   active(U83(tt, x0, x1))
744.20/262.99	   active(U84(tt, x0, x1))
744.20/262.99	   active(U91(tt, x0))
744.20/262.99	   active(U92(tt))
744.20/262.99	   active(isNat(0))
744.20/262.99	   active(isNat(plus(x0, x1)))
744.20/262.99	   active(isNat(s(x0)))
744.20/262.99	   active(isNat(x(x0, x1)))
744.20/262.99	   active(isNatKind(0))
744.20/262.99	   active(isNatKind(plus(x0, x1)))
744.20/262.99	   active(isNatKind(s(x0)))
744.20/262.99	   active(isNatKind(x(x0, x1)))
744.20/262.99	   active(plus(x0, 0))
744.20/262.99	   active(plus(x0, s(x1)))
744.20/262.99	   active(x(x0, 0))
744.20/262.99	   active(x(x0, s(x1)))
744.20/262.99	   mark(U101(x0, x1, x2))
744.20/262.99	   mark(tt)
744.20/262.99	   mark(U102(x0, x1, x2))
744.20/262.99	   mark(isNatKind(x0))
744.20/262.99	   mark(U103(x0, x1, x2))
744.20/262.99	   mark(isNat(x0))
744.20/262.99	   mark(U104(x0, x1, x2))
744.20/262.99	   mark(plus(x0, x1))
744.20/262.99	   mark(x(x0, x1))
744.20/262.99	   mark(U11(x0, x1, x2))
744.20/262.99	   mark(U12(x0, x1, x2))
744.20/262.99	   mark(U13(x0, x1, x2))
744.20/262.99	   mark(U14(x0, x1, x2))
744.20/262.99	   mark(U15(x0, x1))
744.20/262.99	   mark(U16(x0))
744.20/262.99	   mark(U21(x0, x1))
744.20/262.99	   mark(U22(x0, x1))
744.20/262.99	   mark(U23(x0))
744.20/262.99	   mark(U31(x0, x1, x2))
744.20/262.99	   mark(U32(x0, x1, x2))
744.20/262.99	   mark(U33(x0, x1, x2))
744.20/262.99	   mark(U34(x0, x1, x2))
744.20/262.99	   mark(U35(x0, x1))
744.20/262.99	   mark(U36(x0))
744.20/262.99	   mark(U41(x0, x1))
744.20/262.99	   mark(U42(x0))
744.20/262.99	   mark(U51(x0))
744.20/262.99	   mark(U61(x0, x1))
744.20/262.99	   mark(U62(x0))
744.20/262.99	   mark(U71(x0, x1))
744.20/262.99	   mark(U72(x0, x1))
744.20/262.99	   mark(U81(x0, x1, x2))
744.20/262.99	   mark(U82(x0, x1, x2))
744.20/262.99	   mark(U83(x0, x1, x2))
744.20/262.99	   mark(U84(x0, x1, x2))
744.20/262.99	   mark(s(x0))
744.20/262.99	   mark(U91(x0, x1))
744.20/262.99	   mark(U92(x0))
744.20/262.99	   mark(0)
744.20/262.99	   U101(mark(x0), x1, x2)
744.20/262.99	   U101(x0, mark(x1), x2)
744.20/262.99	   U101(x0, x1, mark(x2))
744.20/262.99	   U101(active(x0), x1, x2)
744.20/262.99	   U101(x0, active(x1), x2)
744.20/262.99	   U101(x0, x1, active(x2))
744.20/262.99	   U102(mark(x0), x1, x2)
744.20/262.99	   U102(x0, mark(x1), x2)
744.20/262.99	   U102(x0, x1, mark(x2))
744.20/262.99	   U102(active(x0), x1, x2)
744.20/262.99	   U102(x0, active(x1), x2)
744.20/262.99	   U102(x0, x1, active(x2))
744.20/262.99	   isNatKind(mark(x0))
744.20/262.99	   isNatKind(active(x0))
744.20/262.99	   U103(mark(x0), x1, x2)
744.20/262.99	   U103(x0, mark(x1), x2)
744.20/262.99	   U103(x0, x1, mark(x2))
744.20/262.99	   U103(active(x0), x1, x2)
744.20/262.99	   U103(x0, active(x1), x2)
744.20/262.99	   U103(x0, x1, active(x2))
744.20/262.99	   isNat(mark(x0))
744.20/262.99	   isNat(active(x0))
744.20/262.99	   U104(mark(x0), x1, x2)
744.20/262.99	   U104(x0, mark(x1), x2)
744.20/262.99	   U104(x0, x1, mark(x2))
744.20/262.99	   U104(active(x0), x1, x2)
744.20/262.99	   U104(x0, active(x1), x2)
744.20/262.99	   U104(x0, x1, active(x2))
744.20/262.99	   plus(mark(x0), x1)
744.20/262.99	   plus(x0, mark(x1))
744.20/262.99	   plus(active(x0), x1)
744.20/262.99	   plus(x0, active(x1))
744.20/262.99	   x(mark(x0), x1)
744.20/262.99	   x(x0, mark(x1))
744.20/262.99	   x(active(x0), x1)
744.20/262.99	   x(x0, active(x1))
744.20/262.99	   U11(mark(x0), x1, x2)
744.20/262.99	   U11(x0, mark(x1), x2)
744.20/262.99	   U11(x0, x1, mark(x2))
744.20/262.99	   U11(active(x0), x1, x2)
744.20/262.99	   U11(x0, active(x1), x2)
744.20/262.99	   U11(x0, x1, active(x2))
744.20/262.99	   U12(mark(x0), x1, x2)
744.20/262.99	   U12(x0, mark(x1), x2)
744.20/262.99	   U12(x0, x1, mark(x2))
744.20/262.99	   U12(active(x0), x1, x2)
744.20/262.99	   U12(x0, active(x1), x2)
744.20/262.99	   U12(x0, x1, active(x2))
744.20/262.99	   U13(mark(x0), x1, x2)
744.20/262.99	   U13(x0, mark(x1), x2)
744.20/262.99	   U13(x0, x1, mark(x2))
744.20/262.99	   U13(active(x0), x1, x2)
744.20/262.99	   U13(x0, active(x1), x2)
744.20/262.99	   U13(x0, x1, active(x2))
744.20/262.99	   U14(mark(x0), x1, x2)
744.20/262.99	   U14(x0, mark(x1), x2)
744.20/262.99	   U14(x0, x1, mark(x2))
744.20/262.99	   U14(active(x0), x1, x2)
744.20/262.99	   U14(x0, active(x1), x2)
744.20/262.99	   U14(x0, x1, active(x2))
744.20/262.99	   U15(mark(x0), x1)
744.20/262.99	   U15(x0, mark(x1))
744.20/262.99	   U15(active(x0), x1)
744.20/262.99	   U15(x0, active(x1))
744.20/262.99	   U16(mark(x0))
744.20/262.99	   U16(active(x0))
744.20/262.99	   U21(mark(x0), x1)
744.20/262.99	   U21(x0, mark(x1))
744.20/262.99	   U21(active(x0), x1)
744.20/262.99	   U21(x0, active(x1))
744.20/262.99	   U22(mark(x0), x1)
744.20/262.99	   U22(x0, mark(x1))
744.20/262.99	   U22(active(x0), x1)
744.20/262.99	   U22(x0, active(x1))
744.20/262.99	   U23(mark(x0))
744.20/262.99	   U23(active(x0))
744.20/262.99	   U31(mark(x0), x1, x2)
744.20/262.99	   U31(x0, mark(x1), x2)
744.20/262.99	   U31(x0, x1, mark(x2))
744.20/262.99	   U31(active(x0), x1, x2)
744.20/262.99	   U31(x0, active(x1), x2)
744.20/262.99	   U31(x0, x1, active(x2))
744.20/262.99	   U32(mark(x0), x1, x2)
744.20/262.99	   U32(x0, mark(x1), x2)
744.20/262.99	   U32(x0, x1, mark(x2))
744.20/262.99	   U32(active(x0), x1, x2)
744.20/262.99	   U32(x0, active(x1), x2)
744.20/262.99	   U32(x0, x1, active(x2))
744.20/262.99	   U33(mark(x0), x1, x2)
744.20/262.99	   U33(x0, mark(x1), x2)
744.20/262.99	   U33(x0, x1, mark(x2))
744.20/262.99	   U33(active(x0), x1, x2)
744.20/262.99	   U33(x0, active(x1), x2)
744.20/262.99	   U33(x0, x1, active(x2))
744.20/262.99	   U34(mark(x0), x1, x2)
744.20/262.99	   U34(x0, mark(x1), x2)
744.20/262.99	   U34(x0, x1, mark(x2))
744.20/262.99	   U34(active(x0), x1, x2)
744.20/262.99	   U34(x0, active(x1), x2)
744.20/262.99	   U34(x0, x1, active(x2))
744.20/262.99	   U35(mark(x0), x1)
744.20/262.99	   U35(x0, mark(x1))
744.20/262.99	   U35(active(x0), x1)
744.20/262.99	   U35(x0, active(x1))
744.20/262.99	   U36(mark(x0))
744.20/262.99	   U36(active(x0))
744.20/262.99	   U41(mark(x0), x1)
744.20/262.99	   U41(x0, mark(x1))
744.20/262.99	   U41(active(x0), x1)
744.20/262.99	   U41(x0, active(x1))
744.20/262.99	   U42(mark(x0))
744.20/262.99	   U42(active(x0))
744.20/262.99	   U51(mark(x0))
744.20/262.99	   U51(active(x0))
744.20/262.99	   U61(mark(x0), x1)
744.20/262.99	   U61(x0, mark(x1))
744.20/262.99	   U61(active(x0), x1)
744.20/262.99	   U61(x0, active(x1))
744.20/262.99	   U62(mark(x0))
744.20/262.99	   U62(active(x0))
744.20/262.99	   U71(mark(x0), x1)
744.20/262.99	   U71(x0, mark(x1))
744.20/262.99	   U71(active(x0), x1)
744.20/262.99	   U71(x0, active(x1))
744.20/262.99	   U72(mark(x0), x1)
744.20/262.99	   U72(x0, mark(x1))
744.20/262.99	   U72(active(x0), x1)
744.20/262.99	   U72(x0, active(x1))
744.20/262.99	   U81(mark(x0), x1, x2)
744.20/262.99	   U81(x0, mark(x1), x2)
744.20/262.99	   U81(x0, x1, mark(x2))
744.20/262.99	   U81(active(x0), x1, x2)
744.20/262.99	   U81(x0, active(x1), x2)
744.20/262.99	   U81(x0, x1, active(x2))
744.20/262.99	   U82(mark(x0), x1, x2)
744.20/262.99	   U82(x0, mark(x1), x2)
744.20/262.99	   U82(x0, x1, mark(x2))
744.20/262.99	   U82(active(x0), x1, x2)
744.20/262.99	   U82(x0, active(x1), x2)
744.20/262.99	   U82(x0, x1, active(x2))
744.20/262.99	   U83(mark(x0), x1, x2)
744.20/262.99	   U83(x0, mark(x1), x2)
744.20/262.99	   U83(x0, x1, mark(x2))
744.20/262.99	   U83(active(x0), x1, x2)
744.20/262.99	   U83(x0, active(x1), x2)
744.20/262.99	   U83(x0, x1, active(x2))
744.20/262.99	   U84(mark(x0), x1, x2)
744.20/262.99	   U84(x0, mark(x1), x2)
744.20/262.99	   U84(x0, x1, mark(x2))
744.20/262.99	   U84(active(x0), x1, x2)
744.20/262.99	   U84(x0, active(x1), x2)
744.20/262.99	   U84(x0, x1, active(x2))
744.20/262.99	   s(mark(x0))
744.20/262.99	   s(active(x0))
744.20/262.99	   U91(mark(x0), x1)
744.20/262.99	   U91(x0, mark(x1))
744.20/262.99	   U91(active(x0), x1)
744.20/262.99	   U91(x0, active(x1))
744.20/262.99	   U92(mark(x0))
744.20/262.99	   U92(active(x0))
744.20/262.99	
744.20/262.99	We have to consider all minimal (P,Q,R)-chains.
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(273) DependencyGraphProof (EQUIVALENT)
744.20/262.99	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(274)
744.20/262.99	Obligation:
744.20/262.99	Q DP problem:
744.20/262.99	The TRS P consists of the following rules:
744.20/262.99	
744.20/262.99	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.99	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.99	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.99	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.99	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.99	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.99	   MARK(U16(X)) -> MARK(X)
744.20/262.99	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.99	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.99	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.99	   MARK(U23(X)) -> MARK(X)
744.20/262.99	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.99	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.99	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.99	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.99	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.99	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.99	   MARK(U36(X)) -> MARK(X)
744.20/262.99	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.99	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.99	   MARK(U42(X)) -> MARK(X)
744.20/262.99	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.99	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.99	   MARK(U62(X)) -> MARK(X)
744.20/262.99	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.99	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.99	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.99	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.99	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.99	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.99	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U51(X)) -> MARK(X)
744.20/262.99	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.99	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.99	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.99	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.99	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.99	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.99	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.99	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.99	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.99	
744.20/262.99	The TRS R consists of the following rules:
744.20/262.99	
744.20/262.99	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.99	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.99	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.99	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.99	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.99	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.99	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.99	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.99	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.99	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.99	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.99	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.99	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.99	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.99	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.99	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.99	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.99	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.99	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.99	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.99	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.99	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.99	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.99	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.99	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.99	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.99	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.99	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.99	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.99	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.99	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.99	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.99	   active(U72(tt, N)) -> mark(N)
744.20/262.99	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.99	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.99	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.99	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.99	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.99	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.99	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.99	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.99	   mark(s(X)) -> active(s(mark(X)))
744.20/262.99	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.99	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.99	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.99	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.99	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.99	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.99	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.99	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.99	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.99	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.99	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.99	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.99	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.99	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.99	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.99	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.99	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.99	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.99	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.99	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.99	   mark(isNat(X)) -> active(isNat(X))
744.20/262.99	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.99	   mark(tt) -> active(tt)
744.20/262.99	   mark(0) -> active(0)
744.20/262.99	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.99	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.99	   active(U16(tt)) -> mark(tt)
744.20/262.99	   active(U23(tt)) -> mark(tt)
744.20/262.99	   active(U36(tt)) -> mark(tt)
744.20/262.99	   active(U42(tt)) -> mark(tt)
744.20/262.99	   active(U51(tt)) -> mark(tt)
744.20/262.99	   active(U62(tt)) -> mark(tt)
744.20/262.99	   active(U92(tt)) -> mark(0)
744.20/262.99	   active(isNat(0)) -> mark(tt)
744.20/262.99	   active(isNatKind(0)) -> mark(tt)
744.20/262.99	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.99	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.99	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.99	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.99	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.99	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.99	   U16(active(X)) -> U16(X)
744.20/262.99	   U16(mark(X)) -> U16(X)
744.20/262.99	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.99	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.99	   U23(active(X)) -> U23(X)
744.20/262.99	   U23(mark(X)) -> U23(X)
744.20/262.99	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.99	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.99	   U36(active(X)) -> U36(X)
744.20/262.99	   U36(mark(X)) -> U36(X)
744.20/262.99	   U42(active(X)) -> U42(X)
744.20/262.99	   U42(mark(X)) -> U42(X)
744.20/262.99	   U62(active(X)) -> U62(X)
744.20/262.99	   U62(mark(X)) -> U62(X)
744.20/262.99	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.99	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.99	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.99	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.99	   s(active(X)) -> s(X)
744.20/262.99	   s(mark(X)) -> s(X)
744.20/262.99	   U92(active(X)) -> U92(X)
744.20/262.99	   U92(mark(X)) -> U92(X)
744.20/262.99	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.99	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.99	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.99	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.99	   U51(active(X)) -> U51(X)
744.20/262.99	   U51(mark(X)) -> U51(X)
744.20/262.99	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.99	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.99	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.99	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.99	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.99	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.99	   x(active(X1), X2) -> x(X1, X2)
744.20/262.99	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.99	
744.20/262.99	The set Q consists of the following terms:
744.20/262.99	
744.20/262.99	   active(U101(tt, x0, x1))
744.20/262.99	   active(U102(tt, x0, x1))
744.20/262.99	   active(U103(tt, x0, x1))
744.20/262.99	   active(U104(tt, x0, x1))
744.20/262.99	   active(U11(tt, x0, x1))
744.20/262.99	   active(U12(tt, x0, x1))
744.20/262.99	   active(U13(tt, x0, x1))
744.20/262.99	   active(U14(tt, x0, x1))
744.20/262.99	   active(U15(tt, x0))
744.20/262.99	   active(U16(tt))
744.20/262.99	   active(U21(tt, x0))
744.20/262.99	   active(U22(tt, x0))
744.20/262.99	   active(U23(tt))
744.20/262.99	   active(U31(tt, x0, x1))
744.20/262.99	   active(U32(tt, x0, x1))
744.20/262.99	   active(U33(tt, x0, x1))
744.20/262.99	   active(U34(tt, x0, x1))
744.20/262.99	   active(U35(tt, x0))
744.20/262.99	   active(U36(tt))
744.20/262.99	   active(U41(tt, x0))
744.20/262.99	   active(U42(tt))
744.20/262.99	   active(U51(tt))
744.20/262.99	   active(U61(tt, x0))
744.20/262.99	   active(U62(tt))
744.20/262.99	   active(U71(tt, x0))
744.20/262.99	   active(U72(tt, x0))
744.20/262.99	   active(U81(tt, x0, x1))
744.20/262.99	   active(U82(tt, x0, x1))
744.20/262.99	   active(U83(tt, x0, x1))
744.20/262.99	   active(U84(tt, x0, x1))
744.20/262.99	   active(U91(tt, x0))
744.20/262.99	   active(U92(tt))
744.20/262.99	   active(isNat(0))
744.20/262.99	   active(isNat(plus(x0, x1)))
744.20/262.99	   active(isNat(s(x0)))
744.20/262.99	   active(isNat(x(x0, x1)))
744.20/262.99	   active(isNatKind(0))
744.20/262.99	   active(isNatKind(plus(x0, x1)))
744.20/262.99	   active(isNatKind(s(x0)))
744.20/262.99	   active(isNatKind(x(x0, x1)))
744.20/262.99	   active(plus(x0, 0))
744.20/262.99	   active(plus(x0, s(x1)))
744.20/262.99	   active(x(x0, 0))
744.20/262.99	   active(x(x0, s(x1)))
744.20/262.99	   mark(U101(x0, x1, x2))
744.20/262.99	   mark(tt)
744.20/262.99	   mark(U102(x0, x1, x2))
744.20/262.99	   mark(isNatKind(x0))
744.20/262.99	   mark(U103(x0, x1, x2))
744.20/262.99	   mark(isNat(x0))
744.20/262.99	   mark(U104(x0, x1, x2))
744.20/262.99	   mark(plus(x0, x1))
744.20/262.99	   mark(x(x0, x1))
744.20/262.99	   mark(U11(x0, x1, x2))
744.20/262.99	   mark(U12(x0, x1, x2))
744.20/262.99	   mark(U13(x0, x1, x2))
744.20/262.99	   mark(U14(x0, x1, x2))
744.20/262.99	   mark(U15(x0, x1))
744.20/262.99	   mark(U16(x0))
744.20/262.99	   mark(U21(x0, x1))
744.20/262.99	   mark(U22(x0, x1))
744.20/262.99	   mark(U23(x0))
744.20/262.99	   mark(U31(x0, x1, x2))
744.20/262.99	   mark(U32(x0, x1, x2))
744.20/262.99	   mark(U33(x0, x1, x2))
744.20/262.99	   mark(U34(x0, x1, x2))
744.20/262.99	   mark(U35(x0, x1))
744.20/262.99	   mark(U36(x0))
744.20/262.99	   mark(U41(x0, x1))
744.20/262.99	   mark(U42(x0))
744.20/262.99	   mark(U51(x0))
744.20/262.99	   mark(U61(x0, x1))
744.20/262.99	   mark(U62(x0))
744.20/262.99	   mark(U71(x0, x1))
744.20/262.99	   mark(U72(x0, x1))
744.20/262.99	   mark(U81(x0, x1, x2))
744.20/262.99	   mark(U82(x0, x1, x2))
744.20/262.99	   mark(U83(x0, x1, x2))
744.20/262.99	   mark(U84(x0, x1, x2))
744.20/262.99	   mark(s(x0))
744.20/262.99	   mark(U91(x0, x1))
744.20/262.99	   mark(U92(x0))
744.20/262.99	   mark(0)
744.20/262.99	   U101(mark(x0), x1, x2)
744.20/262.99	   U101(x0, mark(x1), x2)
744.20/262.99	   U101(x0, x1, mark(x2))
744.20/262.99	   U101(active(x0), x1, x2)
744.20/262.99	   U101(x0, active(x1), x2)
744.20/262.99	   U101(x0, x1, active(x2))
744.20/262.99	   U102(mark(x0), x1, x2)
744.20/262.99	   U102(x0, mark(x1), x2)
744.20/262.99	   U102(x0, x1, mark(x2))
744.20/262.99	   U102(active(x0), x1, x2)
744.20/262.99	   U102(x0, active(x1), x2)
744.20/262.99	   U102(x0, x1, active(x2))
744.20/262.99	   isNatKind(mark(x0))
744.20/262.99	   isNatKind(active(x0))
744.20/262.99	   U103(mark(x0), x1, x2)
744.20/262.99	   U103(x0, mark(x1), x2)
744.20/262.99	   U103(x0, x1, mark(x2))
744.20/262.99	   U103(active(x0), x1, x2)
744.20/262.99	   U103(x0, active(x1), x2)
744.20/262.99	   U103(x0, x1, active(x2))
744.20/262.99	   isNat(mark(x0))
744.20/262.99	   isNat(active(x0))
744.20/262.99	   U104(mark(x0), x1, x2)
744.20/262.99	   U104(x0, mark(x1), x2)
744.20/262.99	   U104(x0, x1, mark(x2))
744.20/262.99	   U104(active(x0), x1, x2)
744.20/262.99	   U104(x0, active(x1), x2)
744.20/262.99	   U104(x0, x1, active(x2))
744.20/262.99	   plus(mark(x0), x1)
744.20/262.99	   plus(x0, mark(x1))
744.20/262.99	   plus(active(x0), x1)
744.20/262.99	   plus(x0, active(x1))
744.20/262.99	   x(mark(x0), x1)
744.20/262.99	   x(x0, mark(x1))
744.20/262.99	   x(active(x0), x1)
744.20/262.99	   x(x0, active(x1))
744.20/262.99	   U11(mark(x0), x1, x2)
744.20/262.99	   U11(x0, mark(x1), x2)
744.20/262.99	   U11(x0, x1, mark(x2))
744.20/262.99	   U11(active(x0), x1, x2)
744.20/262.99	   U11(x0, active(x1), x2)
744.20/262.99	   U11(x0, x1, active(x2))
744.20/262.99	   U12(mark(x0), x1, x2)
744.20/262.99	   U12(x0, mark(x1), x2)
744.20/262.99	   U12(x0, x1, mark(x2))
744.20/262.99	   U12(active(x0), x1, x2)
744.20/262.99	   U12(x0, active(x1), x2)
744.20/262.99	   U12(x0, x1, active(x2))
744.20/262.99	   U13(mark(x0), x1, x2)
744.20/262.99	   U13(x0, mark(x1), x2)
744.20/262.99	   U13(x0, x1, mark(x2))
744.20/262.99	   U13(active(x0), x1, x2)
744.20/262.99	   U13(x0, active(x1), x2)
744.20/262.99	   U13(x0, x1, active(x2))
744.20/262.99	   U14(mark(x0), x1, x2)
744.20/262.99	   U14(x0, mark(x1), x2)
744.20/262.99	   U14(x0, x1, mark(x2))
744.20/262.99	   U14(active(x0), x1, x2)
744.20/262.99	   U14(x0, active(x1), x2)
744.20/262.99	   U14(x0, x1, active(x2))
744.20/262.99	   U15(mark(x0), x1)
744.20/262.99	   U15(x0, mark(x1))
744.20/262.99	   U15(active(x0), x1)
744.20/262.99	   U15(x0, active(x1))
744.20/262.99	   U16(mark(x0))
744.20/262.99	   U16(active(x0))
744.20/262.99	   U21(mark(x0), x1)
744.20/262.99	   U21(x0, mark(x1))
744.20/262.99	   U21(active(x0), x1)
744.20/262.99	   U21(x0, active(x1))
744.20/262.99	   U22(mark(x0), x1)
744.20/262.99	   U22(x0, mark(x1))
744.20/262.99	   U22(active(x0), x1)
744.20/262.99	   U22(x0, active(x1))
744.20/262.99	   U23(mark(x0))
744.20/262.99	   U23(active(x0))
744.20/262.99	   U31(mark(x0), x1, x2)
744.20/262.99	   U31(x0, mark(x1), x2)
744.20/262.99	   U31(x0, x1, mark(x2))
744.20/262.99	   U31(active(x0), x1, x2)
744.20/262.99	   U31(x0, active(x1), x2)
744.20/262.99	   U31(x0, x1, active(x2))
744.20/262.99	   U32(mark(x0), x1, x2)
744.20/262.99	   U32(x0, mark(x1), x2)
744.20/262.99	   U32(x0, x1, mark(x2))
744.20/262.99	   U32(active(x0), x1, x2)
744.20/262.99	   U32(x0, active(x1), x2)
744.20/262.99	   U32(x0, x1, active(x2))
744.20/262.99	   U33(mark(x0), x1, x2)
744.20/262.99	   U33(x0, mark(x1), x2)
744.20/262.99	   U33(x0, x1, mark(x2))
744.20/262.99	   U33(active(x0), x1, x2)
744.20/262.99	   U33(x0, active(x1), x2)
744.20/262.99	   U33(x0, x1, active(x2))
744.20/262.99	   U34(mark(x0), x1, x2)
744.20/262.99	   U34(x0, mark(x1), x2)
744.20/262.99	   U34(x0, x1, mark(x2))
744.20/262.99	   U34(active(x0), x1, x2)
744.20/262.99	   U34(x0, active(x1), x2)
744.20/262.99	   U34(x0, x1, active(x2))
744.20/262.99	   U35(mark(x0), x1)
744.20/262.99	   U35(x0, mark(x1))
744.20/262.99	   U35(active(x0), x1)
744.20/262.99	   U35(x0, active(x1))
744.20/262.99	   U36(mark(x0))
744.20/262.99	   U36(active(x0))
744.20/262.99	   U41(mark(x0), x1)
744.20/262.99	   U41(x0, mark(x1))
744.20/262.99	   U41(active(x0), x1)
744.20/262.99	   U41(x0, active(x1))
744.20/262.99	   U42(mark(x0))
744.20/262.99	   U42(active(x0))
744.20/262.99	   U51(mark(x0))
744.20/262.99	   U51(active(x0))
744.20/262.99	   U61(mark(x0), x1)
744.20/262.99	   U61(x0, mark(x1))
744.20/262.99	   U61(active(x0), x1)
744.20/262.99	   U61(x0, active(x1))
744.20/262.99	   U62(mark(x0))
744.20/262.99	   U62(active(x0))
744.20/262.99	   U71(mark(x0), x1)
744.20/262.99	   U71(x0, mark(x1))
744.20/262.99	   U71(active(x0), x1)
744.20/262.99	   U71(x0, active(x1))
744.20/262.99	   U72(mark(x0), x1)
744.20/262.99	   U72(x0, mark(x1))
744.20/262.99	   U72(active(x0), x1)
744.20/262.99	   U72(x0, active(x1))
744.20/262.99	   U81(mark(x0), x1, x2)
744.20/262.99	   U81(x0, mark(x1), x2)
744.20/262.99	   U81(x0, x1, mark(x2))
744.20/262.99	   U81(active(x0), x1, x2)
744.20/262.99	   U81(x0, active(x1), x2)
744.20/262.99	   U81(x0, x1, active(x2))
744.20/262.99	   U82(mark(x0), x1, x2)
744.20/262.99	   U82(x0, mark(x1), x2)
744.20/262.99	   U82(x0, x1, mark(x2))
744.20/262.99	   U82(active(x0), x1, x2)
744.20/262.99	   U82(x0, active(x1), x2)
744.20/262.99	   U82(x0, x1, active(x2))
744.20/262.99	   U83(mark(x0), x1, x2)
744.20/262.99	   U83(x0, mark(x1), x2)
744.20/262.99	   U83(x0, x1, mark(x2))
744.20/262.99	   U83(active(x0), x1, x2)
744.20/262.99	   U83(x0, active(x1), x2)
744.20/262.99	   U83(x0, x1, active(x2))
744.20/262.99	   U84(mark(x0), x1, x2)
744.20/262.99	   U84(x0, mark(x1), x2)
744.20/262.99	   U84(x0, x1, mark(x2))
744.20/262.99	   U84(active(x0), x1, x2)
744.20/262.99	   U84(x0, active(x1), x2)
744.20/262.99	   U84(x0, x1, active(x2))
744.20/262.99	   s(mark(x0))
744.20/262.99	   s(active(x0))
744.20/262.99	   U91(mark(x0), x1)
744.20/262.99	   U91(x0, mark(x1))
744.20/262.99	   U91(active(x0), x1)
744.20/262.99	   U91(x0, active(x1))
744.20/262.99	   U92(mark(x0))
744.20/262.99	   U92(active(x0))
744.20/262.99	
744.20/262.99	We have to consider all minimal (P,Q,R)-chains.
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(275) QDPQMonotonicMRRProof (EQUIVALENT)
744.20/262.99	By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain.
744.20/262.99	
744.20/262.99	Strictly oriented dependency pairs:
744.20/262.99	
744.20/262.99	   MARK(U104(X1, X2, X3)) -> ACTIVE(U104(mark(X1), X2, X3))
744.20/262.99	   MARK(plus(X1, X2)) -> ACTIVE(plus(mark(X1), mark(X2)))
744.20/262.99	   MARK(x(X1, X2)) -> ACTIVE(x(mark(X1), mark(X2)))
744.20/262.99	   MARK(U84(X1, X2, X3)) -> ACTIVE(U84(mark(X1), X2, X3))
744.20/262.99	   MARK(U71(X1, X2)) -> ACTIVE(U71(mark(X1), X2))
744.20/262.99	   MARK(U72(X1, X2)) -> ACTIVE(U72(mark(X1), X2))
744.20/262.99	   MARK(U91(X1, X2)) -> ACTIVE(U91(mark(X1), X2))
744.20/262.99	
744.20/262.99	
744.20/262.99	Used ordering: Polynomial interpretation [POLO]:
744.20/262.99	
744.20/262.99	   POL(0) = 0
744.20/262.99	   POL(ACTIVE(x_1)) = 2*x_1
744.20/262.99	   POL(MARK(x_1)) = 2
744.20/262.99	   POL(U101(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U102(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U103(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U104(x_1, x_2, x_3)) = 0
744.20/262.99	   POL(U11(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U12(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U13(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U14(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U15(x_1, x_2)) = 1
744.20/262.99	   POL(U16(x_1)) = 0
744.20/262.99	   POL(U21(x_1, x_2)) = 1
744.20/262.99	   POL(U22(x_1, x_2)) = 1
744.20/262.99	   POL(U23(x_1)) = 0
744.20/262.99	   POL(U31(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U32(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U33(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U34(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U35(x_1, x_2)) = 1
744.20/262.99	   POL(U36(x_1)) = 0
744.20/262.99	   POL(U41(x_1, x_2)) = 1
744.20/262.99	   POL(U42(x_1)) = 0
744.20/262.99	   POL(U51(x_1)) = 0
744.20/262.99	   POL(U61(x_1, x_2)) = 1
744.20/262.99	   POL(U62(x_1)) = 0
744.20/262.99	   POL(U71(x_1, x_2)) = 0
744.20/262.99	   POL(U72(x_1, x_2)) = 0
744.20/262.99	   POL(U81(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U82(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U83(x_1, x_2, x_3)) = 1
744.20/262.99	   POL(U84(x_1, x_2, x_3)) = 0
744.20/262.99	   POL(U91(x_1, x_2)) = 0
744.20/262.99	   POL(U92(x_1)) = 0
744.20/262.99	   POL(active(x_1)) = 0
744.20/262.99	   POL(isNat(x_1)) = 1
744.20/262.99	   POL(isNatKind(x_1)) = 1
744.20/262.99	   POL(mark(x_1)) = 0
744.20/262.99	   POL(plus(x_1, x_2)) = 0
744.20/262.99	   POL(s(x_1)) = 0
744.20/262.99	   POL(tt) = 0
744.20/262.99	   POL(x(x_1, x_2)) = 0
744.20/262.99	
744.20/262.99	
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(276)
744.20/262.99	Obligation:
744.20/262.99	Q DP problem:
744.20/262.99	The TRS P consists of the following rules:
744.20/262.99	
744.20/262.99	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.99	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.99	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U103(tt, M, N)) -> MARK(U104(isNatKind(N), M, N))
744.20/262.99	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.99	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.99	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.99	   MARK(U16(X)) -> MARK(X)
744.20/262.99	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.99	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.99	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.99	   MARK(U23(X)) -> MARK(X)
744.20/262.99	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.99	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.99	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.99	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.99	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.99	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.99	   MARK(U36(X)) -> MARK(X)
744.20/262.99	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.99	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.99	   MARK(U42(X)) -> MARK(X)
744.20/262.99	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.99	   MARK(U62(X)) -> MARK(X)
744.20/262.99	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.99	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.99	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U83(tt, M, N)) -> MARK(U84(isNatKind(N), M, N))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.99	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.99	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U51(X)) -> MARK(X)
744.20/262.99	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.99	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.99	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.99	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.99	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.99	
744.20/262.99	The TRS R consists of the following rules:
744.20/262.99	
744.20/262.99	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.99	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.99	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.99	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.99	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.99	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.99	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.99	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.99	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.99	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.99	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.99	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.99	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.99	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.99	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.99	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.99	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.99	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.99	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.99	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.99	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.99	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.99	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.99	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.99	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.99	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.99	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.99	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.99	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.99	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.99	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.99	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.99	   active(U72(tt, N)) -> mark(N)
744.20/262.99	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.99	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.99	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.99	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.99	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.99	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.99	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.99	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.99	   mark(s(X)) -> active(s(mark(X)))
744.20/262.99	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.99	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.99	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.99	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.99	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.99	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.99	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.99	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.99	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.99	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.99	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.99	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.99	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.99	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.99	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.99	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.99	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.99	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.99	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.99	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.99	   mark(isNat(X)) -> active(isNat(X))
744.20/262.99	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.99	   mark(tt) -> active(tt)
744.20/262.99	   mark(0) -> active(0)
744.20/262.99	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.99	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.99	   active(U16(tt)) -> mark(tt)
744.20/262.99	   active(U23(tt)) -> mark(tt)
744.20/262.99	   active(U36(tt)) -> mark(tt)
744.20/262.99	   active(U42(tt)) -> mark(tt)
744.20/262.99	   active(U51(tt)) -> mark(tt)
744.20/262.99	   active(U62(tt)) -> mark(tt)
744.20/262.99	   active(U92(tt)) -> mark(0)
744.20/262.99	   active(isNat(0)) -> mark(tt)
744.20/262.99	   active(isNatKind(0)) -> mark(tt)
744.20/262.99	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.99	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.99	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.99	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.99	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.99	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.99	   U16(active(X)) -> U16(X)
744.20/262.99	   U16(mark(X)) -> U16(X)
744.20/262.99	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.99	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.99	   U23(active(X)) -> U23(X)
744.20/262.99	   U23(mark(X)) -> U23(X)
744.20/262.99	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.99	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.99	   U36(active(X)) -> U36(X)
744.20/262.99	   U36(mark(X)) -> U36(X)
744.20/262.99	   U42(active(X)) -> U42(X)
744.20/262.99	   U42(mark(X)) -> U42(X)
744.20/262.99	   U62(active(X)) -> U62(X)
744.20/262.99	   U62(mark(X)) -> U62(X)
744.20/262.99	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.99	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.99	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.99	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.99	   s(active(X)) -> s(X)
744.20/262.99	   s(mark(X)) -> s(X)
744.20/262.99	   U92(active(X)) -> U92(X)
744.20/262.99	   U92(mark(X)) -> U92(X)
744.20/262.99	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.99	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.99	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.99	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/262.99	   U51(active(X)) -> U51(X)
744.20/262.99	   U51(mark(X)) -> U51(X)
744.20/262.99	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/262.99	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(active(X1), X2) -> U71(X1, X2)
744.20/262.99	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/262.99	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/262.99	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/262.99	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/262.99	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(active(X1), X2) -> U91(X1, X2)
744.20/262.99	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/262.99	   x(X1, mark(X2)) -> x(X1, X2)
744.20/262.99	   x(mark(X1), X2) -> x(X1, X2)
744.20/262.99	   x(active(X1), X2) -> x(X1, X2)
744.20/262.99	   x(X1, active(X2)) -> x(X1, X2)
744.20/262.99	
744.20/262.99	The set Q consists of the following terms:
744.20/262.99	
744.20/262.99	   active(U101(tt, x0, x1))
744.20/262.99	   active(U102(tt, x0, x1))
744.20/262.99	   active(U103(tt, x0, x1))
744.20/262.99	   active(U104(tt, x0, x1))
744.20/262.99	   active(U11(tt, x0, x1))
744.20/262.99	   active(U12(tt, x0, x1))
744.20/262.99	   active(U13(tt, x0, x1))
744.20/262.99	   active(U14(tt, x0, x1))
744.20/262.99	   active(U15(tt, x0))
744.20/262.99	   active(U16(tt))
744.20/262.99	   active(U21(tt, x0))
744.20/262.99	   active(U22(tt, x0))
744.20/262.99	   active(U23(tt))
744.20/262.99	   active(U31(tt, x0, x1))
744.20/262.99	   active(U32(tt, x0, x1))
744.20/262.99	   active(U33(tt, x0, x1))
744.20/262.99	   active(U34(tt, x0, x1))
744.20/262.99	   active(U35(tt, x0))
744.20/262.99	   active(U36(tt))
744.20/262.99	   active(U41(tt, x0))
744.20/262.99	   active(U42(tt))
744.20/262.99	   active(U51(tt))
744.20/262.99	   active(U61(tt, x0))
744.20/262.99	   active(U62(tt))
744.20/262.99	   active(U71(tt, x0))
744.20/262.99	   active(U72(tt, x0))
744.20/262.99	   active(U81(tt, x0, x1))
744.20/262.99	   active(U82(tt, x0, x1))
744.20/262.99	   active(U83(tt, x0, x1))
744.20/262.99	   active(U84(tt, x0, x1))
744.20/262.99	   active(U91(tt, x0))
744.20/262.99	   active(U92(tt))
744.20/262.99	   active(isNat(0))
744.20/262.99	   active(isNat(plus(x0, x1)))
744.20/262.99	   active(isNat(s(x0)))
744.20/262.99	   active(isNat(x(x0, x1)))
744.20/262.99	   active(isNatKind(0))
744.20/262.99	   active(isNatKind(plus(x0, x1)))
744.20/262.99	   active(isNatKind(s(x0)))
744.20/262.99	   active(isNatKind(x(x0, x1)))
744.20/262.99	   active(plus(x0, 0))
744.20/262.99	   active(plus(x0, s(x1)))
744.20/262.99	   active(x(x0, 0))
744.20/262.99	   active(x(x0, s(x1)))
744.20/262.99	   mark(U101(x0, x1, x2))
744.20/262.99	   mark(tt)
744.20/262.99	   mark(U102(x0, x1, x2))
744.20/262.99	   mark(isNatKind(x0))
744.20/262.99	   mark(U103(x0, x1, x2))
744.20/262.99	   mark(isNat(x0))
744.20/262.99	   mark(U104(x0, x1, x2))
744.20/262.99	   mark(plus(x0, x1))
744.20/262.99	   mark(x(x0, x1))
744.20/262.99	   mark(U11(x0, x1, x2))
744.20/262.99	   mark(U12(x0, x1, x2))
744.20/262.99	   mark(U13(x0, x1, x2))
744.20/262.99	   mark(U14(x0, x1, x2))
744.20/262.99	   mark(U15(x0, x1))
744.20/262.99	   mark(U16(x0))
744.20/262.99	   mark(U21(x0, x1))
744.20/262.99	   mark(U22(x0, x1))
744.20/262.99	   mark(U23(x0))
744.20/262.99	   mark(U31(x0, x1, x2))
744.20/262.99	   mark(U32(x0, x1, x2))
744.20/262.99	   mark(U33(x0, x1, x2))
744.20/262.99	   mark(U34(x0, x1, x2))
744.20/262.99	   mark(U35(x0, x1))
744.20/262.99	   mark(U36(x0))
744.20/262.99	   mark(U41(x0, x1))
744.20/262.99	   mark(U42(x0))
744.20/262.99	   mark(U51(x0))
744.20/262.99	   mark(U61(x0, x1))
744.20/262.99	   mark(U62(x0))
744.20/262.99	   mark(U71(x0, x1))
744.20/262.99	   mark(U72(x0, x1))
744.20/262.99	   mark(U81(x0, x1, x2))
744.20/262.99	   mark(U82(x0, x1, x2))
744.20/262.99	   mark(U83(x0, x1, x2))
744.20/262.99	   mark(U84(x0, x1, x2))
744.20/262.99	   mark(s(x0))
744.20/262.99	   mark(U91(x0, x1))
744.20/262.99	   mark(U92(x0))
744.20/262.99	   mark(0)
744.20/262.99	   U101(mark(x0), x1, x2)
744.20/262.99	   U101(x0, mark(x1), x2)
744.20/262.99	   U101(x0, x1, mark(x2))
744.20/262.99	   U101(active(x0), x1, x2)
744.20/262.99	   U101(x0, active(x1), x2)
744.20/262.99	   U101(x0, x1, active(x2))
744.20/262.99	   U102(mark(x0), x1, x2)
744.20/262.99	   U102(x0, mark(x1), x2)
744.20/262.99	   U102(x0, x1, mark(x2))
744.20/262.99	   U102(active(x0), x1, x2)
744.20/262.99	   U102(x0, active(x1), x2)
744.20/262.99	   U102(x0, x1, active(x2))
744.20/262.99	   isNatKind(mark(x0))
744.20/262.99	   isNatKind(active(x0))
744.20/262.99	   U103(mark(x0), x1, x2)
744.20/262.99	   U103(x0, mark(x1), x2)
744.20/262.99	   U103(x0, x1, mark(x2))
744.20/262.99	   U103(active(x0), x1, x2)
744.20/262.99	   U103(x0, active(x1), x2)
744.20/262.99	   U103(x0, x1, active(x2))
744.20/262.99	   isNat(mark(x0))
744.20/262.99	   isNat(active(x0))
744.20/262.99	   U104(mark(x0), x1, x2)
744.20/262.99	   U104(x0, mark(x1), x2)
744.20/262.99	   U104(x0, x1, mark(x2))
744.20/262.99	   U104(active(x0), x1, x2)
744.20/262.99	   U104(x0, active(x1), x2)
744.20/262.99	   U104(x0, x1, active(x2))
744.20/262.99	   plus(mark(x0), x1)
744.20/262.99	   plus(x0, mark(x1))
744.20/262.99	   plus(active(x0), x1)
744.20/262.99	   plus(x0, active(x1))
744.20/262.99	   x(mark(x0), x1)
744.20/262.99	   x(x0, mark(x1))
744.20/262.99	   x(active(x0), x1)
744.20/262.99	   x(x0, active(x1))
744.20/262.99	   U11(mark(x0), x1, x2)
744.20/262.99	   U11(x0, mark(x1), x2)
744.20/262.99	   U11(x0, x1, mark(x2))
744.20/262.99	   U11(active(x0), x1, x2)
744.20/262.99	   U11(x0, active(x1), x2)
744.20/262.99	   U11(x0, x1, active(x2))
744.20/262.99	   U12(mark(x0), x1, x2)
744.20/262.99	   U12(x0, mark(x1), x2)
744.20/262.99	   U12(x0, x1, mark(x2))
744.20/262.99	   U12(active(x0), x1, x2)
744.20/262.99	   U12(x0, active(x1), x2)
744.20/262.99	   U12(x0, x1, active(x2))
744.20/262.99	   U13(mark(x0), x1, x2)
744.20/262.99	   U13(x0, mark(x1), x2)
744.20/262.99	   U13(x0, x1, mark(x2))
744.20/262.99	   U13(active(x0), x1, x2)
744.20/262.99	   U13(x0, active(x1), x2)
744.20/262.99	   U13(x0, x1, active(x2))
744.20/262.99	   U14(mark(x0), x1, x2)
744.20/262.99	   U14(x0, mark(x1), x2)
744.20/262.99	   U14(x0, x1, mark(x2))
744.20/262.99	   U14(active(x0), x1, x2)
744.20/262.99	   U14(x0, active(x1), x2)
744.20/262.99	   U14(x0, x1, active(x2))
744.20/262.99	   U15(mark(x0), x1)
744.20/262.99	   U15(x0, mark(x1))
744.20/262.99	   U15(active(x0), x1)
744.20/262.99	   U15(x0, active(x1))
744.20/262.99	   U16(mark(x0))
744.20/262.99	   U16(active(x0))
744.20/262.99	   U21(mark(x0), x1)
744.20/262.99	   U21(x0, mark(x1))
744.20/262.99	   U21(active(x0), x1)
744.20/262.99	   U21(x0, active(x1))
744.20/262.99	   U22(mark(x0), x1)
744.20/262.99	   U22(x0, mark(x1))
744.20/262.99	   U22(active(x0), x1)
744.20/262.99	   U22(x0, active(x1))
744.20/262.99	   U23(mark(x0))
744.20/262.99	   U23(active(x0))
744.20/262.99	   U31(mark(x0), x1, x2)
744.20/262.99	   U31(x0, mark(x1), x2)
744.20/262.99	   U31(x0, x1, mark(x2))
744.20/262.99	   U31(active(x0), x1, x2)
744.20/262.99	   U31(x0, active(x1), x2)
744.20/262.99	   U31(x0, x1, active(x2))
744.20/262.99	   U32(mark(x0), x1, x2)
744.20/262.99	   U32(x0, mark(x1), x2)
744.20/262.99	   U32(x0, x1, mark(x2))
744.20/262.99	   U32(active(x0), x1, x2)
744.20/262.99	   U32(x0, active(x1), x2)
744.20/262.99	   U32(x0, x1, active(x2))
744.20/262.99	   U33(mark(x0), x1, x2)
744.20/262.99	   U33(x0, mark(x1), x2)
744.20/262.99	   U33(x0, x1, mark(x2))
744.20/262.99	   U33(active(x0), x1, x2)
744.20/262.99	   U33(x0, active(x1), x2)
744.20/262.99	   U33(x0, x1, active(x2))
744.20/262.99	   U34(mark(x0), x1, x2)
744.20/262.99	   U34(x0, mark(x1), x2)
744.20/262.99	   U34(x0, x1, mark(x2))
744.20/262.99	   U34(active(x0), x1, x2)
744.20/262.99	   U34(x0, active(x1), x2)
744.20/262.99	   U34(x0, x1, active(x2))
744.20/262.99	   U35(mark(x0), x1)
744.20/262.99	   U35(x0, mark(x1))
744.20/262.99	   U35(active(x0), x1)
744.20/262.99	   U35(x0, active(x1))
744.20/262.99	   U36(mark(x0))
744.20/262.99	   U36(active(x0))
744.20/262.99	   U41(mark(x0), x1)
744.20/262.99	   U41(x0, mark(x1))
744.20/262.99	   U41(active(x0), x1)
744.20/262.99	   U41(x0, active(x1))
744.20/262.99	   U42(mark(x0))
744.20/262.99	   U42(active(x0))
744.20/262.99	   U51(mark(x0))
744.20/262.99	   U51(active(x0))
744.20/262.99	   U61(mark(x0), x1)
744.20/262.99	   U61(x0, mark(x1))
744.20/262.99	   U61(active(x0), x1)
744.20/262.99	   U61(x0, active(x1))
744.20/262.99	   U62(mark(x0))
744.20/262.99	   U62(active(x0))
744.20/262.99	   U71(mark(x0), x1)
744.20/262.99	   U71(x0, mark(x1))
744.20/262.99	   U71(active(x0), x1)
744.20/262.99	   U71(x0, active(x1))
744.20/262.99	   U72(mark(x0), x1)
744.20/262.99	   U72(x0, mark(x1))
744.20/262.99	   U72(active(x0), x1)
744.20/262.99	   U72(x0, active(x1))
744.20/262.99	   U81(mark(x0), x1, x2)
744.20/262.99	   U81(x0, mark(x1), x2)
744.20/262.99	   U81(x0, x1, mark(x2))
744.20/262.99	   U81(active(x0), x1, x2)
744.20/262.99	   U81(x0, active(x1), x2)
744.20/262.99	   U81(x0, x1, active(x2))
744.20/262.99	   U82(mark(x0), x1, x2)
744.20/262.99	   U82(x0, mark(x1), x2)
744.20/262.99	   U82(x0, x1, mark(x2))
744.20/262.99	   U82(active(x0), x1, x2)
744.20/262.99	   U82(x0, active(x1), x2)
744.20/262.99	   U82(x0, x1, active(x2))
744.20/262.99	   U83(mark(x0), x1, x2)
744.20/262.99	   U83(x0, mark(x1), x2)
744.20/262.99	   U83(x0, x1, mark(x2))
744.20/262.99	   U83(active(x0), x1, x2)
744.20/262.99	   U83(x0, active(x1), x2)
744.20/262.99	   U83(x0, x1, active(x2))
744.20/262.99	   U84(mark(x0), x1, x2)
744.20/262.99	   U84(x0, mark(x1), x2)
744.20/262.99	   U84(x0, x1, mark(x2))
744.20/262.99	   U84(active(x0), x1, x2)
744.20/262.99	   U84(x0, active(x1), x2)
744.20/262.99	   U84(x0, x1, active(x2))
744.20/262.99	   s(mark(x0))
744.20/262.99	   s(active(x0))
744.20/262.99	   U91(mark(x0), x1)
744.20/262.99	   U91(x0, mark(x1))
744.20/262.99	   U91(active(x0), x1)
744.20/262.99	   U91(x0, active(x1))
744.20/262.99	   U92(mark(x0))
744.20/262.99	   U92(active(x0))
744.20/262.99	
744.20/262.99	We have to consider all minimal (P,Q,R)-chains.
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(277) DependencyGraphProof (EQUIVALENT)
744.20/262.99	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
744.20/262.99	----------------------------------------
744.20/262.99	
744.20/262.99	(278)
744.20/262.99	Obligation:
744.20/262.99	Q DP problem:
744.20/262.99	The TRS P consists of the following rules:
744.20/262.99	
744.20/262.99	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/262.99	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/262.99	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/262.99	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/262.99	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/262.99	   MARK(U16(X)) -> MARK(X)
744.20/262.99	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/262.99	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/262.99	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/262.99	   MARK(U23(X)) -> MARK(X)
744.20/262.99	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/262.99	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/262.99	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/262.99	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/262.99	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/262.99	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/262.99	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/262.99	   MARK(U36(X)) -> MARK(X)
744.20/262.99	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/262.99	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/262.99	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/262.99	   MARK(U42(X)) -> MARK(X)
744.20/262.99	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/262.99	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/262.99	   MARK(U62(X)) -> MARK(X)
744.20/262.99	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/262.99	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/262.99	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/262.99	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/262.99	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U51(X)) -> MARK(X)
744.20/262.99	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/262.99	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/262.99	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/262.99	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/262.99	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/262.99	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/262.99	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/262.99	
744.20/262.99	The TRS R consists of the following rules:
744.20/262.99	
744.20/262.99	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/262.99	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/262.99	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/262.99	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/262.99	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/262.99	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/262.99	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/262.99	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/262.99	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/262.99	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/262.99	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/262.99	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/262.99	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/262.99	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/262.99	   mark(U16(X)) -> active(U16(mark(X)))
744.20/262.99	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/262.99	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/262.99	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/262.99	   mark(U23(X)) -> active(U23(mark(X)))
744.20/262.99	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/262.99	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/262.99	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/262.99	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/262.99	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/262.99	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/262.99	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/262.99	   mark(U36(X)) -> active(U36(mark(X)))
744.20/262.99	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/262.99	   mark(U42(X)) -> active(U42(mark(X)))
744.20/262.99	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/262.99	   mark(U62(X)) -> active(U62(mark(X)))
744.20/262.99	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/262.99	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/262.99	   active(U72(tt, N)) -> mark(N)
744.20/262.99	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/262.99	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/262.99	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/262.99	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/262.99	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/262.99	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/262.99	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/262.99	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/262.99	   mark(s(X)) -> active(s(mark(X)))
744.20/262.99	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/262.99	   mark(U92(X)) -> active(U92(mark(X)))
744.20/262.99	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/262.99	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/262.99	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/262.99	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/262.99	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/262.99	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/262.99	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/262.99	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/262.99	   mark(U51(X)) -> active(U51(mark(X)))
744.20/262.99	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/262.99	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/262.99	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/262.99	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/262.99	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/262.99	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/262.99	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/262.99	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/262.99	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/262.99	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/262.99	   mark(isNat(X)) -> active(isNat(X))
744.20/262.99	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/262.99	   mark(tt) -> active(tt)
744.20/262.99	   mark(0) -> active(0)
744.20/262.99	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/262.99	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(active(X1), X2) -> U61(X1, X2)
744.20/262.99	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/262.99	   active(U16(tt)) -> mark(tt)
744.20/262.99	   active(U23(tt)) -> mark(tt)
744.20/262.99	   active(U36(tt)) -> mark(tt)
744.20/262.99	   active(U42(tt)) -> mark(tt)
744.20/262.99	   active(U51(tt)) -> mark(tt)
744.20/262.99	   active(U62(tt)) -> mark(tt)
744.20/262.99	   active(U92(tt)) -> mark(0)
744.20/262.99	   active(isNat(0)) -> mark(tt)
744.20/262.99	   active(isNatKind(0)) -> mark(tt)
744.20/262.99	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/262.99	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/262.99	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/262.99	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/262.99	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/262.99	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/262.99	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/262.99	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/262.99	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(active(X1), X2) -> plus(X1, X2)
744.20/262.99	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/262.99	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/262.99	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/262.99	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/262.99	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/262.99	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/262.99	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/262.99	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/262.99	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(active(X1), X2) -> U15(X1, X2)
744.20/262.99	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/262.99	   U16(active(X)) -> U16(X)
744.20/262.99	   U16(mark(X)) -> U16(X)
744.20/262.99	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/262.99	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(active(X1), X2) -> U22(X1, X2)
744.20/262.99	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/262.99	   U23(active(X)) -> U23(X)
744.20/262.99	   U23(mark(X)) -> U23(X)
744.20/262.99	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/262.99	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/262.99	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/262.99	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/262.99	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/262.99	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/262.99	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/262.99	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(active(X1), X2) -> U35(X1, X2)
744.20/262.99	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/262.99	   U36(active(X)) -> U36(X)
744.20/262.99	   U36(mark(X)) -> U36(X)
744.20/262.99	   U42(active(X)) -> U42(X)
744.20/262.99	   U42(mark(X)) -> U42(X)
744.20/262.99	   U62(active(X)) -> U62(X)
744.20/262.99	   U62(mark(X)) -> U62(X)
744.20/262.99	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/262.99	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(active(X1), X2) -> U72(X1, X2)
744.20/262.99	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/262.99	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/262.99	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/262.99	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/262.99	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/262.99	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/262.99	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/262.99	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/262.99	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/262.99	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/262.99	   s(active(X)) -> s(X)
744.20/262.99	   s(mark(X)) -> s(X)
744.20/262.99	   U92(active(X)) -> U92(X)
744.20/262.99	   U92(mark(X)) -> U92(X)
744.20/262.99	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/262.99	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/262.99	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/262.99	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(active(X1), X2) -> U21(X1, X2)
744.20/262.99	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/262.99	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/262.99	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/262.99	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/262.99	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(active(X1), X2) -> U41(X1, X2)
744.20/262.99	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U51(active(X)) -> U51(X)
744.20/263.00	   U51(mark(X)) -> U51(X)
744.20/263.00	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.00	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.00	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.00	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.00	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.00	   x(active(X1), X2) -> x(X1, X2)
744.20/263.00	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.00	
744.20/263.00	The set Q consists of the following terms:
744.20/263.00	
744.20/263.00	   active(U101(tt, x0, x1))
744.20/263.00	   active(U102(tt, x0, x1))
744.20/263.00	   active(U103(tt, x0, x1))
744.20/263.00	   active(U104(tt, x0, x1))
744.20/263.00	   active(U11(tt, x0, x1))
744.20/263.00	   active(U12(tt, x0, x1))
744.20/263.00	   active(U13(tt, x0, x1))
744.20/263.00	   active(U14(tt, x0, x1))
744.20/263.00	   active(U15(tt, x0))
744.20/263.00	   active(U16(tt))
744.20/263.00	   active(U21(tt, x0))
744.20/263.00	   active(U22(tt, x0))
744.20/263.00	   active(U23(tt))
744.20/263.00	   active(U31(tt, x0, x1))
744.20/263.00	   active(U32(tt, x0, x1))
744.20/263.00	   active(U33(tt, x0, x1))
744.20/263.00	   active(U34(tt, x0, x1))
744.20/263.00	   active(U35(tt, x0))
744.20/263.00	   active(U36(tt))
744.20/263.00	   active(U41(tt, x0))
744.20/263.00	   active(U42(tt))
744.20/263.00	   active(U51(tt))
744.20/263.00	   active(U61(tt, x0))
744.20/263.00	   active(U62(tt))
744.20/263.00	   active(U71(tt, x0))
744.20/263.00	   active(U72(tt, x0))
744.20/263.00	   active(U81(tt, x0, x1))
744.20/263.00	   active(U82(tt, x0, x1))
744.20/263.00	   active(U83(tt, x0, x1))
744.20/263.00	   active(U84(tt, x0, x1))
744.20/263.00	   active(U91(tt, x0))
744.20/263.00	   active(U92(tt))
744.20/263.00	   active(isNat(0))
744.20/263.00	   active(isNat(plus(x0, x1)))
744.20/263.00	   active(isNat(s(x0)))
744.20/263.00	   active(isNat(x(x0, x1)))
744.20/263.00	   active(isNatKind(0))
744.20/263.00	   active(isNatKind(plus(x0, x1)))
744.20/263.00	   active(isNatKind(s(x0)))
744.20/263.00	   active(isNatKind(x(x0, x1)))
744.20/263.00	   active(plus(x0, 0))
744.20/263.00	   active(plus(x0, s(x1)))
744.20/263.00	   active(x(x0, 0))
744.20/263.00	   active(x(x0, s(x1)))
744.20/263.00	   mark(U101(x0, x1, x2))
744.20/263.00	   mark(tt)
744.20/263.00	   mark(U102(x0, x1, x2))
744.20/263.00	   mark(isNatKind(x0))
744.20/263.00	   mark(U103(x0, x1, x2))
744.20/263.00	   mark(isNat(x0))
744.20/263.00	   mark(U104(x0, x1, x2))
744.20/263.00	   mark(plus(x0, x1))
744.20/263.00	   mark(x(x0, x1))
744.20/263.00	   mark(U11(x0, x1, x2))
744.20/263.00	   mark(U12(x0, x1, x2))
744.20/263.00	   mark(U13(x0, x1, x2))
744.20/263.00	   mark(U14(x0, x1, x2))
744.20/263.00	   mark(U15(x0, x1))
744.20/263.00	   mark(U16(x0))
744.20/263.00	   mark(U21(x0, x1))
744.20/263.00	   mark(U22(x0, x1))
744.20/263.00	   mark(U23(x0))
744.20/263.00	   mark(U31(x0, x1, x2))
744.20/263.00	   mark(U32(x0, x1, x2))
744.20/263.00	   mark(U33(x0, x1, x2))
744.20/263.00	   mark(U34(x0, x1, x2))
744.20/263.00	   mark(U35(x0, x1))
744.20/263.00	   mark(U36(x0))
744.20/263.00	   mark(U41(x0, x1))
744.20/263.00	   mark(U42(x0))
744.20/263.00	   mark(U51(x0))
744.20/263.00	   mark(U61(x0, x1))
744.20/263.00	   mark(U62(x0))
744.20/263.00	   mark(U71(x0, x1))
744.20/263.00	   mark(U72(x0, x1))
744.20/263.00	   mark(U81(x0, x1, x2))
744.20/263.00	   mark(U82(x0, x1, x2))
744.20/263.00	   mark(U83(x0, x1, x2))
744.20/263.00	   mark(U84(x0, x1, x2))
744.20/263.00	   mark(s(x0))
744.20/263.00	   mark(U91(x0, x1))
744.20/263.00	   mark(U92(x0))
744.20/263.00	   mark(0)
744.20/263.00	   U101(mark(x0), x1, x2)
744.20/263.00	   U101(x0, mark(x1), x2)
744.20/263.00	   U101(x0, x1, mark(x2))
744.20/263.00	   U101(active(x0), x1, x2)
744.20/263.00	   U101(x0, active(x1), x2)
744.20/263.00	   U101(x0, x1, active(x2))
744.20/263.00	   U102(mark(x0), x1, x2)
744.20/263.00	   U102(x0, mark(x1), x2)
744.20/263.00	   U102(x0, x1, mark(x2))
744.20/263.00	   U102(active(x0), x1, x2)
744.20/263.00	   U102(x0, active(x1), x2)
744.20/263.00	   U102(x0, x1, active(x2))
744.20/263.00	   isNatKind(mark(x0))
744.20/263.00	   isNatKind(active(x0))
744.20/263.00	   U103(mark(x0), x1, x2)
744.20/263.00	   U103(x0, mark(x1), x2)
744.20/263.00	   U103(x0, x1, mark(x2))
744.20/263.00	   U103(active(x0), x1, x2)
744.20/263.00	   U103(x0, active(x1), x2)
744.20/263.00	   U103(x0, x1, active(x2))
744.20/263.00	   isNat(mark(x0))
744.20/263.00	   isNat(active(x0))
744.20/263.00	   U104(mark(x0), x1, x2)
744.20/263.00	   U104(x0, mark(x1), x2)
744.20/263.00	   U104(x0, x1, mark(x2))
744.20/263.00	   U104(active(x0), x1, x2)
744.20/263.00	   U104(x0, active(x1), x2)
744.20/263.00	   U104(x0, x1, active(x2))
744.20/263.00	   plus(mark(x0), x1)
744.20/263.00	   plus(x0, mark(x1))
744.20/263.00	   plus(active(x0), x1)
744.20/263.00	   plus(x0, active(x1))
744.20/263.00	   x(mark(x0), x1)
744.20/263.00	   x(x0, mark(x1))
744.20/263.00	   x(active(x0), x1)
744.20/263.00	   x(x0, active(x1))
744.20/263.00	   U11(mark(x0), x1, x2)
744.20/263.00	   U11(x0, mark(x1), x2)
744.20/263.00	   U11(x0, x1, mark(x2))
744.20/263.00	   U11(active(x0), x1, x2)
744.20/263.00	   U11(x0, active(x1), x2)
744.20/263.00	   U11(x0, x1, active(x2))
744.20/263.00	   U12(mark(x0), x1, x2)
744.20/263.00	   U12(x0, mark(x1), x2)
744.20/263.00	   U12(x0, x1, mark(x2))
744.20/263.00	   U12(active(x0), x1, x2)
744.20/263.00	   U12(x0, active(x1), x2)
744.20/263.00	   U12(x0, x1, active(x2))
744.20/263.00	   U13(mark(x0), x1, x2)
744.20/263.00	   U13(x0, mark(x1), x2)
744.20/263.00	   U13(x0, x1, mark(x2))
744.20/263.00	   U13(active(x0), x1, x2)
744.20/263.00	   U13(x0, active(x1), x2)
744.20/263.00	   U13(x0, x1, active(x2))
744.20/263.00	   U14(mark(x0), x1, x2)
744.20/263.00	   U14(x0, mark(x1), x2)
744.20/263.00	   U14(x0, x1, mark(x2))
744.20/263.00	   U14(active(x0), x1, x2)
744.20/263.00	   U14(x0, active(x1), x2)
744.20/263.00	   U14(x0, x1, active(x2))
744.20/263.00	   U15(mark(x0), x1)
744.20/263.00	   U15(x0, mark(x1))
744.20/263.00	   U15(active(x0), x1)
744.20/263.00	   U15(x0, active(x1))
744.20/263.00	   U16(mark(x0))
744.20/263.00	   U16(active(x0))
744.20/263.00	   U21(mark(x0), x1)
744.20/263.00	   U21(x0, mark(x1))
744.20/263.00	   U21(active(x0), x1)
744.20/263.00	   U21(x0, active(x1))
744.20/263.00	   U22(mark(x0), x1)
744.20/263.00	   U22(x0, mark(x1))
744.20/263.00	   U22(active(x0), x1)
744.20/263.00	   U22(x0, active(x1))
744.20/263.00	   U23(mark(x0))
744.20/263.00	   U23(active(x0))
744.20/263.00	   U31(mark(x0), x1, x2)
744.20/263.00	   U31(x0, mark(x1), x2)
744.20/263.00	   U31(x0, x1, mark(x2))
744.20/263.00	   U31(active(x0), x1, x2)
744.20/263.00	   U31(x0, active(x1), x2)
744.20/263.00	   U31(x0, x1, active(x2))
744.20/263.00	   U32(mark(x0), x1, x2)
744.20/263.00	   U32(x0, mark(x1), x2)
744.20/263.00	   U32(x0, x1, mark(x2))
744.20/263.00	   U32(active(x0), x1, x2)
744.20/263.00	   U32(x0, active(x1), x2)
744.20/263.00	   U32(x0, x1, active(x2))
744.20/263.00	   U33(mark(x0), x1, x2)
744.20/263.00	   U33(x0, mark(x1), x2)
744.20/263.00	   U33(x0, x1, mark(x2))
744.20/263.00	   U33(active(x0), x1, x2)
744.20/263.00	   U33(x0, active(x1), x2)
744.20/263.00	   U33(x0, x1, active(x2))
744.20/263.00	   U34(mark(x0), x1, x2)
744.20/263.00	   U34(x0, mark(x1), x2)
744.20/263.00	   U34(x0, x1, mark(x2))
744.20/263.00	   U34(active(x0), x1, x2)
744.20/263.00	   U34(x0, active(x1), x2)
744.20/263.00	   U34(x0, x1, active(x2))
744.20/263.00	   U35(mark(x0), x1)
744.20/263.00	   U35(x0, mark(x1))
744.20/263.00	   U35(active(x0), x1)
744.20/263.00	   U35(x0, active(x1))
744.20/263.00	   U36(mark(x0))
744.20/263.00	   U36(active(x0))
744.20/263.00	   U41(mark(x0), x1)
744.20/263.00	   U41(x0, mark(x1))
744.20/263.00	   U41(active(x0), x1)
744.20/263.00	   U41(x0, active(x1))
744.20/263.00	   U42(mark(x0))
744.20/263.00	   U42(active(x0))
744.20/263.00	   U51(mark(x0))
744.20/263.00	   U51(active(x0))
744.20/263.00	   U61(mark(x0), x1)
744.20/263.00	   U61(x0, mark(x1))
744.20/263.00	   U61(active(x0), x1)
744.20/263.00	   U61(x0, active(x1))
744.20/263.00	   U62(mark(x0))
744.20/263.00	   U62(active(x0))
744.20/263.00	   U71(mark(x0), x1)
744.20/263.00	   U71(x0, mark(x1))
744.20/263.00	   U71(active(x0), x1)
744.20/263.00	   U71(x0, active(x1))
744.20/263.00	   U72(mark(x0), x1)
744.20/263.00	   U72(x0, mark(x1))
744.20/263.00	   U72(active(x0), x1)
744.20/263.00	   U72(x0, active(x1))
744.20/263.00	   U81(mark(x0), x1, x2)
744.20/263.00	   U81(x0, mark(x1), x2)
744.20/263.00	   U81(x0, x1, mark(x2))
744.20/263.00	   U81(active(x0), x1, x2)
744.20/263.00	   U81(x0, active(x1), x2)
744.20/263.00	   U81(x0, x1, active(x2))
744.20/263.00	   U82(mark(x0), x1, x2)
744.20/263.00	   U82(x0, mark(x1), x2)
744.20/263.00	   U82(x0, x1, mark(x2))
744.20/263.00	   U82(active(x0), x1, x2)
744.20/263.00	   U82(x0, active(x1), x2)
744.20/263.00	   U82(x0, x1, active(x2))
744.20/263.00	   U83(mark(x0), x1, x2)
744.20/263.00	   U83(x0, mark(x1), x2)
744.20/263.00	   U83(x0, x1, mark(x2))
744.20/263.00	   U83(active(x0), x1, x2)
744.20/263.00	   U83(x0, active(x1), x2)
744.20/263.00	   U83(x0, x1, active(x2))
744.20/263.00	   U84(mark(x0), x1, x2)
744.20/263.00	   U84(x0, mark(x1), x2)
744.20/263.00	   U84(x0, x1, mark(x2))
744.20/263.00	   U84(active(x0), x1, x2)
744.20/263.00	   U84(x0, active(x1), x2)
744.20/263.00	   U84(x0, x1, active(x2))
744.20/263.00	   s(mark(x0))
744.20/263.00	   s(active(x0))
744.20/263.00	   U91(mark(x0), x1)
744.20/263.00	   U91(x0, mark(x1))
744.20/263.00	   U91(active(x0), x1)
744.20/263.00	   U91(x0, active(x1))
744.20/263.00	   U92(mark(x0))
744.20/263.00	   U92(active(x0))
744.20/263.00	
744.20/263.00	We have to consider all minimal (P,Q,R)-chains.
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(279) QDPOrderProof (EQUIVALENT)
744.20/263.00	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.00	
744.20/263.00	
744.20/263.00	The following pairs can be oriented strictly and are deleted.
744.20/263.00	
744.20/263.00	   MARK(U83(X1, X2, X3)) -> ACTIVE(U83(mark(X1), X2, X3))
744.20/263.00	The remaining pairs can at least be oriented weakly.
744.20/263.00	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.00	
744.20/263.00	POL( ACTIVE_1(x_1) ) = x_1
744.20/263.00	POL( U101_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U102_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U103_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U11_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U12_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U13_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U14_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U15_2(x_1, x_2) ) = 2
744.20/263.00	POL( U21_2(x_1, x_2) ) = 2
744.20/263.00	POL( U22_2(x_1, x_2) ) = 2
744.20/263.00	POL( U31_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U32_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U33_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U34_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U35_2(x_1, x_2) ) = 2
744.20/263.00	POL( U41_2(x_1, x_2) ) = 2
744.20/263.00	POL( U61_2(x_1, x_2) ) = 2
744.20/263.00	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U82_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U83_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.00	POL( mark_1(x_1) ) = 2
744.20/263.00	POL( active_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.00	POL( tt ) = 0
744.20/263.00	POL( isNatKind_1(x_1) ) = 2
744.20/263.00	POL( isNat_1(x_1) ) = 2
744.20/263.00	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.20/263.00	POL( plus_2(x_1, x_2) ) = max{0, x_2 - 1}
744.20/263.00	POL( x_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.20/263.00	POL( U16_1(x_1) ) = max{0, -2}
744.20/263.00	POL( U23_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U36_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U42_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U62_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.00	POL( U71_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.20/263.00	POL( U72_2(x_1, x_2) ) = 2
744.20/263.00	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_3 - 1}
744.20/263.00	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.20/263.00	POL( U92_1(x_1) ) = x_1 + 1
744.20/263.00	POL( U51_1(x_1) ) = 2
744.20/263.00	POL( 0 ) = 0
744.20/263.00	POL( MARK_1(x_1) ) = 2
744.20/263.00	
744.20/263.00	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.00	
744.20/263.00	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.00	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.00	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.00	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.00	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.00	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.00	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.00	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.00	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.00	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.00	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.00	
744.20/263.00	
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(280)
744.20/263.00	Obligation:
744.20/263.00	Q DP problem:
744.20/263.00	The TRS P consists of the following rules:
744.20/263.00	
744.20/263.00	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.00	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/263.00	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.00	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.00	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.00	   MARK(U16(X)) -> MARK(X)
744.20/263.00	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.00	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.00	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.00	   MARK(U23(X)) -> MARK(X)
744.20/263.00	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.00	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.00	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.00	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.00	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.00	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.00	   MARK(U36(X)) -> MARK(X)
744.20/263.00	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.00	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.00	   MARK(U42(X)) -> MARK(X)
744.20/263.00	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.00	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.00	   MARK(U62(X)) -> MARK(X)
744.20/263.00	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/263.00	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U82(tt, M, N)) -> MARK(U83(isNat(N), M, N))
744.20/263.00	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U51(X)) -> MARK(X)
744.20/263.00	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.00	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.00	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.00	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.00	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.00	
744.20/263.00	The TRS R consists of the following rules:
744.20/263.00	
744.20/263.00	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.00	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.00	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.00	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.00	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.00	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.00	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.00	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.00	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.00	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.00	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.00	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.00	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.00	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.00	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.00	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.00	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.00	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.00	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.00	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.00	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.00	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.00	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.00	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.00	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.00	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.00	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.00	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.00	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.00	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.00	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.00	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.00	   active(U72(tt, N)) -> mark(N)
744.20/263.00	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.00	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.00	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.00	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.00	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.00	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.00	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.00	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.00	   mark(s(X)) -> active(s(mark(X)))
744.20/263.00	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.00	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.00	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.00	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.00	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.00	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.00	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.00	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.00	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.00	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.00	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.00	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.00	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.00	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.00	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.00	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.00	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.00	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.00	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.00	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.00	   mark(isNat(X)) -> active(isNat(X))
744.20/263.00	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.00	   mark(tt) -> active(tt)
744.20/263.00	   mark(0) -> active(0)
744.20/263.00	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.00	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.00	   active(U16(tt)) -> mark(tt)
744.20/263.00	   active(U23(tt)) -> mark(tt)
744.20/263.00	   active(U36(tt)) -> mark(tt)
744.20/263.00	   active(U42(tt)) -> mark(tt)
744.20/263.00	   active(U51(tt)) -> mark(tt)
744.20/263.00	   active(U62(tt)) -> mark(tt)
744.20/263.00	   active(U92(tt)) -> mark(0)
744.20/263.00	   active(isNat(0)) -> mark(tt)
744.20/263.00	   active(isNatKind(0)) -> mark(tt)
744.20/263.00	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.00	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.00	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.00	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.00	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.00	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.00	   U16(active(X)) -> U16(X)
744.20/263.00	   U16(mark(X)) -> U16(X)
744.20/263.00	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.00	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.00	   U23(active(X)) -> U23(X)
744.20/263.00	   U23(mark(X)) -> U23(X)
744.20/263.00	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.00	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.00	   U36(active(X)) -> U36(X)
744.20/263.00	   U36(mark(X)) -> U36(X)
744.20/263.00	   U42(active(X)) -> U42(X)
744.20/263.00	   U42(mark(X)) -> U42(X)
744.20/263.00	   U62(active(X)) -> U62(X)
744.20/263.00	   U62(mark(X)) -> U62(X)
744.20/263.00	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.00	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.00	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.00	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.00	   s(active(X)) -> s(X)
744.20/263.00	   s(mark(X)) -> s(X)
744.20/263.00	   U92(active(X)) -> U92(X)
744.20/263.00	   U92(mark(X)) -> U92(X)
744.20/263.00	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.00	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.00	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.00	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U51(active(X)) -> U51(X)
744.20/263.00	   U51(mark(X)) -> U51(X)
744.20/263.00	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.00	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.00	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.00	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.00	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.00	   x(active(X1), X2) -> x(X1, X2)
744.20/263.00	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.00	
744.20/263.00	The set Q consists of the following terms:
744.20/263.00	
744.20/263.00	   active(U101(tt, x0, x1))
744.20/263.00	   active(U102(tt, x0, x1))
744.20/263.00	   active(U103(tt, x0, x1))
744.20/263.00	   active(U104(tt, x0, x1))
744.20/263.00	   active(U11(tt, x0, x1))
744.20/263.00	   active(U12(tt, x0, x1))
744.20/263.00	   active(U13(tt, x0, x1))
744.20/263.00	   active(U14(tt, x0, x1))
744.20/263.00	   active(U15(tt, x0))
744.20/263.00	   active(U16(tt))
744.20/263.00	   active(U21(tt, x0))
744.20/263.00	   active(U22(tt, x0))
744.20/263.00	   active(U23(tt))
744.20/263.00	   active(U31(tt, x0, x1))
744.20/263.00	   active(U32(tt, x0, x1))
744.20/263.00	   active(U33(tt, x0, x1))
744.20/263.00	   active(U34(tt, x0, x1))
744.20/263.00	   active(U35(tt, x0))
744.20/263.00	   active(U36(tt))
744.20/263.00	   active(U41(tt, x0))
744.20/263.00	   active(U42(tt))
744.20/263.00	   active(U51(tt))
744.20/263.00	   active(U61(tt, x0))
744.20/263.00	   active(U62(tt))
744.20/263.00	   active(U71(tt, x0))
744.20/263.00	   active(U72(tt, x0))
744.20/263.00	   active(U81(tt, x0, x1))
744.20/263.00	   active(U82(tt, x0, x1))
744.20/263.00	   active(U83(tt, x0, x1))
744.20/263.00	   active(U84(tt, x0, x1))
744.20/263.00	   active(U91(tt, x0))
744.20/263.00	   active(U92(tt))
744.20/263.00	   active(isNat(0))
744.20/263.00	   active(isNat(plus(x0, x1)))
744.20/263.00	   active(isNat(s(x0)))
744.20/263.00	   active(isNat(x(x0, x1)))
744.20/263.00	   active(isNatKind(0))
744.20/263.00	   active(isNatKind(plus(x0, x1)))
744.20/263.00	   active(isNatKind(s(x0)))
744.20/263.00	   active(isNatKind(x(x0, x1)))
744.20/263.00	   active(plus(x0, 0))
744.20/263.00	   active(plus(x0, s(x1)))
744.20/263.00	   active(x(x0, 0))
744.20/263.00	   active(x(x0, s(x1)))
744.20/263.00	   mark(U101(x0, x1, x2))
744.20/263.00	   mark(tt)
744.20/263.00	   mark(U102(x0, x1, x2))
744.20/263.00	   mark(isNatKind(x0))
744.20/263.00	   mark(U103(x0, x1, x2))
744.20/263.00	   mark(isNat(x0))
744.20/263.00	   mark(U104(x0, x1, x2))
744.20/263.00	   mark(plus(x0, x1))
744.20/263.00	   mark(x(x0, x1))
744.20/263.00	   mark(U11(x0, x1, x2))
744.20/263.00	   mark(U12(x0, x1, x2))
744.20/263.00	   mark(U13(x0, x1, x2))
744.20/263.00	   mark(U14(x0, x1, x2))
744.20/263.00	   mark(U15(x0, x1))
744.20/263.00	   mark(U16(x0))
744.20/263.00	   mark(U21(x0, x1))
744.20/263.00	   mark(U22(x0, x1))
744.20/263.00	   mark(U23(x0))
744.20/263.00	   mark(U31(x0, x1, x2))
744.20/263.00	   mark(U32(x0, x1, x2))
744.20/263.00	   mark(U33(x0, x1, x2))
744.20/263.00	   mark(U34(x0, x1, x2))
744.20/263.00	   mark(U35(x0, x1))
744.20/263.00	   mark(U36(x0))
744.20/263.00	   mark(U41(x0, x1))
744.20/263.00	   mark(U42(x0))
744.20/263.00	   mark(U51(x0))
744.20/263.00	   mark(U61(x0, x1))
744.20/263.00	   mark(U62(x0))
744.20/263.00	   mark(U71(x0, x1))
744.20/263.00	   mark(U72(x0, x1))
744.20/263.00	   mark(U81(x0, x1, x2))
744.20/263.00	   mark(U82(x0, x1, x2))
744.20/263.00	   mark(U83(x0, x1, x2))
744.20/263.00	   mark(U84(x0, x1, x2))
744.20/263.00	   mark(s(x0))
744.20/263.00	   mark(U91(x0, x1))
744.20/263.00	   mark(U92(x0))
744.20/263.00	   mark(0)
744.20/263.00	   U101(mark(x0), x1, x2)
744.20/263.00	   U101(x0, mark(x1), x2)
744.20/263.00	   U101(x0, x1, mark(x2))
744.20/263.00	   U101(active(x0), x1, x2)
744.20/263.00	   U101(x0, active(x1), x2)
744.20/263.00	   U101(x0, x1, active(x2))
744.20/263.00	   U102(mark(x0), x1, x2)
744.20/263.00	   U102(x0, mark(x1), x2)
744.20/263.00	   U102(x0, x1, mark(x2))
744.20/263.00	   U102(active(x0), x1, x2)
744.20/263.00	   U102(x0, active(x1), x2)
744.20/263.00	   U102(x0, x1, active(x2))
744.20/263.00	   isNatKind(mark(x0))
744.20/263.00	   isNatKind(active(x0))
744.20/263.00	   U103(mark(x0), x1, x2)
744.20/263.00	   U103(x0, mark(x1), x2)
744.20/263.00	   U103(x0, x1, mark(x2))
744.20/263.00	   U103(active(x0), x1, x2)
744.20/263.00	   U103(x0, active(x1), x2)
744.20/263.00	   U103(x0, x1, active(x2))
744.20/263.00	   isNat(mark(x0))
744.20/263.00	   isNat(active(x0))
744.20/263.00	   U104(mark(x0), x1, x2)
744.20/263.00	   U104(x0, mark(x1), x2)
744.20/263.00	   U104(x0, x1, mark(x2))
744.20/263.00	   U104(active(x0), x1, x2)
744.20/263.00	   U104(x0, active(x1), x2)
744.20/263.00	   U104(x0, x1, active(x2))
744.20/263.00	   plus(mark(x0), x1)
744.20/263.00	   plus(x0, mark(x1))
744.20/263.00	   plus(active(x0), x1)
744.20/263.00	   plus(x0, active(x1))
744.20/263.00	   x(mark(x0), x1)
744.20/263.00	   x(x0, mark(x1))
744.20/263.00	   x(active(x0), x1)
744.20/263.00	   x(x0, active(x1))
744.20/263.00	   U11(mark(x0), x1, x2)
744.20/263.00	   U11(x0, mark(x1), x2)
744.20/263.00	   U11(x0, x1, mark(x2))
744.20/263.00	   U11(active(x0), x1, x2)
744.20/263.00	   U11(x0, active(x1), x2)
744.20/263.00	   U11(x0, x1, active(x2))
744.20/263.00	   U12(mark(x0), x1, x2)
744.20/263.00	   U12(x0, mark(x1), x2)
744.20/263.00	   U12(x0, x1, mark(x2))
744.20/263.00	   U12(active(x0), x1, x2)
744.20/263.00	   U12(x0, active(x1), x2)
744.20/263.00	   U12(x0, x1, active(x2))
744.20/263.00	   U13(mark(x0), x1, x2)
744.20/263.00	   U13(x0, mark(x1), x2)
744.20/263.00	   U13(x0, x1, mark(x2))
744.20/263.00	   U13(active(x0), x1, x2)
744.20/263.00	   U13(x0, active(x1), x2)
744.20/263.00	   U13(x0, x1, active(x2))
744.20/263.00	   U14(mark(x0), x1, x2)
744.20/263.00	   U14(x0, mark(x1), x2)
744.20/263.00	   U14(x0, x1, mark(x2))
744.20/263.00	   U14(active(x0), x1, x2)
744.20/263.00	   U14(x0, active(x1), x2)
744.20/263.00	   U14(x0, x1, active(x2))
744.20/263.00	   U15(mark(x0), x1)
744.20/263.00	   U15(x0, mark(x1))
744.20/263.00	   U15(active(x0), x1)
744.20/263.00	   U15(x0, active(x1))
744.20/263.00	   U16(mark(x0))
744.20/263.00	   U16(active(x0))
744.20/263.00	   U21(mark(x0), x1)
744.20/263.00	   U21(x0, mark(x1))
744.20/263.00	   U21(active(x0), x1)
744.20/263.00	   U21(x0, active(x1))
744.20/263.00	   U22(mark(x0), x1)
744.20/263.00	   U22(x0, mark(x1))
744.20/263.00	   U22(active(x0), x1)
744.20/263.00	   U22(x0, active(x1))
744.20/263.00	   U23(mark(x0))
744.20/263.00	   U23(active(x0))
744.20/263.00	   U31(mark(x0), x1, x2)
744.20/263.00	   U31(x0, mark(x1), x2)
744.20/263.00	   U31(x0, x1, mark(x2))
744.20/263.00	   U31(active(x0), x1, x2)
744.20/263.00	   U31(x0, active(x1), x2)
744.20/263.00	   U31(x0, x1, active(x2))
744.20/263.00	   U32(mark(x0), x1, x2)
744.20/263.00	   U32(x0, mark(x1), x2)
744.20/263.00	   U32(x0, x1, mark(x2))
744.20/263.00	   U32(active(x0), x1, x2)
744.20/263.00	   U32(x0, active(x1), x2)
744.20/263.00	   U32(x0, x1, active(x2))
744.20/263.00	   U33(mark(x0), x1, x2)
744.20/263.00	   U33(x0, mark(x1), x2)
744.20/263.00	   U33(x0, x1, mark(x2))
744.20/263.00	   U33(active(x0), x1, x2)
744.20/263.00	   U33(x0, active(x1), x2)
744.20/263.00	   U33(x0, x1, active(x2))
744.20/263.00	   U34(mark(x0), x1, x2)
744.20/263.00	   U34(x0, mark(x1), x2)
744.20/263.00	   U34(x0, x1, mark(x2))
744.20/263.00	   U34(active(x0), x1, x2)
744.20/263.00	   U34(x0, active(x1), x2)
744.20/263.00	   U34(x0, x1, active(x2))
744.20/263.00	   U35(mark(x0), x1)
744.20/263.00	   U35(x0, mark(x1))
744.20/263.00	   U35(active(x0), x1)
744.20/263.00	   U35(x0, active(x1))
744.20/263.00	   U36(mark(x0))
744.20/263.00	   U36(active(x0))
744.20/263.00	   U41(mark(x0), x1)
744.20/263.00	   U41(x0, mark(x1))
744.20/263.00	   U41(active(x0), x1)
744.20/263.00	   U41(x0, active(x1))
744.20/263.00	   U42(mark(x0))
744.20/263.00	   U42(active(x0))
744.20/263.00	   U51(mark(x0))
744.20/263.00	   U51(active(x0))
744.20/263.00	   U61(mark(x0), x1)
744.20/263.00	   U61(x0, mark(x1))
744.20/263.00	   U61(active(x0), x1)
744.20/263.00	   U61(x0, active(x1))
744.20/263.00	   U62(mark(x0))
744.20/263.00	   U62(active(x0))
744.20/263.00	   U71(mark(x0), x1)
744.20/263.00	   U71(x0, mark(x1))
744.20/263.00	   U71(active(x0), x1)
744.20/263.00	   U71(x0, active(x1))
744.20/263.00	   U72(mark(x0), x1)
744.20/263.00	   U72(x0, mark(x1))
744.20/263.00	   U72(active(x0), x1)
744.20/263.00	   U72(x0, active(x1))
744.20/263.00	   U81(mark(x0), x1, x2)
744.20/263.00	   U81(x0, mark(x1), x2)
744.20/263.00	   U81(x0, x1, mark(x2))
744.20/263.00	   U81(active(x0), x1, x2)
744.20/263.00	   U81(x0, active(x1), x2)
744.20/263.00	   U81(x0, x1, active(x2))
744.20/263.00	   U82(mark(x0), x1, x2)
744.20/263.00	   U82(x0, mark(x1), x2)
744.20/263.00	   U82(x0, x1, mark(x2))
744.20/263.00	   U82(active(x0), x1, x2)
744.20/263.00	   U82(x0, active(x1), x2)
744.20/263.00	   U82(x0, x1, active(x2))
744.20/263.00	   U83(mark(x0), x1, x2)
744.20/263.00	   U83(x0, mark(x1), x2)
744.20/263.00	   U83(x0, x1, mark(x2))
744.20/263.00	   U83(active(x0), x1, x2)
744.20/263.00	   U83(x0, active(x1), x2)
744.20/263.00	   U83(x0, x1, active(x2))
744.20/263.00	   U84(mark(x0), x1, x2)
744.20/263.00	   U84(x0, mark(x1), x2)
744.20/263.00	   U84(x0, x1, mark(x2))
744.20/263.00	   U84(active(x0), x1, x2)
744.20/263.00	   U84(x0, active(x1), x2)
744.20/263.00	   U84(x0, x1, active(x2))
744.20/263.00	   s(mark(x0))
744.20/263.00	   s(active(x0))
744.20/263.00	   U91(mark(x0), x1)
744.20/263.00	   U91(x0, mark(x1))
744.20/263.00	   U91(active(x0), x1)
744.20/263.00	   U91(x0, active(x1))
744.20/263.00	   U92(mark(x0))
744.20/263.00	   U92(active(x0))
744.20/263.00	
744.20/263.00	We have to consider all minimal (P,Q,R)-chains.
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(281) DependencyGraphProof (EQUIVALENT)
744.20/263.00	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(282)
744.20/263.00	Obligation:
744.20/263.00	Q DP problem:
744.20/263.00	The TRS P consists of the following rules:
744.20/263.00	
744.20/263.00	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.00	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/263.00	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.00	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.00	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.00	   MARK(U16(X)) -> MARK(X)
744.20/263.00	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.00	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.00	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.00	   MARK(U23(X)) -> MARK(X)
744.20/263.00	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.00	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.00	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.00	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.00	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.00	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.00	   MARK(U36(X)) -> MARK(X)
744.20/263.00	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.00	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.00	   MARK(U42(X)) -> MARK(X)
744.20/263.00	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.00	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.00	   MARK(U62(X)) -> MARK(X)
744.20/263.00	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/263.00	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/263.00	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U51(X)) -> MARK(X)
744.20/263.00	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.00	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.00	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.00	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.00	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.00	
744.20/263.00	The TRS R consists of the following rules:
744.20/263.00	
744.20/263.00	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.00	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.00	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.00	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.00	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.00	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.00	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.00	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.00	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.00	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.00	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.00	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.00	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.00	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.00	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.00	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.00	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.00	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.00	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.00	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.00	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.00	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.00	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.00	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.00	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.00	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.00	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.00	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.00	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.00	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.00	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.00	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.00	   active(U72(tt, N)) -> mark(N)
744.20/263.00	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.00	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.00	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.00	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.00	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.00	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.00	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.00	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.00	   mark(s(X)) -> active(s(mark(X)))
744.20/263.00	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.00	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.00	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.00	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.00	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.00	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.00	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.00	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.00	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.00	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.00	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.00	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.00	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.00	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.00	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.00	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.00	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.00	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.00	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.00	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.00	   mark(isNat(X)) -> active(isNat(X))
744.20/263.00	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.00	   mark(tt) -> active(tt)
744.20/263.00	   mark(0) -> active(0)
744.20/263.00	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.00	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.00	   active(U16(tt)) -> mark(tt)
744.20/263.00	   active(U23(tt)) -> mark(tt)
744.20/263.00	   active(U36(tt)) -> mark(tt)
744.20/263.00	   active(U42(tt)) -> mark(tt)
744.20/263.00	   active(U51(tt)) -> mark(tt)
744.20/263.00	   active(U62(tt)) -> mark(tt)
744.20/263.00	   active(U92(tt)) -> mark(0)
744.20/263.00	   active(isNat(0)) -> mark(tt)
744.20/263.00	   active(isNatKind(0)) -> mark(tt)
744.20/263.00	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.00	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.00	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.00	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.00	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.00	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.00	   U16(active(X)) -> U16(X)
744.20/263.00	   U16(mark(X)) -> U16(X)
744.20/263.00	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.00	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.00	   U23(active(X)) -> U23(X)
744.20/263.00	   U23(mark(X)) -> U23(X)
744.20/263.00	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.00	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.00	   U36(active(X)) -> U36(X)
744.20/263.00	   U36(mark(X)) -> U36(X)
744.20/263.00	   U42(active(X)) -> U42(X)
744.20/263.00	   U42(mark(X)) -> U42(X)
744.20/263.00	   U62(active(X)) -> U62(X)
744.20/263.00	   U62(mark(X)) -> U62(X)
744.20/263.00	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.00	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.00	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.00	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.00	   s(active(X)) -> s(X)
744.20/263.00	   s(mark(X)) -> s(X)
744.20/263.00	   U92(active(X)) -> U92(X)
744.20/263.00	   U92(mark(X)) -> U92(X)
744.20/263.00	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.00	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.00	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.00	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U51(active(X)) -> U51(X)
744.20/263.00	   U51(mark(X)) -> U51(X)
744.20/263.00	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.00	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.00	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.00	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.00	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.00	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.00	   x(active(X1), X2) -> x(X1, X2)
744.20/263.00	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.00	
744.20/263.00	The set Q consists of the following terms:
744.20/263.00	
744.20/263.00	   active(U101(tt, x0, x1))
744.20/263.00	   active(U102(tt, x0, x1))
744.20/263.00	   active(U103(tt, x0, x1))
744.20/263.00	   active(U104(tt, x0, x1))
744.20/263.00	   active(U11(tt, x0, x1))
744.20/263.00	   active(U12(tt, x0, x1))
744.20/263.00	   active(U13(tt, x0, x1))
744.20/263.00	   active(U14(tt, x0, x1))
744.20/263.00	   active(U15(tt, x0))
744.20/263.00	   active(U16(tt))
744.20/263.00	   active(U21(tt, x0))
744.20/263.00	   active(U22(tt, x0))
744.20/263.00	   active(U23(tt))
744.20/263.00	   active(U31(tt, x0, x1))
744.20/263.00	   active(U32(tt, x0, x1))
744.20/263.00	   active(U33(tt, x0, x1))
744.20/263.00	   active(U34(tt, x0, x1))
744.20/263.00	   active(U35(tt, x0))
744.20/263.00	   active(U36(tt))
744.20/263.00	   active(U41(tt, x0))
744.20/263.00	   active(U42(tt))
744.20/263.00	   active(U51(tt))
744.20/263.00	   active(U61(tt, x0))
744.20/263.00	   active(U62(tt))
744.20/263.00	   active(U71(tt, x0))
744.20/263.00	   active(U72(tt, x0))
744.20/263.00	   active(U81(tt, x0, x1))
744.20/263.00	   active(U82(tt, x0, x1))
744.20/263.00	   active(U83(tt, x0, x1))
744.20/263.00	   active(U84(tt, x0, x1))
744.20/263.00	   active(U91(tt, x0))
744.20/263.00	   active(U92(tt))
744.20/263.00	   active(isNat(0))
744.20/263.00	   active(isNat(plus(x0, x1)))
744.20/263.00	   active(isNat(s(x0)))
744.20/263.00	   active(isNat(x(x0, x1)))
744.20/263.00	   active(isNatKind(0))
744.20/263.00	   active(isNatKind(plus(x0, x1)))
744.20/263.00	   active(isNatKind(s(x0)))
744.20/263.00	   active(isNatKind(x(x0, x1)))
744.20/263.00	   active(plus(x0, 0))
744.20/263.00	   active(plus(x0, s(x1)))
744.20/263.00	   active(x(x0, 0))
744.20/263.00	   active(x(x0, s(x1)))
744.20/263.00	   mark(U101(x0, x1, x2))
744.20/263.00	   mark(tt)
744.20/263.00	   mark(U102(x0, x1, x2))
744.20/263.00	   mark(isNatKind(x0))
744.20/263.00	   mark(U103(x0, x1, x2))
744.20/263.00	   mark(isNat(x0))
744.20/263.00	   mark(U104(x0, x1, x2))
744.20/263.00	   mark(plus(x0, x1))
744.20/263.00	   mark(x(x0, x1))
744.20/263.00	   mark(U11(x0, x1, x2))
744.20/263.00	   mark(U12(x0, x1, x2))
744.20/263.00	   mark(U13(x0, x1, x2))
744.20/263.00	   mark(U14(x0, x1, x2))
744.20/263.00	   mark(U15(x0, x1))
744.20/263.00	   mark(U16(x0))
744.20/263.00	   mark(U21(x0, x1))
744.20/263.00	   mark(U22(x0, x1))
744.20/263.00	   mark(U23(x0))
744.20/263.00	   mark(U31(x0, x1, x2))
744.20/263.00	   mark(U32(x0, x1, x2))
744.20/263.00	   mark(U33(x0, x1, x2))
744.20/263.00	   mark(U34(x0, x1, x2))
744.20/263.00	   mark(U35(x0, x1))
744.20/263.00	   mark(U36(x0))
744.20/263.00	   mark(U41(x0, x1))
744.20/263.00	   mark(U42(x0))
744.20/263.00	   mark(U51(x0))
744.20/263.00	   mark(U61(x0, x1))
744.20/263.00	   mark(U62(x0))
744.20/263.00	   mark(U71(x0, x1))
744.20/263.00	   mark(U72(x0, x1))
744.20/263.00	   mark(U81(x0, x1, x2))
744.20/263.00	   mark(U82(x0, x1, x2))
744.20/263.00	   mark(U83(x0, x1, x2))
744.20/263.00	   mark(U84(x0, x1, x2))
744.20/263.00	   mark(s(x0))
744.20/263.00	   mark(U91(x0, x1))
744.20/263.00	   mark(U92(x0))
744.20/263.00	   mark(0)
744.20/263.00	   U101(mark(x0), x1, x2)
744.20/263.00	   U101(x0, mark(x1), x2)
744.20/263.00	   U101(x0, x1, mark(x2))
744.20/263.00	   U101(active(x0), x1, x2)
744.20/263.00	   U101(x0, active(x1), x2)
744.20/263.00	   U101(x0, x1, active(x2))
744.20/263.00	   U102(mark(x0), x1, x2)
744.20/263.00	   U102(x0, mark(x1), x2)
744.20/263.00	   U102(x0, x1, mark(x2))
744.20/263.00	   U102(active(x0), x1, x2)
744.20/263.00	   U102(x0, active(x1), x2)
744.20/263.00	   U102(x0, x1, active(x2))
744.20/263.00	   isNatKind(mark(x0))
744.20/263.00	   isNatKind(active(x0))
744.20/263.00	   U103(mark(x0), x1, x2)
744.20/263.00	   U103(x0, mark(x1), x2)
744.20/263.00	   U103(x0, x1, mark(x2))
744.20/263.00	   U103(active(x0), x1, x2)
744.20/263.00	   U103(x0, active(x1), x2)
744.20/263.00	   U103(x0, x1, active(x2))
744.20/263.00	   isNat(mark(x0))
744.20/263.00	   isNat(active(x0))
744.20/263.00	   U104(mark(x0), x1, x2)
744.20/263.00	   U104(x0, mark(x1), x2)
744.20/263.00	   U104(x0, x1, mark(x2))
744.20/263.00	   U104(active(x0), x1, x2)
744.20/263.00	   U104(x0, active(x1), x2)
744.20/263.00	   U104(x0, x1, active(x2))
744.20/263.00	   plus(mark(x0), x1)
744.20/263.00	   plus(x0, mark(x1))
744.20/263.00	   plus(active(x0), x1)
744.20/263.00	   plus(x0, active(x1))
744.20/263.00	   x(mark(x0), x1)
744.20/263.00	   x(x0, mark(x1))
744.20/263.00	   x(active(x0), x1)
744.20/263.00	   x(x0, active(x1))
744.20/263.00	   U11(mark(x0), x1, x2)
744.20/263.00	   U11(x0, mark(x1), x2)
744.20/263.00	   U11(x0, x1, mark(x2))
744.20/263.00	   U11(active(x0), x1, x2)
744.20/263.00	   U11(x0, active(x1), x2)
744.20/263.00	   U11(x0, x1, active(x2))
744.20/263.00	   U12(mark(x0), x1, x2)
744.20/263.00	   U12(x0, mark(x1), x2)
744.20/263.00	   U12(x0, x1, mark(x2))
744.20/263.00	   U12(active(x0), x1, x2)
744.20/263.00	   U12(x0, active(x1), x2)
744.20/263.00	   U12(x0, x1, active(x2))
744.20/263.00	   U13(mark(x0), x1, x2)
744.20/263.00	   U13(x0, mark(x1), x2)
744.20/263.00	   U13(x0, x1, mark(x2))
744.20/263.00	   U13(active(x0), x1, x2)
744.20/263.00	   U13(x0, active(x1), x2)
744.20/263.00	   U13(x0, x1, active(x2))
744.20/263.00	   U14(mark(x0), x1, x2)
744.20/263.00	   U14(x0, mark(x1), x2)
744.20/263.00	   U14(x0, x1, mark(x2))
744.20/263.00	   U14(active(x0), x1, x2)
744.20/263.00	   U14(x0, active(x1), x2)
744.20/263.00	   U14(x0, x1, active(x2))
744.20/263.00	   U15(mark(x0), x1)
744.20/263.00	   U15(x0, mark(x1))
744.20/263.00	   U15(active(x0), x1)
744.20/263.00	   U15(x0, active(x1))
744.20/263.00	   U16(mark(x0))
744.20/263.00	   U16(active(x0))
744.20/263.00	   U21(mark(x0), x1)
744.20/263.00	   U21(x0, mark(x1))
744.20/263.00	   U21(active(x0), x1)
744.20/263.00	   U21(x0, active(x1))
744.20/263.00	   U22(mark(x0), x1)
744.20/263.00	   U22(x0, mark(x1))
744.20/263.00	   U22(active(x0), x1)
744.20/263.00	   U22(x0, active(x1))
744.20/263.00	   U23(mark(x0))
744.20/263.00	   U23(active(x0))
744.20/263.00	   U31(mark(x0), x1, x2)
744.20/263.00	   U31(x0, mark(x1), x2)
744.20/263.00	   U31(x0, x1, mark(x2))
744.20/263.00	   U31(active(x0), x1, x2)
744.20/263.00	   U31(x0, active(x1), x2)
744.20/263.00	   U31(x0, x1, active(x2))
744.20/263.00	   U32(mark(x0), x1, x2)
744.20/263.00	   U32(x0, mark(x1), x2)
744.20/263.00	   U32(x0, x1, mark(x2))
744.20/263.00	   U32(active(x0), x1, x2)
744.20/263.00	   U32(x0, active(x1), x2)
744.20/263.00	   U32(x0, x1, active(x2))
744.20/263.00	   U33(mark(x0), x1, x2)
744.20/263.00	   U33(x0, mark(x1), x2)
744.20/263.00	   U33(x0, x1, mark(x2))
744.20/263.00	   U33(active(x0), x1, x2)
744.20/263.00	   U33(x0, active(x1), x2)
744.20/263.00	   U33(x0, x1, active(x2))
744.20/263.00	   U34(mark(x0), x1, x2)
744.20/263.00	   U34(x0, mark(x1), x2)
744.20/263.00	   U34(x0, x1, mark(x2))
744.20/263.00	   U34(active(x0), x1, x2)
744.20/263.00	   U34(x0, active(x1), x2)
744.20/263.00	   U34(x0, x1, active(x2))
744.20/263.00	   U35(mark(x0), x1)
744.20/263.00	   U35(x0, mark(x1))
744.20/263.00	   U35(active(x0), x1)
744.20/263.00	   U35(x0, active(x1))
744.20/263.00	   U36(mark(x0))
744.20/263.00	   U36(active(x0))
744.20/263.00	   U41(mark(x0), x1)
744.20/263.00	   U41(x0, mark(x1))
744.20/263.00	   U41(active(x0), x1)
744.20/263.00	   U41(x0, active(x1))
744.20/263.00	   U42(mark(x0))
744.20/263.00	   U42(active(x0))
744.20/263.00	   U51(mark(x0))
744.20/263.00	   U51(active(x0))
744.20/263.00	   U61(mark(x0), x1)
744.20/263.00	   U61(x0, mark(x1))
744.20/263.00	   U61(active(x0), x1)
744.20/263.00	   U61(x0, active(x1))
744.20/263.00	   U62(mark(x0))
744.20/263.00	   U62(active(x0))
744.20/263.00	   U71(mark(x0), x1)
744.20/263.00	   U71(x0, mark(x1))
744.20/263.00	   U71(active(x0), x1)
744.20/263.00	   U71(x0, active(x1))
744.20/263.00	   U72(mark(x0), x1)
744.20/263.00	   U72(x0, mark(x1))
744.20/263.00	   U72(active(x0), x1)
744.20/263.00	   U72(x0, active(x1))
744.20/263.00	   U81(mark(x0), x1, x2)
744.20/263.00	   U81(x0, mark(x1), x2)
744.20/263.00	   U81(x0, x1, mark(x2))
744.20/263.00	   U81(active(x0), x1, x2)
744.20/263.00	   U81(x0, active(x1), x2)
744.20/263.00	   U81(x0, x1, active(x2))
744.20/263.00	   U82(mark(x0), x1, x2)
744.20/263.00	   U82(x0, mark(x1), x2)
744.20/263.00	   U82(x0, x1, mark(x2))
744.20/263.00	   U82(active(x0), x1, x2)
744.20/263.00	   U82(x0, active(x1), x2)
744.20/263.00	   U82(x0, x1, active(x2))
744.20/263.00	   U83(mark(x0), x1, x2)
744.20/263.00	   U83(x0, mark(x1), x2)
744.20/263.00	   U83(x0, x1, mark(x2))
744.20/263.00	   U83(active(x0), x1, x2)
744.20/263.00	   U83(x0, active(x1), x2)
744.20/263.00	   U83(x0, x1, active(x2))
744.20/263.00	   U84(mark(x0), x1, x2)
744.20/263.00	   U84(x0, mark(x1), x2)
744.20/263.00	   U84(x0, x1, mark(x2))
744.20/263.00	   U84(active(x0), x1, x2)
744.20/263.00	   U84(x0, active(x1), x2)
744.20/263.00	   U84(x0, x1, active(x2))
744.20/263.00	   s(mark(x0))
744.20/263.00	   s(active(x0))
744.20/263.00	   U91(mark(x0), x1)
744.20/263.00	   U91(x0, mark(x1))
744.20/263.00	   U91(active(x0), x1)
744.20/263.00	   U91(x0, active(x1))
744.20/263.00	   U92(mark(x0))
744.20/263.00	   U92(active(x0))
744.20/263.00	
744.20/263.00	We have to consider all minimal (P,Q,R)-chains.
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(283) QDPOrderProof (EQUIVALENT)
744.20/263.00	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.00	
744.20/263.00	
744.20/263.00	The following pairs can be oriented strictly and are deleted.
744.20/263.00	
744.20/263.00	   MARK(U103(X1, X2, X3)) -> ACTIVE(U103(mark(X1), X2, X3))
744.20/263.00	   MARK(U82(X1, X2, X3)) -> ACTIVE(U82(mark(X1), X2, X3))
744.20/263.00	The remaining pairs can at least be oriented weakly.
744.20/263.00	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.00	
744.20/263.00	POL( ACTIVE_1(x_1) ) = max{0, x_1 - 1}
744.20/263.00	POL( U101_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U102_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U103_3(x_1, ..., x_3) ) = 0
744.20/263.00	POL( U11_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U12_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U13_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U14_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U15_2(x_1, x_2) ) = 2
744.20/263.00	POL( U21_2(x_1, x_2) ) = 2
744.20/263.00	POL( U22_2(x_1, x_2) ) = 2
744.20/263.00	POL( U31_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U32_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U33_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U34_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U35_2(x_1, x_2) ) = 2
744.20/263.00	POL( U41_2(x_1, x_2) ) = 2
744.20/263.00	POL( U61_2(x_1, x_2) ) = 2
744.20/263.00	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/263.00	POL( U82_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.00	POL( mark_1(x_1) ) = 2
744.20/263.00	POL( active_1(x_1) ) = max{0, -2}
744.20/263.00	POL( tt ) = 0
744.20/263.00	POL( isNatKind_1(x_1) ) = 2
744.20/263.00	POL( isNat_1(x_1) ) = 2
744.20/263.00	POL( U104_3(x_1, ..., x_3) ) = x_2 + 2
744.20/263.00	POL( plus_2(x_1, x_2) ) = max{0, x_1 - 2}
744.20/263.00	POL( x_2(x_1, x_2) ) = 2
744.20/263.00	POL( U16_1(x_1) ) = 0
744.20/263.00	POL( U23_1(x_1) ) = max{0, -2}
744.20/263.00	POL( U36_1(x_1) ) = max{0, -2}
744.20/263.00	POL( U42_1(x_1) ) = max{0, -2}
744.20/263.00	POL( U62_1(x_1) ) = x_1 + 2
744.20/263.00	POL( U71_2(x_1, x_2) ) = 2
744.20/263.00	POL( U72_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.20/263.00	POL( U83_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 - 2}
744.20/263.00	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.20/263.00	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U91_2(x_1, x_2) ) = max{0, x_1 + 2x_2 - 2}
744.20/263.00	POL( U92_1(x_1) ) = max{0, x_1 - 2}
744.20/263.00	POL( U51_1(x_1) ) = max{0, -2}
744.20/263.00	POL( 0 ) = 0
744.20/263.00	POL( MARK_1(x_1) ) = 1
744.20/263.00	
744.20/263.00	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.00	
744.20/263.00	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.00	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.00	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.00	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.00	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.00	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.00	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.00	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.00	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.00	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.00	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.00	
744.20/263.00	
744.20/263.00	----------------------------------------
744.20/263.00	
744.20/263.00	(284)
744.20/263.00	Obligation:
744.20/263.00	Q DP problem:
744.20/263.00	The TRS P consists of the following rules:
744.20/263.00	
744.20/263.00	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.00	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U102(tt, M, N)) -> MARK(U103(isNat(N), M, N))
744.20/263.00	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.00	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.00	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.00	   MARK(U16(X)) -> MARK(X)
744.20/263.00	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.00	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.00	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.00	   MARK(U23(X)) -> MARK(X)
744.20/263.00	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.00	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.00	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.00	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.00	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.00	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.00	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.00	   MARK(U36(X)) -> MARK(X)
744.20/263.00	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.00	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.00	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.00	   MARK(U42(X)) -> MARK(X)
744.20/263.00	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.00	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.00	   MARK(U62(X)) -> MARK(X)
744.20/263.00	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(U81(tt, M, N)) -> MARK(U82(isNatKind(M), M, N))
744.20/263.00	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.00	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U51(X)) -> MARK(X)
744.20/263.00	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.00	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.00	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/263.00	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.00	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.00	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.00	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.00	
744.20/263.00	The TRS R consists of the following rules:
744.20/263.00	
744.20/263.00	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.00	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.00	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.00	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.00	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.00	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.00	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.00	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.00	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.00	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.00	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.00	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.00	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.00	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.00	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.00	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.00	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.00	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.00	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.00	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.00	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.00	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.00	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.00	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.00	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.00	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.00	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.00	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.00	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.00	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.00	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.00	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.00	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.00	   active(U72(tt, N)) -> mark(N)
744.20/263.00	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.00	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.00	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.00	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.00	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.00	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.00	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.00	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.00	   mark(s(X)) -> active(s(mark(X)))
744.20/263.00	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.00	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.00	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.00	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.00	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.00	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.00	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.00	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.00	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.00	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.00	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.00	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.00	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.00	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.00	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.00	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.00	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.00	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.00	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.00	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.00	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.00	   mark(isNat(X)) -> active(isNat(X))
744.20/263.00	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.00	   mark(tt) -> active(tt)
744.20/263.00	   mark(0) -> active(0)
744.20/263.00	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.00	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.00	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.00	   active(U16(tt)) -> mark(tt)
744.20/263.00	   active(U23(tt)) -> mark(tt)
744.20/263.00	   active(U36(tt)) -> mark(tt)
744.20/263.00	   active(U42(tt)) -> mark(tt)
744.20/263.00	   active(U51(tt)) -> mark(tt)
744.20/263.00	   active(U62(tt)) -> mark(tt)
744.20/263.00	   active(U92(tt)) -> mark(0)
744.20/263.00	   active(isNat(0)) -> mark(tt)
744.20/263.00	   active(isNatKind(0)) -> mark(tt)
744.20/263.00	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.00	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.00	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.00	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.00	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.00	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.00	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.00	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.00	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.00	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.00	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.00	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.00	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.00	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.00	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.00	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.00	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.00	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.00	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.00	   U16(active(X)) -> U16(X)
744.20/263.00	   U16(mark(X)) -> U16(X)
744.20/263.00	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.00	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.00	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.00	   U23(active(X)) -> U23(X)
744.20/263.00	   U23(mark(X)) -> U23(X)
744.20/263.00	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.00	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.00	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.00	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.00	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.00	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.00	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.00	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.00	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.00	   U36(active(X)) -> U36(X)
744.20/263.00	   U36(mark(X)) -> U36(X)
744.20/263.00	   U42(active(X)) -> U42(X)
744.20/263.00	   U42(mark(X)) -> U42(X)
744.20/263.00	   U62(active(X)) -> U62(X)
744.20/263.00	   U62(mark(X)) -> U62(X)
744.20/263.00	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.00	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.00	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.00	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.00	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.00	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.00	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.00	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.00	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.00	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.00	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.00	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.00	   s(active(X)) -> s(X)
744.20/263.00	   s(mark(X)) -> s(X)
744.20/263.00	   U92(active(X)) -> U92(X)
744.20/263.00	   U92(mark(X)) -> U92(X)
744.20/263.00	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.00	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.00	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.00	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.00	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.00	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.00	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.00	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.00	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.00	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.00	   U51(active(X)) -> U51(X)
744.20/263.00	   U51(mark(X)) -> U51(X)
744.20/263.00	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.00	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.00	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.00	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.00	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.00	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.01	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.01	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.01	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.01	   x(active(X1), X2) -> x(X1, X2)
744.20/263.01	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.01	
744.20/263.01	The set Q consists of the following terms:
744.20/263.01	
744.20/263.01	   active(U101(tt, x0, x1))
744.20/263.01	   active(U102(tt, x0, x1))
744.20/263.01	   active(U103(tt, x0, x1))
744.20/263.01	   active(U104(tt, x0, x1))
744.20/263.01	   active(U11(tt, x0, x1))
744.20/263.01	   active(U12(tt, x0, x1))
744.20/263.01	   active(U13(tt, x0, x1))
744.20/263.01	   active(U14(tt, x0, x1))
744.20/263.01	   active(U15(tt, x0))
744.20/263.01	   active(U16(tt))
744.20/263.01	   active(U21(tt, x0))
744.20/263.01	   active(U22(tt, x0))
744.20/263.01	   active(U23(tt))
744.20/263.01	   active(U31(tt, x0, x1))
744.20/263.01	   active(U32(tt, x0, x1))
744.20/263.01	   active(U33(tt, x0, x1))
744.20/263.01	   active(U34(tt, x0, x1))
744.20/263.01	   active(U35(tt, x0))
744.20/263.01	   active(U36(tt))
744.20/263.01	   active(U41(tt, x0))
744.20/263.01	   active(U42(tt))
744.20/263.01	   active(U51(tt))
744.20/263.01	   active(U61(tt, x0))
744.20/263.01	   active(U62(tt))
744.20/263.01	   active(U71(tt, x0))
744.20/263.01	   active(U72(tt, x0))
744.20/263.01	   active(U81(tt, x0, x1))
744.20/263.01	   active(U82(tt, x0, x1))
744.20/263.01	   active(U83(tt, x0, x1))
744.20/263.01	   active(U84(tt, x0, x1))
744.20/263.01	   active(U91(tt, x0))
744.20/263.01	   active(U92(tt))
744.20/263.01	   active(isNat(0))
744.20/263.01	   active(isNat(plus(x0, x1)))
744.20/263.01	   active(isNat(s(x0)))
744.20/263.01	   active(isNat(x(x0, x1)))
744.20/263.01	   active(isNatKind(0))
744.20/263.01	   active(isNatKind(plus(x0, x1)))
744.20/263.01	   active(isNatKind(s(x0)))
744.20/263.01	   active(isNatKind(x(x0, x1)))
744.20/263.01	   active(plus(x0, 0))
744.20/263.01	   active(plus(x0, s(x1)))
744.20/263.01	   active(x(x0, 0))
744.20/263.01	   active(x(x0, s(x1)))
744.20/263.01	   mark(U101(x0, x1, x2))
744.20/263.01	   mark(tt)
744.20/263.01	   mark(U102(x0, x1, x2))
744.20/263.01	   mark(isNatKind(x0))
744.20/263.01	   mark(U103(x0, x1, x2))
744.20/263.01	   mark(isNat(x0))
744.20/263.01	   mark(U104(x0, x1, x2))
744.20/263.01	   mark(plus(x0, x1))
744.20/263.01	   mark(x(x0, x1))
744.20/263.01	   mark(U11(x0, x1, x2))
744.20/263.01	   mark(U12(x0, x1, x2))
744.20/263.01	   mark(U13(x0, x1, x2))
744.20/263.01	   mark(U14(x0, x1, x2))
744.20/263.01	   mark(U15(x0, x1))
744.20/263.01	   mark(U16(x0))
744.20/263.01	   mark(U21(x0, x1))
744.20/263.01	   mark(U22(x0, x1))
744.20/263.01	   mark(U23(x0))
744.20/263.01	   mark(U31(x0, x1, x2))
744.20/263.01	   mark(U32(x0, x1, x2))
744.20/263.01	   mark(U33(x0, x1, x2))
744.20/263.01	   mark(U34(x0, x1, x2))
744.20/263.01	   mark(U35(x0, x1))
744.20/263.01	   mark(U36(x0))
744.20/263.01	   mark(U41(x0, x1))
744.20/263.01	   mark(U42(x0))
744.20/263.01	   mark(U51(x0))
744.20/263.01	   mark(U61(x0, x1))
744.20/263.01	   mark(U62(x0))
744.20/263.01	   mark(U71(x0, x1))
744.20/263.01	   mark(U72(x0, x1))
744.20/263.01	   mark(U81(x0, x1, x2))
744.20/263.01	   mark(U82(x0, x1, x2))
744.20/263.01	   mark(U83(x0, x1, x2))
744.20/263.01	   mark(U84(x0, x1, x2))
744.20/263.01	   mark(s(x0))
744.20/263.01	   mark(U91(x0, x1))
744.20/263.01	   mark(U92(x0))
744.20/263.01	   mark(0)
744.20/263.01	   U101(mark(x0), x1, x2)
744.20/263.01	   U101(x0, mark(x1), x2)
744.20/263.01	   U101(x0, x1, mark(x2))
744.20/263.01	   U101(active(x0), x1, x2)
744.20/263.01	   U101(x0, active(x1), x2)
744.20/263.01	   U101(x0, x1, active(x2))
744.20/263.01	   U102(mark(x0), x1, x2)
744.20/263.01	   U102(x0, mark(x1), x2)
744.20/263.01	   U102(x0, x1, mark(x2))
744.20/263.01	   U102(active(x0), x1, x2)
744.20/263.01	   U102(x0, active(x1), x2)
744.20/263.01	   U102(x0, x1, active(x2))
744.20/263.01	   isNatKind(mark(x0))
744.20/263.01	   isNatKind(active(x0))
744.20/263.01	   U103(mark(x0), x1, x2)
744.20/263.01	   U103(x0, mark(x1), x2)
744.20/263.01	   U103(x0, x1, mark(x2))
744.20/263.01	   U103(active(x0), x1, x2)
744.20/263.01	   U103(x0, active(x1), x2)
744.20/263.01	   U103(x0, x1, active(x2))
744.20/263.01	   isNat(mark(x0))
744.20/263.01	   isNat(active(x0))
744.20/263.01	   U104(mark(x0), x1, x2)
744.20/263.01	   U104(x0, mark(x1), x2)
744.20/263.01	   U104(x0, x1, mark(x2))
744.20/263.01	   U104(active(x0), x1, x2)
744.20/263.01	   U104(x0, active(x1), x2)
744.20/263.01	   U104(x0, x1, active(x2))
744.20/263.01	   plus(mark(x0), x1)
744.20/263.01	   plus(x0, mark(x1))
744.20/263.01	   plus(active(x0), x1)
744.20/263.01	   plus(x0, active(x1))
744.20/263.01	   x(mark(x0), x1)
744.20/263.01	   x(x0, mark(x1))
744.20/263.01	   x(active(x0), x1)
744.20/263.01	   x(x0, active(x1))
744.20/263.01	   U11(mark(x0), x1, x2)
744.20/263.01	   U11(x0, mark(x1), x2)
744.20/263.01	   U11(x0, x1, mark(x2))
744.20/263.01	   U11(active(x0), x1, x2)
744.20/263.01	   U11(x0, active(x1), x2)
744.20/263.01	   U11(x0, x1, active(x2))
744.20/263.01	   U12(mark(x0), x1, x2)
744.20/263.01	   U12(x0, mark(x1), x2)
744.20/263.01	   U12(x0, x1, mark(x2))
744.20/263.01	   U12(active(x0), x1, x2)
744.20/263.01	   U12(x0, active(x1), x2)
744.20/263.01	   U12(x0, x1, active(x2))
744.20/263.01	   U13(mark(x0), x1, x2)
744.20/263.01	   U13(x0, mark(x1), x2)
744.20/263.01	   U13(x0, x1, mark(x2))
744.20/263.01	   U13(active(x0), x1, x2)
744.20/263.01	   U13(x0, active(x1), x2)
744.20/263.01	   U13(x0, x1, active(x2))
744.20/263.01	   U14(mark(x0), x1, x2)
744.20/263.01	   U14(x0, mark(x1), x2)
744.20/263.01	   U14(x0, x1, mark(x2))
744.20/263.01	   U14(active(x0), x1, x2)
744.20/263.01	   U14(x0, active(x1), x2)
744.20/263.01	   U14(x0, x1, active(x2))
744.20/263.01	   U15(mark(x0), x1)
744.20/263.01	   U15(x0, mark(x1))
744.20/263.01	   U15(active(x0), x1)
744.20/263.01	   U15(x0, active(x1))
744.20/263.01	   U16(mark(x0))
744.20/263.01	   U16(active(x0))
744.20/263.01	   U21(mark(x0), x1)
744.20/263.01	   U21(x0, mark(x1))
744.20/263.01	   U21(active(x0), x1)
744.20/263.01	   U21(x0, active(x1))
744.20/263.01	   U22(mark(x0), x1)
744.20/263.01	   U22(x0, mark(x1))
744.20/263.01	   U22(active(x0), x1)
744.20/263.01	   U22(x0, active(x1))
744.20/263.01	   U23(mark(x0))
744.20/263.01	   U23(active(x0))
744.20/263.01	   U31(mark(x0), x1, x2)
744.20/263.01	   U31(x0, mark(x1), x2)
744.20/263.01	   U31(x0, x1, mark(x2))
744.20/263.01	   U31(active(x0), x1, x2)
744.20/263.01	   U31(x0, active(x1), x2)
744.20/263.01	   U31(x0, x1, active(x2))
744.20/263.01	   U32(mark(x0), x1, x2)
744.20/263.01	   U32(x0, mark(x1), x2)
744.20/263.01	   U32(x0, x1, mark(x2))
744.20/263.01	   U32(active(x0), x1, x2)
744.20/263.01	   U32(x0, active(x1), x2)
744.20/263.01	   U32(x0, x1, active(x2))
744.20/263.01	   U33(mark(x0), x1, x2)
744.20/263.01	   U33(x0, mark(x1), x2)
744.20/263.01	   U33(x0, x1, mark(x2))
744.20/263.01	   U33(active(x0), x1, x2)
744.20/263.01	   U33(x0, active(x1), x2)
744.20/263.01	   U33(x0, x1, active(x2))
744.20/263.01	   U34(mark(x0), x1, x2)
744.20/263.01	   U34(x0, mark(x1), x2)
744.20/263.01	   U34(x0, x1, mark(x2))
744.20/263.01	   U34(active(x0), x1, x2)
744.20/263.01	   U34(x0, active(x1), x2)
744.20/263.01	   U34(x0, x1, active(x2))
744.20/263.01	   U35(mark(x0), x1)
744.20/263.01	   U35(x0, mark(x1))
744.20/263.01	   U35(active(x0), x1)
744.20/263.01	   U35(x0, active(x1))
744.20/263.01	   U36(mark(x0))
744.20/263.01	   U36(active(x0))
744.20/263.01	   U41(mark(x0), x1)
744.20/263.01	   U41(x0, mark(x1))
744.20/263.01	   U41(active(x0), x1)
744.20/263.01	   U41(x0, active(x1))
744.20/263.01	   U42(mark(x0))
744.20/263.01	   U42(active(x0))
744.20/263.01	   U51(mark(x0))
744.20/263.01	   U51(active(x0))
744.20/263.01	   U61(mark(x0), x1)
744.20/263.01	   U61(x0, mark(x1))
744.20/263.01	   U61(active(x0), x1)
744.20/263.01	   U61(x0, active(x1))
744.20/263.01	   U62(mark(x0))
744.20/263.01	   U62(active(x0))
744.20/263.01	   U71(mark(x0), x1)
744.20/263.01	   U71(x0, mark(x1))
744.20/263.01	   U71(active(x0), x1)
744.20/263.01	   U71(x0, active(x1))
744.20/263.01	   U72(mark(x0), x1)
744.20/263.01	   U72(x0, mark(x1))
744.20/263.01	   U72(active(x0), x1)
744.20/263.01	   U72(x0, active(x1))
744.20/263.01	   U81(mark(x0), x1, x2)
744.20/263.01	   U81(x0, mark(x1), x2)
744.20/263.01	   U81(x0, x1, mark(x2))
744.20/263.01	   U81(active(x0), x1, x2)
744.20/263.01	   U81(x0, active(x1), x2)
744.20/263.01	   U81(x0, x1, active(x2))
744.20/263.01	   U82(mark(x0), x1, x2)
744.20/263.01	   U82(x0, mark(x1), x2)
744.20/263.01	   U82(x0, x1, mark(x2))
744.20/263.01	   U82(active(x0), x1, x2)
744.20/263.01	   U82(x0, active(x1), x2)
744.20/263.01	   U82(x0, x1, active(x2))
744.20/263.01	   U83(mark(x0), x1, x2)
744.20/263.01	   U83(x0, mark(x1), x2)
744.20/263.01	   U83(x0, x1, mark(x2))
744.20/263.01	   U83(active(x0), x1, x2)
744.20/263.01	   U83(x0, active(x1), x2)
744.20/263.01	   U83(x0, x1, active(x2))
744.20/263.01	   U84(mark(x0), x1, x2)
744.20/263.01	   U84(x0, mark(x1), x2)
744.20/263.01	   U84(x0, x1, mark(x2))
744.20/263.01	   U84(active(x0), x1, x2)
744.20/263.01	   U84(x0, active(x1), x2)
744.20/263.01	   U84(x0, x1, active(x2))
744.20/263.01	   s(mark(x0))
744.20/263.01	   s(active(x0))
744.20/263.01	   U91(mark(x0), x1)
744.20/263.01	   U91(x0, mark(x1))
744.20/263.01	   U91(active(x0), x1)
744.20/263.01	   U91(x0, active(x1))
744.20/263.01	   U92(mark(x0))
744.20/263.01	   U92(active(x0))
744.20/263.01	
744.20/263.01	We have to consider all minimal (P,Q,R)-chains.
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(285) DependencyGraphProof (EQUIVALENT)
744.20/263.01	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(286)
744.20/263.01	Obligation:
744.20/263.01	Q DP problem:
744.20/263.01	The TRS P consists of the following rules:
744.20/263.01	
744.20/263.01	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.01	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.01	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.01	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.01	   MARK(U16(X)) -> MARK(X)
744.20/263.01	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.01	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.01	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.01	   MARK(U23(X)) -> MARK(X)
744.20/263.01	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.01	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.01	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.01	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.01	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.01	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.01	   MARK(U36(X)) -> MARK(X)
744.20/263.01	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.01	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.01	   MARK(U42(X)) -> MARK(X)
744.20/263.01	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.01	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.01	   MARK(U62(X)) -> MARK(X)
744.20/263.01	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.01	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U51(X)) -> MARK(X)
744.20/263.01	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.01	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.01	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.01	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.01	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.01	
744.20/263.01	The TRS R consists of the following rules:
744.20/263.01	
744.20/263.01	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.01	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.01	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.01	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.01	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.01	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.01	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.01	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.01	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.01	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.01	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.01	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.01	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.01	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.01	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.01	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.01	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.01	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.01	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.01	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.01	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.01	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.01	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.01	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.01	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.01	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.01	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.01	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.01	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.01	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.01	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.01	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.01	   active(U72(tt, N)) -> mark(N)
744.20/263.01	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.01	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.01	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.01	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.01	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.01	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.01	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.01	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.01	   mark(s(X)) -> active(s(mark(X)))
744.20/263.01	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.01	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.01	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.01	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.01	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.01	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.01	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.01	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.01	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.01	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.01	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.01	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.01	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.01	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.01	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.01	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.01	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.01	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.01	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.01	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.01	   mark(isNat(X)) -> active(isNat(X))
744.20/263.01	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.01	   mark(tt) -> active(tt)
744.20/263.01	   mark(0) -> active(0)
744.20/263.01	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.01	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.01	   active(U16(tt)) -> mark(tt)
744.20/263.01	   active(U23(tt)) -> mark(tt)
744.20/263.01	   active(U36(tt)) -> mark(tt)
744.20/263.01	   active(U42(tt)) -> mark(tt)
744.20/263.01	   active(U51(tt)) -> mark(tt)
744.20/263.01	   active(U62(tt)) -> mark(tt)
744.20/263.01	   active(U92(tt)) -> mark(0)
744.20/263.01	   active(isNat(0)) -> mark(tt)
744.20/263.01	   active(isNatKind(0)) -> mark(tt)
744.20/263.01	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.01	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.01	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.01	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.01	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.01	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.01	   U16(active(X)) -> U16(X)
744.20/263.01	   U16(mark(X)) -> U16(X)
744.20/263.01	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.01	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.01	   U23(active(X)) -> U23(X)
744.20/263.01	   U23(mark(X)) -> U23(X)
744.20/263.01	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.01	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.01	   U36(active(X)) -> U36(X)
744.20/263.01	   U36(mark(X)) -> U36(X)
744.20/263.01	   U42(active(X)) -> U42(X)
744.20/263.01	   U42(mark(X)) -> U42(X)
744.20/263.01	   U62(active(X)) -> U62(X)
744.20/263.01	   U62(mark(X)) -> U62(X)
744.20/263.01	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.01	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.01	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.01	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.01	   s(active(X)) -> s(X)
744.20/263.01	   s(mark(X)) -> s(X)
744.20/263.01	   U92(active(X)) -> U92(X)
744.20/263.01	   U92(mark(X)) -> U92(X)
744.20/263.01	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.01	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.01	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.01	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.01	   U51(active(X)) -> U51(X)
744.20/263.01	   U51(mark(X)) -> U51(X)
744.20/263.01	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.01	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.01	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.01	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.01	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.01	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.01	   x(active(X1), X2) -> x(X1, X2)
744.20/263.01	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.01	
744.20/263.01	The set Q consists of the following terms:
744.20/263.01	
744.20/263.01	   active(U101(tt, x0, x1))
744.20/263.01	   active(U102(tt, x0, x1))
744.20/263.01	   active(U103(tt, x0, x1))
744.20/263.01	   active(U104(tt, x0, x1))
744.20/263.01	   active(U11(tt, x0, x1))
744.20/263.01	   active(U12(tt, x0, x1))
744.20/263.01	   active(U13(tt, x0, x1))
744.20/263.01	   active(U14(tt, x0, x1))
744.20/263.01	   active(U15(tt, x0))
744.20/263.01	   active(U16(tt))
744.20/263.01	   active(U21(tt, x0))
744.20/263.01	   active(U22(tt, x0))
744.20/263.01	   active(U23(tt))
744.20/263.01	   active(U31(tt, x0, x1))
744.20/263.01	   active(U32(tt, x0, x1))
744.20/263.01	   active(U33(tt, x0, x1))
744.20/263.01	   active(U34(tt, x0, x1))
744.20/263.01	   active(U35(tt, x0))
744.20/263.01	   active(U36(tt))
744.20/263.01	   active(U41(tt, x0))
744.20/263.01	   active(U42(tt))
744.20/263.01	   active(U51(tt))
744.20/263.01	   active(U61(tt, x0))
744.20/263.01	   active(U62(tt))
744.20/263.01	   active(U71(tt, x0))
744.20/263.01	   active(U72(tt, x0))
744.20/263.01	   active(U81(tt, x0, x1))
744.20/263.01	   active(U82(tt, x0, x1))
744.20/263.01	   active(U83(tt, x0, x1))
744.20/263.01	   active(U84(tt, x0, x1))
744.20/263.01	   active(U91(tt, x0))
744.20/263.01	   active(U92(tt))
744.20/263.01	   active(isNat(0))
744.20/263.01	   active(isNat(plus(x0, x1)))
744.20/263.01	   active(isNat(s(x0)))
744.20/263.01	   active(isNat(x(x0, x1)))
744.20/263.01	   active(isNatKind(0))
744.20/263.01	   active(isNatKind(plus(x0, x1)))
744.20/263.01	   active(isNatKind(s(x0)))
744.20/263.01	   active(isNatKind(x(x0, x1)))
744.20/263.01	   active(plus(x0, 0))
744.20/263.01	   active(plus(x0, s(x1)))
744.20/263.01	   active(x(x0, 0))
744.20/263.01	   active(x(x0, s(x1)))
744.20/263.01	   mark(U101(x0, x1, x2))
744.20/263.01	   mark(tt)
744.20/263.01	   mark(U102(x0, x1, x2))
744.20/263.01	   mark(isNatKind(x0))
744.20/263.01	   mark(U103(x0, x1, x2))
744.20/263.01	   mark(isNat(x0))
744.20/263.01	   mark(U104(x0, x1, x2))
744.20/263.01	   mark(plus(x0, x1))
744.20/263.01	   mark(x(x0, x1))
744.20/263.01	   mark(U11(x0, x1, x2))
744.20/263.01	   mark(U12(x0, x1, x2))
744.20/263.01	   mark(U13(x0, x1, x2))
744.20/263.01	   mark(U14(x0, x1, x2))
744.20/263.01	   mark(U15(x0, x1))
744.20/263.01	   mark(U16(x0))
744.20/263.01	   mark(U21(x0, x1))
744.20/263.01	   mark(U22(x0, x1))
744.20/263.01	   mark(U23(x0))
744.20/263.01	   mark(U31(x0, x1, x2))
744.20/263.01	   mark(U32(x0, x1, x2))
744.20/263.01	   mark(U33(x0, x1, x2))
744.20/263.01	   mark(U34(x0, x1, x2))
744.20/263.01	   mark(U35(x0, x1))
744.20/263.01	   mark(U36(x0))
744.20/263.01	   mark(U41(x0, x1))
744.20/263.01	   mark(U42(x0))
744.20/263.01	   mark(U51(x0))
744.20/263.01	   mark(U61(x0, x1))
744.20/263.01	   mark(U62(x0))
744.20/263.01	   mark(U71(x0, x1))
744.20/263.01	   mark(U72(x0, x1))
744.20/263.01	   mark(U81(x0, x1, x2))
744.20/263.01	   mark(U82(x0, x1, x2))
744.20/263.01	   mark(U83(x0, x1, x2))
744.20/263.01	   mark(U84(x0, x1, x2))
744.20/263.01	   mark(s(x0))
744.20/263.01	   mark(U91(x0, x1))
744.20/263.01	   mark(U92(x0))
744.20/263.01	   mark(0)
744.20/263.01	   U101(mark(x0), x1, x2)
744.20/263.01	   U101(x0, mark(x1), x2)
744.20/263.01	   U101(x0, x1, mark(x2))
744.20/263.01	   U101(active(x0), x1, x2)
744.20/263.01	   U101(x0, active(x1), x2)
744.20/263.01	   U101(x0, x1, active(x2))
744.20/263.01	   U102(mark(x0), x1, x2)
744.20/263.01	   U102(x0, mark(x1), x2)
744.20/263.01	   U102(x0, x1, mark(x2))
744.20/263.01	   U102(active(x0), x1, x2)
744.20/263.01	   U102(x0, active(x1), x2)
744.20/263.01	   U102(x0, x1, active(x2))
744.20/263.01	   isNatKind(mark(x0))
744.20/263.01	   isNatKind(active(x0))
744.20/263.01	   U103(mark(x0), x1, x2)
744.20/263.01	   U103(x0, mark(x1), x2)
744.20/263.01	   U103(x0, x1, mark(x2))
744.20/263.01	   U103(active(x0), x1, x2)
744.20/263.01	   U103(x0, active(x1), x2)
744.20/263.01	   U103(x0, x1, active(x2))
744.20/263.01	   isNat(mark(x0))
744.20/263.01	   isNat(active(x0))
744.20/263.01	   U104(mark(x0), x1, x2)
744.20/263.01	   U104(x0, mark(x1), x2)
744.20/263.01	   U104(x0, x1, mark(x2))
744.20/263.01	   U104(active(x0), x1, x2)
744.20/263.01	   U104(x0, active(x1), x2)
744.20/263.01	   U104(x0, x1, active(x2))
744.20/263.01	   plus(mark(x0), x1)
744.20/263.01	   plus(x0, mark(x1))
744.20/263.01	   plus(active(x0), x1)
744.20/263.01	   plus(x0, active(x1))
744.20/263.01	   x(mark(x0), x1)
744.20/263.01	   x(x0, mark(x1))
744.20/263.01	   x(active(x0), x1)
744.20/263.01	   x(x0, active(x1))
744.20/263.01	   U11(mark(x0), x1, x2)
744.20/263.01	   U11(x0, mark(x1), x2)
744.20/263.01	   U11(x0, x1, mark(x2))
744.20/263.01	   U11(active(x0), x1, x2)
744.20/263.01	   U11(x0, active(x1), x2)
744.20/263.01	   U11(x0, x1, active(x2))
744.20/263.01	   U12(mark(x0), x1, x2)
744.20/263.01	   U12(x0, mark(x1), x2)
744.20/263.01	   U12(x0, x1, mark(x2))
744.20/263.01	   U12(active(x0), x1, x2)
744.20/263.01	   U12(x0, active(x1), x2)
744.20/263.01	   U12(x0, x1, active(x2))
744.20/263.01	   U13(mark(x0), x1, x2)
744.20/263.01	   U13(x0, mark(x1), x2)
744.20/263.01	   U13(x0, x1, mark(x2))
744.20/263.01	   U13(active(x0), x1, x2)
744.20/263.01	   U13(x0, active(x1), x2)
744.20/263.01	   U13(x0, x1, active(x2))
744.20/263.01	   U14(mark(x0), x1, x2)
744.20/263.01	   U14(x0, mark(x1), x2)
744.20/263.01	   U14(x0, x1, mark(x2))
744.20/263.01	   U14(active(x0), x1, x2)
744.20/263.01	   U14(x0, active(x1), x2)
744.20/263.01	   U14(x0, x1, active(x2))
744.20/263.01	   U15(mark(x0), x1)
744.20/263.01	   U15(x0, mark(x1))
744.20/263.01	   U15(active(x0), x1)
744.20/263.01	   U15(x0, active(x1))
744.20/263.01	   U16(mark(x0))
744.20/263.01	   U16(active(x0))
744.20/263.01	   U21(mark(x0), x1)
744.20/263.01	   U21(x0, mark(x1))
744.20/263.01	   U21(active(x0), x1)
744.20/263.01	   U21(x0, active(x1))
744.20/263.01	   U22(mark(x0), x1)
744.20/263.01	   U22(x0, mark(x1))
744.20/263.01	   U22(active(x0), x1)
744.20/263.01	   U22(x0, active(x1))
744.20/263.01	   U23(mark(x0))
744.20/263.01	   U23(active(x0))
744.20/263.01	   U31(mark(x0), x1, x2)
744.20/263.01	   U31(x0, mark(x1), x2)
744.20/263.01	   U31(x0, x1, mark(x2))
744.20/263.01	   U31(active(x0), x1, x2)
744.20/263.01	   U31(x0, active(x1), x2)
744.20/263.01	   U31(x0, x1, active(x2))
744.20/263.01	   U32(mark(x0), x1, x2)
744.20/263.01	   U32(x0, mark(x1), x2)
744.20/263.01	   U32(x0, x1, mark(x2))
744.20/263.01	   U32(active(x0), x1, x2)
744.20/263.01	   U32(x0, active(x1), x2)
744.20/263.01	   U32(x0, x1, active(x2))
744.20/263.01	   U33(mark(x0), x1, x2)
744.20/263.01	   U33(x0, mark(x1), x2)
744.20/263.01	   U33(x0, x1, mark(x2))
744.20/263.01	   U33(active(x0), x1, x2)
744.20/263.01	   U33(x0, active(x1), x2)
744.20/263.01	   U33(x0, x1, active(x2))
744.20/263.01	   U34(mark(x0), x1, x2)
744.20/263.01	   U34(x0, mark(x1), x2)
744.20/263.01	   U34(x0, x1, mark(x2))
744.20/263.01	   U34(active(x0), x1, x2)
744.20/263.01	   U34(x0, active(x1), x2)
744.20/263.01	   U34(x0, x1, active(x2))
744.20/263.01	   U35(mark(x0), x1)
744.20/263.01	   U35(x0, mark(x1))
744.20/263.01	   U35(active(x0), x1)
744.20/263.01	   U35(x0, active(x1))
744.20/263.01	   U36(mark(x0))
744.20/263.01	   U36(active(x0))
744.20/263.01	   U41(mark(x0), x1)
744.20/263.01	   U41(x0, mark(x1))
744.20/263.01	   U41(active(x0), x1)
744.20/263.01	   U41(x0, active(x1))
744.20/263.01	   U42(mark(x0))
744.20/263.01	   U42(active(x0))
744.20/263.01	   U51(mark(x0))
744.20/263.01	   U51(active(x0))
744.20/263.01	   U61(mark(x0), x1)
744.20/263.01	   U61(x0, mark(x1))
744.20/263.01	   U61(active(x0), x1)
744.20/263.01	   U61(x0, active(x1))
744.20/263.01	   U62(mark(x0))
744.20/263.01	   U62(active(x0))
744.20/263.01	   U71(mark(x0), x1)
744.20/263.01	   U71(x0, mark(x1))
744.20/263.01	   U71(active(x0), x1)
744.20/263.01	   U71(x0, active(x1))
744.20/263.01	   U72(mark(x0), x1)
744.20/263.01	   U72(x0, mark(x1))
744.20/263.01	   U72(active(x0), x1)
744.20/263.01	   U72(x0, active(x1))
744.20/263.01	   U81(mark(x0), x1, x2)
744.20/263.01	   U81(x0, mark(x1), x2)
744.20/263.01	   U81(x0, x1, mark(x2))
744.20/263.01	   U81(active(x0), x1, x2)
744.20/263.01	   U81(x0, active(x1), x2)
744.20/263.01	   U81(x0, x1, active(x2))
744.20/263.01	   U82(mark(x0), x1, x2)
744.20/263.01	   U82(x0, mark(x1), x2)
744.20/263.01	   U82(x0, x1, mark(x2))
744.20/263.01	   U82(active(x0), x1, x2)
744.20/263.01	   U82(x0, active(x1), x2)
744.20/263.01	   U82(x0, x1, active(x2))
744.20/263.01	   U83(mark(x0), x1, x2)
744.20/263.01	   U83(x0, mark(x1), x2)
744.20/263.01	   U83(x0, x1, mark(x2))
744.20/263.01	   U83(active(x0), x1, x2)
744.20/263.01	   U83(x0, active(x1), x2)
744.20/263.01	   U83(x0, x1, active(x2))
744.20/263.01	   U84(mark(x0), x1, x2)
744.20/263.01	   U84(x0, mark(x1), x2)
744.20/263.01	   U84(x0, x1, mark(x2))
744.20/263.01	   U84(active(x0), x1, x2)
744.20/263.01	   U84(x0, active(x1), x2)
744.20/263.01	   U84(x0, x1, active(x2))
744.20/263.01	   s(mark(x0))
744.20/263.01	   s(active(x0))
744.20/263.01	   U91(mark(x0), x1)
744.20/263.01	   U91(x0, mark(x1))
744.20/263.01	   U91(active(x0), x1)
744.20/263.01	   U91(x0, active(x1))
744.20/263.01	   U92(mark(x0))
744.20/263.01	   U92(active(x0))
744.20/263.01	
744.20/263.01	We have to consider all minimal (P,Q,R)-chains.
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(287) QDPOrderProof (EQUIVALENT)
744.20/263.01	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.01	
744.20/263.01	
744.20/263.01	The following pairs can be oriented strictly and are deleted.
744.20/263.01	
744.20/263.01	   MARK(U101(X1, X2, X3)) -> ACTIVE(U101(mark(X1), X2, X3))
744.20/263.01	   MARK(U81(X1, X2, X3)) -> ACTIVE(U81(mark(X1), X2, X3))
744.20/263.01	The remaining pairs can at least be oriented weakly.
744.20/263.01	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.01	
744.20/263.01	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.20/263.01	POL( U101_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.20/263.01	POL( U102_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U11_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U12_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U13_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U14_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U21_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U22_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U31_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U32_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U33_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U34_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.01	POL( U35_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U41_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U61_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.01	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/263.01	POL( mark_1(x_1) ) = 0
744.20/263.01	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.20/263.01	POL( tt ) = 0
744.20/263.01	POL( isNatKind_1(x_1) ) = 0
744.20/263.01	POL( U103_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + 2x_3 - 2}
744.20/263.01	POL( isNat_1(x_1) ) = 0
744.20/263.01	POL( U104_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 - 2}
744.20/263.01	POL( plus_2(x_1, x_2) ) = x_1 + x_2 + 2
744.20/263.01	POL( x_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.20/263.01	POL( U16_1(x_1) ) = x_1 + 1
744.20/263.01	POL( U23_1(x_1) ) = 2x_1 + 1
744.20/263.01	POL( U36_1(x_1) ) = x_1 + 1
744.20/263.01	POL( U42_1(x_1) ) = 2x_1 + 1
744.20/263.01	POL( U62_1(x_1) ) = x_1 + 1
744.20/263.01	POL( U71_2(x_1, x_2) ) = 2x_1 + 2
744.20/263.01	POL( U72_2(x_1, x_2) ) = 2
744.20/263.01	POL( U82_3(x_1, ..., x_3) ) = 2
744.20/263.01	POL( U83_3(x_1, ..., x_3) ) = x_2 + 2x_3 + 2
744.20/263.01	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( s_1(x_1) ) = max{0, x_1 - 1}
744.20/263.01	POL( U91_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2}
744.20/263.01	POL( U92_1(x_1) ) = max{0, x_1 - 2}
744.20/263.01	POL( U51_1(x_1) ) = 2x_1 + 1
744.20/263.01	POL( 0 ) = 2
744.20/263.01	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.20/263.01	
744.20/263.01	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.01	none
744.20/263.01	
744.20/263.01	
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(288)
744.20/263.01	Obligation:
744.20/263.01	Q DP problem:
744.20/263.01	The TRS P consists of the following rules:
744.20/263.01	
744.20/263.01	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.01	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.01	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.01	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.01	   MARK(U16(X)) -> MARK(X)
744.20/263.01	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.01	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.01	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.01	   MARK(U23(X)) -> MARK(X)
744.20/263.01	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.01	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.01	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.01	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.01	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.01	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.01	   MARK(U36(X)) -> MARK(X)
744.20/263.01	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.01	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.01	   MARK(U42(X)) -> MARK(X)
744.20/263.01	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.01	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.01	   MARK(U62(X)) -> MARK(X)
744.20/263.01	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.01	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U51(X)) -> MARK(X)
744.20/263.01	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.01	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.01	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.01	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.01	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.01	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.01	
744.20/263.01	The TRS R consists of the following rules:
744.20/263.01	
744.20/263.01	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.01	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.01	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.01	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.01	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.01	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.01	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.01	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.01	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.01	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.01	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.01	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.01	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.01	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.01	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.01	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.01	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.01	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.01	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.01	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.01	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.01	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.01	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.01	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.01	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.01	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.01	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.01	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.01	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.01	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.01	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.01	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.01	   active(U72(tt, N)) -> mark(N)
744.20/263.01	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.01	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.01	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.01	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.01	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.01	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.01	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.01	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.01	   mark(s(X)) -> active(s(mark(X)))
744.20/263.01	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.01	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.01	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.01	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.01	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.01	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.01	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.01	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.01	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.01	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.01	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.01	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.01	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.01	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.01	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.01	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.01	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.01	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.01	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.01	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.01	   mark(isNat(X)) -> active(isNat(X))
744.20/263.01	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.01	   mark(tt) -> active(tt)
744.20/263.01	   mark(0) -> active(0)
744.20/263.01	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.01	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.01	   active(U16(tt)) -> mark(tt)
744.20/263.01	   active(U23(tt)) -> mark(tt)
744.20/263.01	   active(U36(tt)) -> mark(tt)
744.20/263.01	   active(U42(tt)) -> mark(tt)
744.20/263.01	   active(U51(tt)) -> mark(tt)
744.20/263.01	   active(U62(tt)) -> mark(tt)
744.20/263.01	   active(U92(tt)) -> mark(0)
744.20/263.01	   active(isNat(0)) -> mark(tt)
744.20/263.01	   active(isNatKind(0)) -> mark(tt)
744.20/263.01	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.01	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.01	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.01	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.01	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.01	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.01	   U16(active(X)) -> U16(X)
744.20/263.01	   U16(mark(X)) -> U16(X)
744.20/263.01	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.01	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.01	   U23(active(X)) -> U23(X)
744.20/263.01	   U23(mark(X)) -> U23(X)
744.20/263.01	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.01	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.01	   U36(active(X)) -> U36(X)
744.20/263.01	   U36(mark(X)) -> U36(X)
744.20/263.01	   U42(active(X)) -> U42(X)
744.20/263.01	   U42(mark(X)) -> U42(X)
744.20/263.01	   U62(active(X)) -> U62(X)
744.20/263.01	   U62(mark(X)) -> U62(X)
744.20/263.01	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.01	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.01	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.01	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.01	   s(active(X)) -> s(X)
744.20/263.01	   s(mark(X)) -> s(X)
744.20/263.01	   U92(active(X)) -> U92(X)
744.20/263.01	   U92(mark(X)) -> U92(X)
744.20/263.01	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.01	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.01	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.01	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.01	   U51(active(X)) -> U51(X)
744.20/263.01	   U51(mark(X)) -> U51(X)
744.20/263.01	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.01	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.01	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.01	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.01	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.01	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.01	   x(active(X1), X2) -> x(X1, X2)
744.20/263.01	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.01	
744.20/263.01	The set Q consists of the following terms:
744.20/263.01	
744.20/263.01	   active(U101(tt, x0, x1))
744.20/263.01	   active(U102(tt, x0, x1))
744.20/263.01	   active(U103(tt, x0, x1))
744.20/263.01	   active(U104(tt, x0, x1))
744.20/263.01	   active(U11(tt, x0, x1))
744.20/263.01	   active(U12(tt, x0, x1))
744.20/263.01	   active(U13(tt, x0, x1))
744.20/263.01	   active(U14(tt, x0, x1))
744.20/263.01	   active(U15(tt, x0))
744.20/263.01	   active(U16(tt))
744.20/263.01	   active(U21(tt, x0))
744.20/263.01	   active(U22(tt, x0))
744.20/263.01	   active(U23(tt))
744.20/263.01	   active(U31(tt, x0, x1))
744.20/263.01	   active(U32(tt, x0, x1))
744.20/263.01	   active(U33(tt, x0, x1))
744.20/263.01	   active(U34(tt, x0, x1))
744.20/263.01	   active(U35(tt, x0))
744.20/263.01	   active(U36(tt))
744.20/263.01	   active(U41(tt, x0))
744.20/263.01	   active(U42(tt))
744.20/263.01	   active(U51(tt))
744.20/263.01	   active(U61(tt, x0))
744.20/263.01	   active(U62(tt))
744.20/263.01	   active(U71(tt, x0))
744.20/263.01	   active(U72(tt, x0))
744.20/263.01	   active(U81(tt, x0, x1))
744.20/263.01	   active(U82(tt, x0, x1))
744.20/263.01	   active(U83(tt, x0, x1))
744.20/263.01	   active(U84(tt, x0, x1))
744.20/263.01	   active(U91(tt, x0))
744.20/263.01	   active(U92(tt))
744.20/263.01	   active(isNat(0))
744.20/263.01	   active(isNat(plus(x0, x1)))
744.20/263.01	   active(isNat(s(x0)))
744.20/263.01	   active(isNat(x(x0, x1)))
744.20/263.01	   active(isNatKind(0))
744.20/263.01	   active(isNatKind(plus(x0, x1)))
744.20/263.01	   active(isNatKind(s(x0)))
744.20/263.01	   active(isNatKind(x(x0, x1)))
744.20/263.01	   active(plus(x0, 0))
744.20/263.01	   active(plus(x0, s(x1)))
744.20/263.01	   active(x(x0, 0))
744.20/263.01	   active(x(x0, s(x1)))
744.20/263.01	   mark(U101(x0, x1, x2))
744.20/263.01	   mark(tt)
744.20/263.01	   mark(U102(x0, x1, x2))
744.20/263.01	   mark(isNatKind(x0))
744.20/263.01	   mark(U103(x0, x1, x2))
744.20/263.01	   mark(isNat(x0))
744.20/263.01	   mark(U104(x0, x1, x2))
744.20/263.01	   mark(plus(x0, x1))
744.20/263.01	   mark(x(x0, x1))
744.20/263.01	   mark(U11(x0, x1, x2))
744.20/263.01	   mark(U12(x0, x1, x2))
744.20/263.01	   mark(U13(x0, x1, x2))
744.20/263.01	   mark(U14(x0, x1, x2))
744.20/263.01	   mark(U15(x0, x1))
744.20/263.01	   mark(U16(x0))
744.20/263.01	   mark(U21(x0, x1))
744.20/263.01	   mark(U22(x0, x1))
744.20/263.01	   mark(U23(x0))
744.20/263.01	   mark(U31(x0, x1, x2))
744.20/263.01	   mark(U32(x0, x1, x2))
744.20/263.01	   mark(U33(x0, x1, x2))
744.20/263.01	   mark(U34(x0, x1, x2))
744.20/263.01	   mark(U35(x0, x1))
744.20/263.01	   mark(U36(x0))
744.20/263.01	   mark(U41(x0, x1))
744.20/263.01	   mark(U42(x0))
744.20/263.01	   mark(U51(x0))
744.20/263.01	   mark(U61(x0, x1))
744.20/263.01	   mark(U62(x0))
744.20/263.01	   mark(U71(x0, x1))
744.20/263.01	   mark(U72(x0, x1))
744.20/263.01	   mark(U81(x0, x1, x2))
744.20/263.01	   mark(U82(x0, x1, x2))
744.20/263.01	   mark(U83(x0, x1, x2))
744.20/263.01	   mark(U84(x0, x1, x2))
744.20/263.01	   mark(s(x0))
744.20/263.01	   mark(U91(x0, x1))
744.20/263.01	   mark(U92(x0))
744.20/263.01	   mark(0)
744.20/263.01	   U101(mark(x0), x1, x2)
744.20/263.01	   U101(x0, mark(x1), x2)
744.20/263.01	   U101(x0, x1, mark(x2))
744.20/263.01	   U101(active(x0), x1, x2)
744.20/263.01	   U101(x0, active(x1), x2)
744.20/263.01	   U101(x0, x1, active(x2))
744.20/263.01	   U102(mark(x0), x1, x2)
744.20/263.01	   U102(x0, mark(x1), x2)
744.20/263.01	   U102(x0, x1, mark(x2))
744.20/263.01	   U102(active(x0), x1, x2)
744.20/263.01	   U102(x0, active(x1), x2)
744.20/263.01	   U102(x0, x1, active(x2))
744.20/263.01	   isNatKind(mark(x0))
744.20/263.01	   isNatKind(active(x0))
744.20/263.01	   U103(mark(x0), x1, x2)
744.20/263.01	   U103(x0, mark(x1), x2)
744.20/263.01	   U103(x0, x1, mark(x2))
744.20/263.01	   U103(active(x0), x1, x2)
744.20/263.01	   U103(x0, active(x1), x2)
744.20/263.01	   U103(x0, x1, active(x2))
744.20/263.01	   isNat(mark(x0))
744.20/263.01	   isNat(active(x0))
744.20/263.01	   U104(mark(x0), x1, x2)
744.20/263.01	   U104(x0, mark(x1), x2)
744.20/263.01	   U104(x0, x1, mark(x2))
744.20/263.01	   U104(active(x0), x1, x2)
744.20/263.01	   U104(x0, active(x1), x2)
744.20/263.01	   U104(x0, x1, active(x2))
744.20/263.01	   plus(mark(x0), x1)
744.20/263.01	   plus(x0, mark(x1))
744.20/263.01	   plus(active(x0), x1)
744.20/263.01	   plus(x0, active(x1))
744.20/263.01	   x(mark(x0), x1)
744.20/263.01	   x(x0, mark(x1))
744.20/263.01	   x(active(x0), x1)
744.20/263.01	   x(x0, active(x1))
744.20/263.01	   U11(mark(x0), x1, x2)
744.20/263.01	   U11(x0, mark(x1), x2)
744.20/263.01	   U11(x0, x1, mark(x2))
744.20/263.01	   U11(active(x0), x1, x2)
744.20/263.01	   U11(x0, active(x1), x2)
744.20/263.01	   U11(x0, x1, active(x2))
744.20/263.01	   U12(mark(x0), x1, x2)
744.20/263.01	   U12(x0, mark(x1), x2)
744.20/263.01	   U12(x0, x1, mark(x2))
744.20/263.01	   U12(active(x0), x1, x2)
744.20/263.01	   U12(x0, active(x1), x2)
744.20/263.01	   U12(x0, x1, active(x2))
744.20/263.01	   U13(mark(x0), x1, x2)
744.20/263.01	   U13(x0, mark(x1), x2)
744.20/263.01	   U13(x0, x1, mark(x2))
744.20/263.01	   U13(active(x0), x1, x2)
744.20/263.01	   U13(x0, active(x1), x2)
744.20/263.01	   U13(x0, x1, active(x2))
744.20/263.01	   U14(mark(x0), x1, x2)
744.20/263.01	   U14(x0, mark(x1), x2)
744.20/263.01	   U14(x0, x1, mark(x2))
744.20/263.01	   U14(active(x0), x1, x2)
744.20/263.01	   U14(x0, active(x1), x2)
744.20/263.01	   U14(x0, x1, active(x2))
744.20/263.01	   U15(mark(x0), x1)
744.20/263.01	   U15(x0, mark(x1))
744.20/263.01	   U15(active(x0), x1)
744.20/263.01	   U15(x0, active(x1))
744.20/263.01	   U16(mark(x0))
744.20/263.01	   U16(active(x0))
744.20/263.01	   U21(mark(x0), x1)
744.20/263.01	   U21(x0, mark(x1))
744.20/263.01	   U21(active(x0), x1)
744.20/263.01	   U21(x0, active(x1))
744.20/263.01	   U22(mark(x0), x1)
744.20/263.01	   U22(x0, mark(x1))
744.20/263.01	   U22(active(x0), x1)
744.20/263.01	   U22(x0, active(x1))
744.20/263.01	   U23(mark(x0))
744.20/263.01	   U23(active(x0))
744.20/263.01	   U31(mark(x0), x1, x2)
744.20/263.01	   U31(x0, mark(x1), x2)
744.20/263.01	   U31(x0, x1, mark(x2))
744.20/263.01	   U31(active(x0), x1, x2)
744.20/263.01	   U31(x0, active(x1), x2)
744.20/263.01	   U31(x0, x1, active(x2))
744.20/263.01	   U32(mark(x0), x1, x2)
744.20/263.01	   U32(x0, mark(x1), x2)
744.20/263.01	   U32(x0, x1, mark(x2))
744.20/263.01	   U32(active(x0), x1, x2)
744.20/263.01	   U32(x0, active(x1), x2)
744.20/263.01	   U32(x0, x1, active(x2))
744.20/263.01	   U33(mark(x0), x1, x2)
744.20/263.01	   U33(x0, mark(x1), x2)
744.20/263.01	   U33(x0, x1, mark(x2))
744.20/263.01	   U33(active(x0), x1, x2)
744.20/263.01	   U33(x0, active(x1), x2)
744.20/263.01	   U33(x0, x1, active(x2))
744.20/263.01	   U34(mark(x0), x1, x2)
744.20/263.01	   U34(x0, mark(x1), x2)
744.20/263.01	   U34(x0, x1, mark(x2))
744.20/263.01	   U34(active(x0), x1, x2)
744.20/263.01	   U34(x0, active(x1), x2)
744.20/263.01	   U34(x0, x1, active(x2))
744.20/263.01	   U35(mark(x0), x1)
744.20/263.01	   U35(x0, mark(x1))
744.20/263.01	   U35(active(x0), x1)
744.20/263.01	   U35(x0, active(x1))
744.20/263.01	   U36(mark(x0))
744.20/263.01	   U36(active(x0))
744.20/263.01	   U41(mark(x0), x1)
744.20/263.01	   U41(x0, mark(x1))
744.20/263.01	   U41(active(x0), x1)
744.20/263.01	   U41(x0, active(x1))
744.20/263.01	   U42(mark(x0))
744.20/263.01	   U42(active(x0))
744.20/263.01	   U51(mark(x0))
744.20/263.01	   U51(active(x0))
744.20/263.01	   U61(mark(x0), x1)
744.20/263.01	   U61(x0, mark(x1))
744.20/263.01	   U61(active(x0), x1)
744.20/263.01	   U61(x0, active(x1))
744.20/263.01	   U62(mark(x0))
744.20/263.01	   U62(active(x0))
744.20/263.01	   U71(mark(x0), x1)
744.20/263.01	   U71(x0, mark(x1))
744.20/263.01	   U71(active(x0), x1)
744.20/263.01	   U71(x0, active(x1))
744.20/263.01	   U72(mark(x0), x1)
744.20/263.01	   U72(x0, mark(x1))
744.20/263.01	   U72(active(x0), x1)
744.20/263.01	   U72(x0, active(x1))
744.20/263.01	   U81(mark(x0), x1, x2)
744.20/263.01	   U81(x0, mark(x1), x2)
744.20/263.01	   U81(x0, x1, mark(x2))
744.20/263.01	   U81(active(x0), x1, x2)
744.20/263.01	   U81(x0, active(x1), x2)
744.20/263.01	   U81(x0, x1, active(x2))
744.20/263.01	   U82(mark(x0), x1, x2)
744.20/263.01	   U82(x0, mark(x1), x2)
744.20/263.01	   U82(x0, x1, mark(x2))
744.20/263.01	   U82(active(x0), x1, x2)
744.20/263.01	   U82(x0, active(x1), x2)
744.20/263.01	   U82(x0, x1, active(x2))
744.20/263.01	   U83(mark(x0), x1, x2)
744.20/263.01	   U83(x0, mark(x1), x2)
744.20/263.01	   U83(x0, x1, mark(x2))
744.20/263.01	   U83(active(x0), x1, x2)
744.20/263.01	   U83(x0, active(x1), x2)
744.20/263.01	   U83(x0, x1, active(x2))
744.20/263.01	   U84(mark(x0), x1, x2)
744.20/263.01	   U84(x0, mark(x1), x2)
744.20/263.01	   U84(x0, x1, mark(x2))
744.20/263.01	   U84(active(x0), x1, x2)
744.20/263.01	   U84(x0, active(x1), x2)
744.20/263.01	   U84(x0, x1, active(x2))
744.20/263.01	   s(mark(x0))
744.20/263.01	   s(active(x0))
744.20/263.01	   U91(mark(x0), x1)
744.20/263.01	   U91(x0, mark(x1))
744.20/263.01	   U91(active(x0), x1)
744.20/263.01	   U91(x0, active(x1))
744.20/263.01	   U92(mark(x0))
744.20/263.01	   U92(active(x0))
744.20/263.01	
744.20/263.01	We have to consider all minimal (P,Q,R)-chains.
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(289) QDPOrderProof (EQUIVALENT)
744.20/263.01	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.01	
744.20/263.01	
744.20/263.01	The following pairs can be oriented strictly and are deleted.
744.20/263.01	
744.20/263.01	   ACTIVE(U101(tt, M, N)) -> MARK(U102(isNatKind(M), M, N))
744.20/263.01	The remaining pairs can at least be oriented weakly.
744.20/263.01	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.01	
744.20/263.01	POL( ACTIVE_1(x_1) ) = x_1 + 2
744.20/263.01	POL( U102_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U11_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U14_3(x_1, ..., x_3) ) = 0
744.20/263.01	POL( U15_2(x_1, x_2) ) = max{0, -2}
744.20/263.01	POL( U21_2(x_1, x_2) ) = max{0, -2}
744.20/263.01	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.20/263.01	POL( U31_3(x_1, ..., x_3) ) = 0
744.20/263.01	POL( U32_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U33_3(x_1, ..., x_3) ) = max{0, -2}
744.20/263.01	POL( U34_3(x_1, ..., x_3) ) = 0
744.20/263.01	POL( U35_2(x_1, x_2) ) = 0
744.20/263.01	POL( U41_2(x_1, x_2) ) = max{0, -2}
744.20/263.01	POL( U61_2(x_1, x_2) ) = max{0, -2}
744.20/263.01	POL( mark_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( active_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( U101_3(x_1, ..., x_3) ) = 1
744.20/263.01	POL( tt ) = 0
744.20/263.01	POL( isNatKind_1(x_1) ) = 0
744.20/263.01	POL( U103_3(x_1, ..., x_3) ) = x_1 + 2x_2 + x_3 + 2
744.20/263.01	POL( isNat_1(x_1) ) = 0
744.20/263.01	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_2 + 2x_3 - 2}
744.20/263.01	POL( plus_2(x_1, x_2) ) = max{0, x_1 - 2}
744.20/263.01	POL( x_2(x_1, x_2) ) = max{0, x_2 - 2}
744.20/263.01	POL( U16_1(x_1) ) = 2
744.20/263.01	POL( U23_1(x_1) ) = x_1 + 2
744.20/263.01	POL( U36_1(x_1) ) = max{0, x_1 - 2}
744.20/263.01	POL( U42_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( U62_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( U71_2(x_1, x_2) ) = 2
744.20/263.01	POL( U72_2(x_1, x_2) ) = max{0, x_1 - 2}
744.20/263.01	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/263.01	POL( U82_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.20/263.01	POL( U83_3(x_1, ..., x_3) ) = x_2 + 2
744.20/263.01	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.20/263.01	POL( U91_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2}
744.20/263.01	POL( U92_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.01	POL( U51_1(x_1) ) = max{0, x_1 - 2}
744.20/263.01	POL( 0 ) = 0
744.20/263.01	POL( MARK_1(x_1) ) = 2
744.20/263.01	
744.20/263.01	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.01	
744.20/263.01	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.01	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.01	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.01	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.01	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.01	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.01	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.01	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.01	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.01	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.01	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.01	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.01	
744.20/263.01	
744.20/263.01	----------------------------------------
744.20/263.01	
744.20/263.01	(290)
744.20/263.01	Obligation:
744.20/263.01	Q DP problem:
744.20/263.01	The TRS P consists of the following rules:
744.20/263.01	
744.20/263.01	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.01	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.01	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.01	   MARK(U16(X)) -> MARK(X)
744.20/263.01	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.01	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.01	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.01	   MARK(U23(X)) -> MARK(X)
744.20/263.01	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.01	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.01	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.01	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.01	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.01	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.01	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.01	   MARK(U36(X)) -> MARK(X)
744.20/263.01	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.01	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.01	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.01	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.01	   MARK(U42(X)) -> MARK(X)
744.20/263.01	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.01	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.01	   MARK(U62(X)) -> MARK(X)
744.20/263.01	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.01	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.01	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.01	   MARK(U51(X)) -> MARK(X)
744.20/263.01	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.01	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.01	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.01	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.01	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.01	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.01	
744.20/263.01	The TRS R consists of the following rules:
744.20/263.01	
744.20/263.01	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.01	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.01	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.01	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.01	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.01	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.01	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.01	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.01	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.01	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.01	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.01	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.01	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.01	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.01	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.01	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.01	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.01	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.01	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.01	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.01	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.01	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.01	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.01	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.01	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.01	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.01	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.01	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.01	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.01	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.01	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.01	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.01	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.01	   active(U72(tt, N)) -> mark(N)
744.20/263.01	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.01	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.01	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.01	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.01	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.01	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.01	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.01	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.01	   mark(s(X)) -> active(s(mark(X)))
744.20/263.01	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.01	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.01	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.01	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.01	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.01	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.01	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.01	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.01	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.01	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.01	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.01	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.01	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.01	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.01	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.01	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.01	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.01	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.01	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.01	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.01	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.01	   mark(isNat(X)) -> active(isNat(X))
744.20/263.01	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.01	   mark(tt) -> active(tt)
744.20/263.01	   mark(0) -> active(0)
744.20/263.01	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.01	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.01	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.01	   active(U16(tt)) -> mark(tt)
744.20/263.01	   active(U23(tt)) -> mark(tt)
744.20/263.01	   active(U36(tt)) -> mark(tt)
744.20/263.01	   active(U42(tt)) -> mark(tt)
744.20/263.01	   active(U51(tt)) -> mark(tt)
744.20/263.01	   active(U62(tt)) -> mark(tt)
744.20/263.01	   active(U92(tt)) -> mark(0)
744.20/263.01	   active(isNat(0)) -> mark(tt)
744.20/263.01	   active(isNatKind(0)) -> mark(tt)
744.20/263.01	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.01	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.01	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.01	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.01	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.01	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.01	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.01	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.01	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.01	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.01	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.01	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.01	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.01	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.01	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.01	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.01	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.01	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.01	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.01	   U16(active(X)) -> U16(X)
744.20/263.01	   U16(mark(X)) -> U16(X)
744.20/263.01	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.01	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.01	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.01	   U23(active(X)) -> U23(X)
744.20/263.01	   U23(mark(X)) -> U23(X)
744.20/263.01	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.01	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.01	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.01	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.01	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.01	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.01	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.01	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.01	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.01	   U36(active(X)) -> U36(X)
744.20/263.01	   U36(mark(X)) -> U36(X)
744.20/263.01	   U42(active(X)) -> U42(X)
744.20/263.01	   U42(mark(X)) -> U42(X)
744.20/263.01	   U62(active(X)) -> U62(X)
744.20/263.01	   U62(mark(X)) -> U62(X)
744.20/263.01	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.01	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.01	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.01	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.01	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.01	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.01	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.01	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.01	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.01	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.01	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.01	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.01	   s(active(X)) -> s(X)
744.20/263.01	   s(mark(X)) -> s(X)
744.20/263.01	   U92(active(X)) -> U92(X)
744.20/263.01	   U92(mark(X)) -> U92(X)
744.20/263.01	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.01	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.01	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.01	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.01	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.01	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.01	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.01	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.01	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.01	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.01	   U51(active(X)) -> U51(X)
744.20/263.01	   U51(mark(X)) -> U51(X)
744.20/263.01	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.01	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.01	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.01	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.01	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.01	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.01	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.01	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.01	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.01	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.01	   x(active(X1), X2) -> x(X1, X2)
744.20/263.01	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.01	
744.20/263.01	The set Q consists of the following terms:
744.20/263.01	
744.20/263.01	   active(U101(tt, x0, x1))
744.20/263.01	   active(U102(tt, x0, x1))
744.20/263.01	   active(U103(tt, x0, x1))
744.20/263.01	   active(U104(tt, x0, x1))
744.20/263.01	   active(U11(tt, x0, x1))
744.20/263.01	   active(U12(tt, x0, x1))
744.20/263.01	   active(U13(tt, x0, x1))
744.20/263.01	   active(U14(tt, x0, x1))
744.20/263.01	   active(U15(tt, x0))
744.20/263.01	   active(U16(tt))
744.20/263.01	   active(U21(tt, x0))
744.20/263.01	   active(U22(tt, x0))
744.20/263.01	   active(U23(tt))
744.20/263.01	   active(U31(tt, x0, x1))
744.20/263.01	   active(U32(tt, x0, x1))
744.20/263.01	   active(U33(tt, x0, x1))
744.20/263.01	   active(U34(tt, x0, x1))
744.20/263.01	   active(U35(tt, x0))
744.20/263.01	   active(U36(tt))
744.20/263.01	   active(U41(tt, x0))
744.20/263.01	   active(U42(tt))
744.20/263.01	   active(U51(tt))
744.20/263.01	   active(U61(tt, x0))
744.20/263.01	   active(U62(tt))
744.20/263.01	   active(U71(tt, x0))
744.20/263.01	   active(U72(tt, x0))
744.20/263.01	   active(U81(tt, x0, x1))
744.20/263.01	   active(U82(tt, x0, x1))
744.20/263.01	   active(U83(tt, x0, x1))
744.20/263.01	   active(U84(tt, x0, x1))
744.20/263.01	   active(U91(tt, x0))
744.20/263.01	   active(U92(tt))
744.20/263.01	   active(isNat(0))
744.20/263.01	   active(isNat(plus(x0, x1)))
744.20/263.01	   active(isNat(s(x0)))
744.20/263.01	   active(isNat(x(x0, x1)))
744.20/263.01	   active(isNatKind(0))
744.20/263.01	   active(isNatKind(plus(x0, x1)))
744.20/263.01	   active(isNatKind(s(x0)))
744.20/263.01	   active(isNatKind(x(x0, x1)))
744.20/263.01	   active(plus(x0, 0))
744.20/263.01	   active(plus(x0, s(x1)))
744.20/263.01	   active(x(x0, 0))
744.20/263.01	   active(x(x0, s(x1)))
744.20/263.01	   mark(U101(x0, x1, x2))
744.20/263.01	   mark(tt)
744.20/263.01	   mark(U102(x0, x1, x2))
744.20/263.01	   mark(isNatKind(x0))
744.20/263.01	   mark(U103(x0, x1, x2))
744.20/263.01	   mark(isNat(x0))
744.20/263.01	   mark(U104(x0, x1, x2))
744.20/263.01	   mark(plus(x0, x1))
744.20/263.01	   mark(x(x0, x1))
744.20/263.01	   mark(U11(x0, x1, x2))
744.20/263.01	   mark(U12(x0, x1, x2))
744.20/263.01	   mark(U13(x0, x1, x2))
744.20/263.01	   mark(U14(x0, x1, x2))
744.20/263.01	   mark(U15(x0, x1))
744.20/263.01	   mark(U16(x0))
744.20/263.01	   mark(U21(x0, x1))
744.20/263.01	   mark(U22(x0, x1))
744.20/263.01	   mark(U23(x0))
744.20/263.01	   mark(U31(x0, x1, x2))
744.20/263.01	   mark(U32(x0, x1, x2))
744.20/263.01	   mark(U33(x0, x1, x2))
744.20/263.01	   mark(U34(x0, x1, x2))
744.20/263.01	   mark(U35(x0, x1))
744.20/263.01	   mark(U36(x0))
744.20/263.01	   mark(U41(x0, x1))
744.20/263.01	   mark(U42(x0))
744.20/263.01	   mark(U51(x0))
744.20/263.01	   mark(U61(x0, x1))
744.20/263.01	   mark(U62(x0))
744.20/263.01	   mark(U71(x0, x1))
744.20/263.01	   mark(U72(x0, x1))
744.20/263.01	   mark(U81(x0, x1, x2))
744.20/263.01	   mark(U82(x0, x1, x2))
744.20/263.01	   mark(U83(x0, x1, x2))
744.20/263.01	   mark(U84(x0, x1, x2))
744.20/263.01	   mark(s(x0))
744.20/263.01	   mark(U91(x0, x1))
744.20/263.01	   mark(U92(x0))
744.20/263.01	   mark(0)
744.20/263.01	   U101(mark(x0), x1, x2)
744.20/263.01	   U101(x0, mark(x1), x2)
744.20/263.01	   U101(x0, x1, mark(x2))
744.20/263.01	   U101(active(x0), x1, x2)
744.20/263.01	   U101(x0, active(x1), x2)
744.20/263.01	   U101(x0, x1, active(x2))
744.20/263.01	   U102(mark(x0), x1, x2)
744.20/263.01	   U102(x0, mark(x1), x2)
744.20/263.01	   U102(x0, x1, mark(x2))
744.20/263.01	   U102(active(x0), x1, x2)
744.20/263.01	   U102(x0, active(x1), x2)
744.20/263.01	   U102(x0, x1, active(x2))
744.20/263.01	   isNatKind(mark(x0))
744.20/263.01	   isNatKind(active(x0))
744.20/263.01	   U103(mark(x0), x1, x2)
744.20/263.01	   U103(x0, mark(x1), x2)
744.20/263.01	   U103(x0, x1, mark(x2))
744.20/263.01	   U103(active(x0), x1, x2)
744.20/263.01	   U103(x0, active(x1), x2)
744.20/263.01	   U103(x0, x1, active(x2))
744.20/263.01	   isNat(mark(x0))
744.20/263.01	   isNat(active(x0))
744.20/263.01	   U104(mark(x0), x1, x2)
744.20/263.01	   U104(x0, mark(x1), x2)
744.20/263.01	   U104(x0, x1, mark(x2))
744.20/263.01	   U104(active(x0), x1, x2)
744.20/263.01	   U104(x0, active(x1), x2)
744.20/263.01	   U104(x0, x1, active(x2))
744.20/263.01	   plus(mark(x0), x1)
744.20/263.01	   plus(x0, mark(x1))
744.20/263.01	   plus(active(x0), x1)
744.20/263.01	   plus(x0, active(x1))
744.20/263.01	   x(mark(x0), x1)
744.20/263.01	   x(x0, mark(x1))
744.20/263.01	   x(active(x0), x1)
744.20/263.01	   x(x0, active(x1))
744.20/263.01	   U11(mark(x0), x1, x2)
744.20/263.01	   U11(x0, mark(x1), x2)
744.20/263.01	   U11(x0, x1, mark(x2))
744.20/263.01	   U11(active(x0), x1, x2)
744.20/263.01	   U11(x0, active(x1), x2)
744.20/263.01	   U11(x0, x1, active(x2))
744.20/263.01	   U12(mark(x0), x1, x2)
744.20/263.01	   U12(x0, mark(x1), x2)
744.20/263.01	   U12(x0, x1, mark(x2))
744.20/263.01	   U12(active(x0), x1, x2)
744.20/263.01	   U12(x0, active(x1), x2)
744.20/263.01	   U12(x0, x1, active(x2))
744.20/263.01	   U13(mark(x0), x1, x2)
744.20/263.01	   U13(x0, mark(x1), x2)
744.20/263.01	   U13(x0, x1, mark(x2))
744.20/263.01	   U13(active(x0), x1, x2)
744.20/263.01	   U13(x0, active(x1), x2)
744.20/263.01	   U13(x0, x1, active(x2))
744.20/263.01	   U14(mark(x0), x1, x2)
744.20/263.01	   U14(x0, mark(x1), x2)
744.20/263.01	   U14(x0, x1, mark(x2))
744.20/263.01	   U14(active(x0), x1, x2)
744.20/263.01	   U14(x0, active(x1), x2)
744.20/263.01	   U14(x0, x1, active(x2))
744.20/263.01	   U15(mark(x0), x1)
744.20/263.01	   U15(x0, mark(x1))
744.20/263.01	   U15(active(x0), x1)
744.20/263.01	   U15(x0, active(x1))
744.20/263.01	   U16(mark(x0))
744.20/263.01	   U16(active(x0))
744.20/263.01	   U21(mark(x0), x1)
744.20/263.01	   U21(x0, mark(x1))
744.20/263.01	   U21(active(x0), x1)
744.20/263.01	   U21(x0, active(x1))
744.20/263.01	   U22(mark(x0), x1)
744.20/263.01	   U22(x0, mark(x1))
744.20/263.01	   U22(active(x0), x1)
744.20/263.01	   U22(x0, active(x1))
744.20/263.01	   U23(mark(x0))
744.20/263.01	   U23(active(x0))
744.20/263.01	   U31(mark(x0), x1, x2)
744.20/263.01	   U31(x0, mark(x1), x2)
744.20/263.01	   U31(x0, x1, mark(x2))
744.20/263.01	   U31(active(x0), x1, x2)
744.20/263.01	   U31(x0, active(x1), x2)
744.20/263.01	   U31(x0, x1, active(x2))
744.20/263.01	   U32(mark(x0), x1, x2)
744.20/263.01	   U32(x0, mark(x1), x2)
744.20/263.01	   U32(x0, x1, mark(x2))
744.20/263.01	   U32(active(x0), x1, x2)
744.20/263.01	   U32(x0, active(x1), x2)
744.20/263.01	   U32(x0, x1, active(x2))
744.20/263.01	   U33(mark(x0), x1, x2)
744.20/263.01	   U33(x0, mark(x1), x2)
744.20/263.01	   U33(x0, x1, mark(x2))
744.20/263.01	   U33(active(x0), x1, x2)
744.20/263.01	   U33(x0, active(x1), x2)
744.20/263.01	   U33(x0, x1, active(x2))
744.20/263.01	   U34(mark(x0), x1, x2)
744.20/263.01	   U34(x0, mark(x1), x2)
744.20/263.01	   U34(x0, x1, mark(x2))
744.20/263.01	   U34(active(x0), x1, x2)
744.20/263.02	   U34(x0, active(x1), x2)
744.20/263.02	   U34(x0, x1, active(x2))
744.20/263.02	   U35(mark(x0), x1)
744.20/263.02	   U35(x0, mark(x1))
744.20/263.02	   U35(active(x0), x1)
744.20/263.02	   U35(x0, active(x1))
744.20/263.02	   U36(mark(x0))
744.20/263.02	   U36(active(x0))
744.20/263.02	   U41(mark(x0), x1)
744.20/263.02	   U41(x0, mark(x1))
744.20/263.02	   U41(active(x0), x1)
744.20/263.02	   U41(x0, active(x1))
744.20/263.02	   U42(mark(x0))
744.20/263.02	   U42(active(x0))
744.20/263.02	   U51(mark(x0))
744.20/263.02	   U51(active(x0))
744.20/263.02	   U61(mark(x0), x1)
744.20/263.02	   U61(x0, mark(x1))
744.20/263.02	   U61(active(x0), x1)
744.20/263.02	   U61(x0, active(x1))
744.20/263.02	   U62(mark(x0))
744.20/263.02	   U62(active(x0))
744.20/263.02	   U71(mark(x0), x1)
744.20/263.02	   U71(x0, mark(x1))
744.20/263.02	   U71(active(x0), x1)
744.20/263.02	   U71(x0, active(x1))
744.20/263.02	   U72(mark(x0), x1)
744.20/263.02	   U72(x0, mark(x1))
744.20/263.02	   U72(active(x0), x1)
744.20/263.02	   U72(x0, active(x1))
744.20/263.02	   U81(mark(x0), x1, x2)
744.20/263.02	   U81(x0, mark(x1), x2)
744.20/263.02	   U81(x0, x1, mark(x2))
744.20/263.02	   U81(active(x0), x1, x2)
744.20/263.02	   U81(x0, active(x1), x2)
744.20/263.02	   U81(x0, x1, active(x2))
744.20/263.02	   U82(mark(x0), x1, x2)
744.20/263.02	   U82(x0, mark(x1), x2)
744.20/263.02	   U82(x0, x1, mark(x2))
744.20/263.02	   U82(active(x0), x1, x2)
744.20/263.02	   U82(x0, active(x1), x2)
744.20/263.02	   U82(x0, x1, active(x2))
744.20/263.02	   U83(mark(x0), x1, x2)
744.20/263.02	   U83(x0, mark(x1), x2)
744.20/263.02	   U83(x0, x1, mark(x2))
744.20/263.02	   U83(active(x0), x1, x2)
744.20/263.02	   U83(x0, active(x1), x2)
744.20/263.02	   U83(x0, x1, active(x2))
744.20/263.02	   U84(mark(x0), x1, x2)
744.20/263.02	   U84(x0, mark(x1), x2)
744.20/263.02	   U84(x0, x1, mark(x2))
744.20/263.02	   U84(active(x0), x1, x2)
744.20/263.02	   U84(x0, active(x1), x2)
744.20/263.02	   U84(x0, x1, active(x2))
744.20/263.02	   s(mark(x0))
744.20/263.02	   s(active(x0))
744.20/263.02	   U91(mark(x0), x1)
744.20/263.02	   U91(x0, mark(x1))
744.20/263.02	   U91(active(x0), x1)
744.20/263.02	   U91(x0, active(x1))
744.20/263.02	   U92(mark(x0))
744.20/263.02	   U92(active(x0))
744.20/263.02	
744.20/263.02	We have to consider all minimal (P,Q,R)-chains.
744.20/263.02	----------------------------------------
744.20/263.02	
744.20/263.02	(291) QDPOrderProof (EQUIVALENT)
744.20/263.02	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.02	
744.20/263.02	
744.20/263.02	The following pairs can be oriented strictly and are deleted.
744.20/263.02	
744.20/263.02	   MARK(U102(X1, X2, X3)) -> ACTIVE(U102(mark(X1), X2, X3))
744.20/263.02	The remaining pairs can at least be oriented weakly.
744.20/263.02	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.02	
744.20/263.02	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.20/263.02	POL( U102_3(x_1, ..., x_3) ) = 2x_3 + 2
744.20/263.02	POL( U11_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.02	POL( U12_3(x_1, ..., x_3) ) = x_1 + 1
744.20/263.02	POL( U13_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.02	POL( U14_3(x_1, ..., x_3) ) = x_1 + 1
744.20/263.02	POL( U15_2(x_1, x_2) ) = x_1 + 1
744.20/263.02	POL( U21_2(x_1, x_2) ) = x_1 + 1
744.20/263.02	POL( U22_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.02	POL( U31_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.02	POL( U32_3(x_1, ..., x_3) ) = x_1 + 1
744.20/263.02	POL( U33_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.02	POL( U34_3(x_1, ..., x_3) ) = x_1 + 1
744.20/263.02	POL( U35_2(x_1, x_2) ) = x_1 + 1
744.20/263.02	POL( U41_2(x_1, x_2) ) = x_1 + 1
744.20/263.02	POL( U61_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.02	POL( mark_1(x_1) ) = 0
744.20/263.02	POL( active_1(x_1) ) = 2
744.20/263.02	POL( U101_3(x_1, ..., x_3) ) = x_1 + 2
744.20/263.02	POL( tt ) = 1
744.20/263.02	POL( isNatKind_1(x_1) ) = 0
744.20/263.02	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + 2x_3 - 2}
744.20/263.02	POL( isNat_1(x_1) ) = 0
744.20/263.02	POL( U104_3(x_1, ..., x_3) ) = x_1 + x_2 + x_3 + 1
744.20/263.02	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.20/263.02	POL( x_2(x_1, x_2) ) = 2
744.20/263.02	POL( U16_1(x_1) ) = 2x_1 + 1
744.20/263.02	POL( U23_1(x_1) ) = x_1 + 1
744.20/263.02	POL( U36_1(x_1) ) = x_1 + 1
744.20/263.02	POL( U42_1(x_1) ) = x_1 + 1
744.20/263.02	POL( U62_1(x_1) ) = x_1 + 1
744.20/263.02	POL( U71_2(x_1, x_2) ) = 2
744.20/263.02	POL( U72_2(x_1, x_2) ) = 2
744.20/263.02	POL( U81_3(x_1, ..., x_3) ) = 2x_1 + 2x_2 + 2
744.20/263.02	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 - 2}
744.20/263.02	POL( U83_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.20/263.02	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.20/263.02	POL( s_1(x_1) ) = 0
744.20/263.02	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.20/263.02	POL( U92_1(x_1) ) = 1
744.20/263.02	POL( U51_1(x_1) ) = x_1 + 1
744.20/263.02	POL( 0 ) = 0
744.20/263.02	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.20/263.02	
744.20/263.02	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.02	none
744.20/263.02	
744.20/263.02	
744.20/263.02	----------------------------------------
744.20/263.02	
744.20/263.02	(292)
744.20/263.02	Obligation:
744.20/263.02	Q DP problem:
744.20/263.02	The TRS P consists of the following rules:
744.20/263.02	
744.20/263.02	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.02	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.02	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.02	   MARK(U16(X)) -> MARK(X)
744.20/263.02	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.02	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.02	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.02	   MARK(U23(X)) -> MARK(X)
744.20/263.02	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.02	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.02	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.02	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.02	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.02	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.02	   MARK(U36(X)) -> MARK(X)
744.20/263.02	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.02	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.02	   MARK(U42(X)) -> MARK(X)
744.20/263.02	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.02	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.02	   MARK(U62(X)) -> MARK(X)
744.20/263.02	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.02	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U51(X)) -> MARK(X)
744.20/263.02	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.02	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.02	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.02	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.02	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.02	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.02	
744.20/263.02	The TRS R consists of the following rules:
744.20/263.02	
744.20/263.02	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.02	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.02	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.02	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.02	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.02	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.02	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.02	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.02	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.02	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.02	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.02	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.02	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.02	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.02	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.02	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.02	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.02	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.02	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.02	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.02	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.02	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.02	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.02	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.02	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.02	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.02	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.02	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.02	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.02	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.02	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.02	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.02	   active(U72(tt, N)) -> mark(N)
744.20/263.02	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.02	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.02	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.02	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.02	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.02	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.02	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.02	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.02	   mark(s(X)) -> active(s(mark(X)))
744.20/263.02	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.02	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.02	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.02	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.02	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.02	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.02	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.02	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.02	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.02	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.02	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.02	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.02	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.02	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.02	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.02	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.02	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.02	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.02	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.02	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.02	   mark(isNat(X)) -> active(isNat(X))
744.20/263.02	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.02	   mark(tt) -> active(tt)
744.20/263.02	   mark(0) -> active(0)
744.20/263.02	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.02	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.02	   active(U16(tt)) -> mark(tt)
744.20/263.02	   active(U23(tt)) -> mark(tt)
744.20/263.02	   active(U36(tt)) -> mark(tt)
744.20/263.02	   active(U42(tt)) -> mark(tt)
744.20/263.02	   active(U51(tt)) -> mark(tt)
744.20/263.02	   active(U62(tt)) -> mark(tt)
744.20/263.02	   active(U92(tt)) -> mark(0)
744.20/263.02	   active(isNat(0)) -> mark(tt)
744.20/263.02	   active(isNatKind(0)) -> mark(tt)
744.20/263.02	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.02	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.02	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.02	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.02	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.02	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.02	   U16(active(X)) -> U16(X)
744.20/263.02	   U16(mark(X)) -> U16(X)
744.20/263.02	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.02	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.02	   U23(active(X)) -> U23(X)
744.20/263.02	   U23(mark(X)) -> U23(X)
744.20/263.02	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.02	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.02	   U36(active(X)) -> U36(X)
744.20/263.02	   U36(mark(X)) -> U36(X)
744.20/263.02	   U42(active(X)) -> U42(X)
744.20/263.02	   U42(mark(X)) -> U42(X)
744.20/263.02	   U62(active(X)) -> U62(X)
744.20/263.02	   U62(mark(X)) -> U62(X)
744.20/263.02	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.02	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.02	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.02	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.02	   s(active(X)) -> s(X)
744.20/263.02	   s(mark(X)) -> s(X)
744.20/263.02	   U92(active(X)) -> U92(X)
744.20/263.02	   U92(mark(X)) -> U92(X)
744.20/263.02	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.02	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.02	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.02	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.02	   U51(active(X)) -> U51(X)
744.20/263.02	   U51(mark(X)) -> U51(X)
744.20/263.02	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.02	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.02	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.02	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.02	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.02	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.02	   x(active(X1), X2) -> x(X1, X2)
744.20/263.02	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.02	
744.20/263.02	The set Q consists of the following terms:
744.20/263.02	
744.20/263.02	   active(U101(tt, x0, x1))
744.20/263.02	   active(U102(tt, x0, x1))
744.20/263.02	   active(U103(tt, x0, x1))
744.20/263.02	   active(U104(tt, x0, x1))
744.20/263.02	   active(U11(tt, x0, x1))
744.20/263.02	   active(U12(tt, x0, x1))
744.20/263.02	   active(U13(tt, x0, x1))
744.20/263.02	   active(U14(tt, x0, x1))
744.20/263.02	   active(U15(tt, x0))
744.20/263.02	   active(U16(tt))
744.20/263.02	   active(U21(tt, x0))
744.20/263.02	   active(U22(tt, x0))
744.20/263.02	   active(U23(tt))
744.20/263.02	   active(U31(tt, x0, x1))
744.20/263.02	   active(U32(tt, x0, x1))
744.20/263.02	   active(U33(tt, x0, x1))
744.20/263.02	   active(U34(tt, x0, x1))
744.20/263.02	   active(U35(tt, x0))
744.20/263.02	   active(U36(tt))
744.20/263.02	   active(U41(tt, x0))
744.20/263.02	   active(U42(tt))
744.20/263.02	   active(U51(tt))
744.20/263.02	   active(U61(tt, x0))
744.20/263.02	   active(U62(tt))
744.20/263.02	   active(U71(tt, x0))
744.20/263.02	   active(U72(tt, x0))
744.20/263.02	   active(U81(tt, x0, x1))
744.20/263.02	   active(U82(tt, x0, x1))
744.20/263.02	   active(U83(tt, x0, x1))
744.20/263.02	   active(U84(tt, x0, x1))
744.20/263.02	   active(U91(tt, x0))
744.20/263.02	   active(U92(tt))
744.20/263.02	   active(isNat(0))
744.20/263.02	   active(isNat(plus(x0, x1)))
744.20/263.02	   active(isNat(s(x0)))
744.20/263.02	   active(isNat(x(x0, x1)))
744.20/263.02	   active(isNatKind(0))
744.20/263.02	   active(isNatKind(plus(x0, x1)))
744.20/263.02	   active(isNatKind(s(x0)))
744.20/263.02	   active(isNatKind(x(x0, x1)))
744.20/263.02	   active(plus(x0, 0))
744.20/263.02	   active(plus(x0, s(x1)))
744.20/263.02	   active(x(x0, 0))
744.20/263.02	   active(x(x0, s(x1)))
744.20/263.02	   mark(U101(x0, x1, x2))
744.20/263.02	   mark(tt)
744.20/263.02	   mark(U102(x0, x1, x2))
744.20/263.02	   mark(isNatKind(x0))
744.20/263.02	   mark(U103(x0, x1, x2))
744.20/263.02	   mark(isNat(x0))
744.20/263.02	   mark(U104(x0, x1, x2))
744.20/263.02	   mark(plus(x0, x1))
744.20/263.02	   mark(x(x0, x1))
744.20/263.02	   mark(U11(x0, x1, x2))
744.20/263.02	   mark(U12(x0, x1, x2))
744.20/263.02	   mark(U13(x0, x1, x2))
744.20/263.02	   mark(U14(x0, x1, x2))
744.20/263.02	   mark(U15(x0, x1))
744.20/263.02	   mark(U16(x0))
744.20/263.02	   mark(U21(x0, x1))
744.20/263.02	   mark(U22(x0, x1))
744.20/263.02	   mark(U23(x0))
744.20/263.02	   mark(U31(x0, x1, x2))
744.20/263.02	   mark(U32(x0, x1, x2))
744.20/263.02	   mark(U33(x0, x1, x2))
744.20/263.02	   mark(U34(x0, x1, x2))
744.20/263.02	   mark(U35(x0, x1))
744.20/263.02	   mark(U36(x0))
744.20/263.02	   mark(U41(x0, x1))
744.20/263.02	   mark(U42(x0))
744.20/263.02	   mark(U51(x0))
744.20/263.02	   mark(U61(x0, x1))
744.20/263.02	   mark(U62(x0))
744.20/263.02	   mark(U71(x0, x1))
744.20/263.02	   mark(U72(x0, x1))
744.20/263.02	   mark(U81(x0, x1, x2))
744.20/263.02	   mark(U82(x0, x1, x2))
744.20/263.02	   mark(U83(x0, x1, x2))
744.20/263.02	   mark(U84(x0, x1, x2))
744.20/263.02	   mark(s(x0))
744.20/263.02	   mark(U91(x0, x1))
744.20/263.02	   mark(U92(x0))
744.20/263.02	   mark(0)
744.20/263.02	   U101(mark(x0), x1, x2)
744.20/263.02	   U101(x0, mark(x1), x2)
744.20/263.02	   U101(x0, x1, mark(x2))
744.20/263.02	   U101(active(x0), x1, x2)
744.20/263.02	   U101(x0, active(x1), x2)
744.20/263.02	   U101(x0, x1, active(x2))
744.20/263.02	   U102(mark(x0), x1, x2)
744.20/263.02	   U102(x0, mark(x1), x2)
744.20/263.02	   U102(x0, x1, mark(x2))
744.20/263.02	   U102(active(x0), x1, x2)
744.20/263.02	   U102(x0, active(x1), x2)
744.20/263.02	   U102(x0, x1, active(x2))
744.20/263.02	   isNatKind(mark(x0))
744.20/263.02	   isNatKind(active(x0))
744.20/263.02	   U103(mark(x0), x1, x2)
744.20/263.02	   U103(x0, mark(x1), x2)
744.20/263.02	   U103(x0, x1, mark(x2))
744.20/263.02	   U103(active(x0), x1, x2)
744.20/263.02	   U103(x0, active(x1), x2)
744.20/263.02	   U103(x0, x1, active(x2))
744.20/263.02	   isNat(mark(x0))
744.20/263.02	   isNat(active(x0))
744.20/263.02	   U104(mark(x0), x1, x2)
744.20/263.02	   U104(x0, mark(x1), x2)
744.20/263.02	   U104(x0, x1, mark(x2))
744.20/263.02	   U104(active(x0), x1, x2)
744.20/263.02	   U104(x0, active(x1), x2)
744.20/263.02	   U104(x0, x1, active(x2))
744.20/263.02	   plus(mark(x0), x1)
744.20/263.02	   plus(x0, mark(x1))
744.20/263.02	   plus(active(x0), x1)
744.20/263.02	   plus(x0, active(x1))
744.20/263.02	   x(mark(x0), x1)
744.20/263.02	   x(x0, mark(x1))
744.20/263.02	   x(active(x0), x1)
744.20/263.02	   x(x0, active(x1))
744.20/263.02	   U11(mark(x0), x1, x2)
744.20/263.02	   U11(x0, mark(x1), x2)
744.20/263.02	   U11(x0, x1, mark(x2))
744.20/263.02	   U11(active(x0), x1, x2)
744.20/263.02	   U11(x0, active(x1), x2)
744.20/263.02	   U11(x0, x1, active(x2))
744.20/263.02	   U12(mark(x0), x1, x2)
744.20/263.02	   U12(x0, mark(x1), x2)
744.20/263.02	   U12(x0, x1, mark(x2))
744.20/263.02	   U12(active(x0), x1, x2)
744.20/263.02	   U12(x0, active(x1), x2)
744.20/263.02	   U12(x0, x1, active(x2))
744.20/263.02	   U13(mark(x0), x1, x2)
744.20/263.02	   U13(x0, mark(x1), x2)
744.20/263.02	   U13(x0, x1, mark(x2))
744.20/263.02	   U13(active(x0), x1, x2)
744.20/263.02	   U13(x0, active(x1), x2)
744.20/263.02	   U13(x0, x1, active(x2))
744.20/263.02	   U14(mark(x0), x1, x2)
744.20/263.02	   U14(x0, mark(x1), x2)
744.20/263.02	   U14(x0, x1, mark(x2))
744.20/263.02	   U14(active(x0), x1, x2)
744.20/263.02	   U14(x0, active(x1), x2)
744.20/263.02	   U14(x0, x1, active(x2))
744.20/263.02	   U15(mark(x0), x1)
744.20/263.02	   U15(x0, mark(x1))
744.20/263.02	   U15(active(x0), x1)
744.20/263.02	   U15(x0, active(x1))
744.20/263.02	   U16(mark(x0))
744.20/263.02	   U16(active(x0))
744.20/263.02	   U21(mark(x0), x1)
744.20/263.02	   U21(x0, mark(x1))
744.20/263.02	   U21(active(x0), x1)
744.20/263.02	   U21(x0, active(x1))
744.20/263.02	   U22(mark(x0), x1)
744.20/263.02	   U22(x0, mark(x1))
744.20/263.02	   U22(active(x0), x1)
744.20/263.02	   U22(x0, active(x1))
744.20/263.02	   U23(mark(x0))
744.20/263.02	   U23(active(x0))
744.20/263.02	   U31(mark(x0), x1, x2)
744.20/263.02	   U31(x0, mark(x1), x2)
744.20/263.02	   U31(x0, x1, mark(x2))
744.20/263.02	   U31(active(x0), x1, x2)
744.20/263.02	   U31(x0, active(x1), x2)
744.20/263.02	   U31(x0, x1, active(x2))
744.20/263.02	   U32(mark(x0), x1, x2)
744.20/263.02	   U32(x0, mark(x1), x2)
744.20/263.02	   U32(x0, x1, mark(x2))
744.20/263.02	   U32(active(x0), x1, x2)
744.20/263.02	   U32(x0, active(x1), x2)
744.20/263.02	   U32(x0, x1, active(x2))
744.20/263.02	   U33(mark(x0), x1, x2)
744.20/263.02	   U33(x0, mark(x1), x2)
744.20/263.02	   U33(x0, x1, mark(x2))
744.20/263.02	   U33(active(x0), x1, x2)
744.20/263.02	   U33(x0, active(x1), x2)
744.20/263.02	   U33(x0, x1, active(x2))
744.20/263.02	   U34(mark(x0), x1, x2)
744.20/263.02	   U34(x0, mark(x1), x2)
744.20/263.02	   U34(x0, x1, mark(x2))
744.20/263.02	   U34(active(x0), x1, x2)
744.20/263.02	   U34(x0, active(x1), x2)
744.20/263.02	   U34(x0, x1, active(x2))
744.20/263.02	   U35(mark(x0), x1)
744.20/263.02	   U35(x0, mark(x1))
744.20/263.02	   U35(active(x0), x1)
744.20/263.02	   U35(x0, active(x1))
744.20/263.02	   U36(mark(x0))
744.20/263.02	   U36(active(x0))
744.20/263.02	   U41(mark(x0), x1)
744.20/263.02	   U41(x0, mark(x1))
744.20/263.02	   U41(active(x0), x1)
744.20/263.02	   U41(x0, active(x1))
744.20/263.02	   U42(mark(x0))
744.20/263.02	   U42(active(x0))
744.20/263.02	   U51(mark(x0))
744.20/263.02	   U51(active(x0))
744.20/263.02	   U61(mark(x0), x1)
744.20/263.02	   U61(x0, mark(x1))
744.20/263.02	   U61(active(x0), x1)
744.20/263.02	   U61(x0, active(x1))
744.20/263.02	   U62(mark(x0))
744.20/263.02	   U62(active(x0))
744.20/263.02	   U71(mark(x0), x1)
744.20/263.02	   U71(x0, mark(x1))
744.20/263.02	   U71(active(x0), x1)
744.20/263.02	   U71(x0, active(x1))
744.20/263.02	   U72(mark(x0), x1)
744.20/263.02	   U72(x0, mark(x1))
744.20/263.02	   U72(active(x0), x1)
744.20/263.02	   U72(x0, active(x1))
744.20/263.02	   U81(mark(x0), x1, x2)
744.20/263.02	   U81(x0, mark(x1), x2)
744.20/263.02	   U81(x0, x1, mark(x2))
744.20/263.02	   U81(active(x0), x1, x2)
744.20/263.02	   U81(x0, active(x1), x2)
744.20/263.02	   U81(x0, x1, active(x2))
744.20/263.02	   U82(mark(x0), x1, x2)
744.20/263.02	   U82(x0, mark(x1), x2)
744.20/263.02	   U82(x0, x1, mark(x2))
744.20/263.02	   U82(active(x0), x1, x2)
744.20/263.02	   U82(x0, active(x1), x2)
744.20/263.02	   U82(x0, x1, active(x2))
744.20/263.02	   U83(mark(x0), x1, x2)
744.20/263.02	   U83(x0, mark(x1), x2)
744.20/263.02	   U83(x0, x1, mark(x2))
744.20/263.02	   U83(active(x0), x1, x2)
744.20/263.02	   U83(x0, active(x1), x2)
744.20/263.02	   U83(x0, x1, active(x2))
744.20/263.02	   U84(mark(x0), x1, x2)
744.20/263.02	   U84(x0, mark(x1), x2)
744.20/263.02	   U84(x0, x1, mark(x2))
744.20/263.02	   U84(active(x0), x1, x2)
744.20/263.02	   U84(x0, active(x1), x2)
744.20/263.02	   U84(x0, x1, active(x2))
744.20/263.02	   s(mark(x0))
744.20/263.02	   s(active(x0))
744.20/263.02	   U91(mark(x0), x1)
744.20/263.02	   U91(x0, mark(x1))
744.20/263.02	   U91(active(x0), x1)
744.20/263.02	   U91(x0, active(x1))
744.20/263.02	   U92(mark(x0))
744.20/263.02	   U92(active(x0))
744.20/263.02	
744.20/263.02	We have to consider all minimal (P,Q,R)-chains.
744.20/263.02	----------------------------------------
744.20/263.02	
744.20/263.02	(293) QDPOrderProof (EQUIVALENT)
744.20/263.02	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.02	
744.20/263.02	
744.20/263.02	The following pairs can be oriented strictly and are deleted.
744.20/263.02	
744.20/263.02	   MARK(U61(X1, X2)) -> MARK(X1)
744.20/263.02	The remaining pairs can at least be oriented weakly.
744.20/263.02	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(ACTIVE(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(tt) =  	[[0A]]
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(MARK(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U22(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U23(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U31(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U32(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U36(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U42(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U101(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U71(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(0) =  	[[0A]]
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	
744.20/263.02	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.02	
744.20/263.02	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.02	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.02	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.02	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.02	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.02	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.02	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.02	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.02	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.02	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.02	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.02	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.02	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.02	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.02	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.02	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.02	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.02	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.02	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.02	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.02	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.02	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.02	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.02	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.02	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.02	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.02	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.02	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.02	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.02	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.02	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.02	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.02	   active(U72(tt, N)) -> mark(N)
744.20/263.02	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.02	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.02	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.02	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.02	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.02	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.02	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.02	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.02	   mark(s(X)) -> active(s(mark(X)))
744.20/263.02	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.02	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.02	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.02	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.02	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.02	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.02	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.02	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.02	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.02	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.02	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.02	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.02	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.02	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.02	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.02	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.02	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.02	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.02	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.02	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.02	   mark(isNat(X)) -> active(isNat(X))
744.20/263.02	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.02	   mark(tt) -> active(tt)
744.20/263.02	   mark(0) -> active(0)
744.20/263.02	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.02	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.02	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.02	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.02	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.02	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.02	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.02	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.02	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.02	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.02	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.02	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.02	   active(U16(tt)) -> mark(tt)
744.20/263.02	   active(U23(tt)) -> mark(tt)
744.20/263.02	   active(U36(tt)) -> mark(tt)
744.20/263.02	   active(U42(tt)) -> mark(tt)
744.20/263.02	   active(U51(tt)) -> mark(tt)
744.20/263.02	   active(U62(tt)) -> mark(tt)
744.20/263.02	   active(U92(tt)) -> mark(0)
744.20/263.02	   active(isNat(0)) -> mark(tt)
744.20/263.02	   active(isNatKind(0)) -> mark(tt)
744.20/263.02	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.02	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.02	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.02	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.02	   U16(active(X)) -> U16(X)
744.20/263.02	   U16(mark(X)) -> U16(X)
744.20/263.02	   U23(active(X)) -> U23(X)
744.20/263.02	   U23(mark(X)) -> U23(X)
744.20/263.02	   U36(active(X)) -> U36(X)
744.20/263.02	   U36(mark(X)) -> U36(X)
744.20/263.02	   U42(active(X)) -> U42(X)
744.20/263.02	   U42(mark(X)) -> U42(X)
744.20/263.02	   U62(active(X)) -> U62(X)
744.20/263.02	   U62(mark(X)) -> U62(X)
744.20/263.02	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.02	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.02	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.02	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.02	   s(active(X)) -> s(X)
744.20/263.02	   s(mark(X)) -> s(X)
744.20/263.02	   U92(active(X)) -> U92(X)
744.20/263.02	   U92(mark(X)) -> U92(X)
744.20/263.02	   U51(active(X)) -> U51(X)
744.20/263.02	   U51(mark(X)) -> U51(X)
744.20/263.02	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.02	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.02	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.02	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.02	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.02	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.02	   x(active(X1), X2) -> x(X1, X2)
744.20/263.02	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.02	
744.20/263.02	
744.20/263.02	----------------------------------------
744.20/263.02	
744.20/263.02	(294)
744.20/263.02	Obligation:
744.20/263.02	Q DP problem:
744.20/263.02	The TRS P consists of the following rules:
744.20/263.02	
744.20/263.02	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.02	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.02	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.02	   MARK(U16(X)) -> MARK(X)
744.20/263.02	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.02	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.02	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.02	   MARK(U23(X)) -> MARK(X)
744.20/263.02	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.02	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.02	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.02	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.02	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.02	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.02	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.02	   MARK(U36(X)) -> MARK(X)
744.20/263.02	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.02	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.02	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.02	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.02	   MARK(U42(X)) -> MARK(X)
744.20/263.02	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.02	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.02	   MARK(U62(X)) -> MARK(X)
744.20/263.02	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.02	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.02	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.02	   MARK(U51(X)) -> MARK(X)
744.20/263.02	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.02	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.02	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.02	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.02	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.02	
744.20/263.02	The TRS R consists of the following rules:
744.20/263.02	
744.20/263.02	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.02	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.02	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.02	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.02	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.02	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.02	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.02	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.02	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.02	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.02	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.02	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.02	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.02	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.02	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.02	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.02	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.02	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.02	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.02	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.02	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.02	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.02	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.02	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.02	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.02	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.02	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.02	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.02	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.02	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.02	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.02	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.02	   active(U72(tt, N)) -> mark(N)
744.20/263.02	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.02	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.02	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.02	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.02	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.02	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.02	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.02	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.02	   mark(s(X)) -> active(s(mark(X)))
744.20/263.02	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.02	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.02	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.02	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.02	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.02	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.02	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.02	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.02	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.02	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.02	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.02	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.02	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.02	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.02	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.02	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.02	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.02	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.02	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.02	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.02	   mark(isNat(X)) -> active(isNat(X))
744.20/263.02	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.02	   mark(tt) -> active(tt)
744.20/263.02	   mark(0) -> active(0)
744.20/263.02	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.02	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.02	   active(U16(tt)) -> mark(tt)
744.20/263.02	   active(U23(tt)) -> mark(tt)
744.20/263.02	   active(U36(tt)) -> mark(tt)
744.20/263.02	   active(U42(tt)) -> mark(tt)
744.20/263.02	   active(U51(tt)) -> mark(tt)
744.20/263.02	   active(U62(tt)) -> mark(tt)
744.20/263.02	   active(U92(tt)) -> mark(0)
744.20/263.02	   active(isNat(0)) -> mark(tt)
744.20/263.02	   active(isNatKind(0)) -> mark(tt)
744.20/263.02	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.02	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.02	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.02	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.02	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.02	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.02	   U16(active(X)) -> U16(X)
744.20/263.02	   U16(mark(X)) -> U16(X)
744.20/263.02	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.02	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.02	   U23(active(X)) -> U23(X)
744.20/263.02	   U23(mark(X)) -> U23(X)
744.20/263.02	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.02	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.02	   U36(active(X)) -> U36(X)
744.20/263.02	   U36(mark(X)) -> U36(X)
744.20/263.02	   U42(active(X)) -> U42(X)
744.20/263.02	   U42(mark(X)) -> U42(X)
744.20/263.02	   U62(active(X)) -> U62(X)
744.20/263.02	   U62(mark(X)) -> U62(X)
744.20/263.02	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.02	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.02	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.02	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.02	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.02	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.02	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.02	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.02	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.02	   s(active(X)) -> s(X)
744.20/263.02	   s(mark(X)) -> s(X)
744.20/263.02	   U92(active(X)) -> U92(X)
744.20/263.02	   U92(mark(X)) -> U92(X)
744.20/263.02	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.02	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.02	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.02	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.02	   U51(active(X)) -> U51(X)
744.20/263.02	   U51(mark(X)) -> U51(X)
744.20/263.02	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.02	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.02	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.02	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.02	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.02	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.02	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.02	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.02	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.02	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.02	   x(active(X1), X2) -> x(X1, X2)
744.20/263.02	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.02	
744.20/263.02	The set Q consists of the following terms:
744.20/263.02	
744.20/263.02	   active(U101(tt, x0, x1))
744.20/263.02	   active(U102(tt, x0, x1))
744.20/263.02	   active(U103(tt, x0, x1))
744.20/263.02	   active(U104(tt, x0, x1))
744.20/263.02	   active(U11(tt, x0, x1))
744.20/263.02	   active(U12(tt, x0, x1))
744.20/263.02	   active(U13(tt, x0, x1))
744.20/263.02	   active(U14(tt, x0, x1))
744.20/263.02	   active(U15(tt, x0))
744.20/263.02	   active(U16(tt))
744.20/263.02	   active(U21(tt, x0))
744.20/263.02	   active(U22(tt, x0))
744.20/263.02	   active(U23(tt))
744.20/263.02	   active(U31(tt, x0, x1))
744.20/263.02	   active(U32(tt, x0, x1))
744.20/263.02	   active(U33(tt, x0, x1))
744.20/263.02	   active(U34(tt, x0, x1))
744.20/263.02	   active(U35(tt, x0))
744.20/263.02	   active(U36(tt))
744.20/263.02	   active(U41(tt, x0))
744.20/263.02	   active(U42(tt))
744.20/263.02	   active(U51(tt))
744.20/263.02	   active(U61(tt, x0))
744.20/263.02	   active(U62(tt))
744.20/263.02	   active(U71(tt, x0))
744.20/263.02	   active(U72(tt, x0))
744.20/263.02	   active(U81(tt, x0, x1))
744.20/263.02	   active(U82(tt, x0, x1))
744.20/263.02	   active(U83(tt, x0, x1))
744.20/263.02	   active(U84(tt, x0, x1))
744.20/263.02	   active(U91(tt, x0))
744.20/263.02	   active(U92(tt))
744.20/263.02	   active(isNat(0))
744.20/263.02	   active(isNat(plus(x0, x1)))
744.20/263.02	   active(isNat(s(x0)))
744.20/263.02	   active(isNat(x(x0, x1)))
744.20/263.02	   active(isNatKind(0))
744.20/263.02	   active(isNatKind(plus(x0, x1)))
744.20/263.02	   active(isNatKind(s(x0)))
744.20/263.02	   active(isNatKind(x(x0, x1)))
744.20/263.02	   active(plus(x0, 0))
744.20/263.02	   active(plus(x0, s(x1)))
744.20/263.02	   active(x(x0, 0))
744.20/263.02	   active(x(x0, s(x1)))
744.20/263.02	   mark(U101(x0, x1, x2))
744.20/263.02	   mark(tt)
744.20/263.02	   mark(U102(x0, x1, x2))
744.20/263.02	   mark(isNatKind(x0))
744.20/263.02	   mark(U103(x0, x1, x2))
744.20/263.02	   mark(isNat(x0))
744.20/263.02	   mark(U104(x0, x1, x2))
744.20/263.02	   mark(plus(x0, x1))
744.20/263.02	   mark(x(x0, x1))
744.20/263.02	   mark(U11(x0, x1, x2))
744.20/263.02	   mark(U12(x0, x1, x2))
744.20/263.02	   mark(U13(x0, x1, x2))
744.20/263.02	   mark(U14(x0, x1, x2))
744.20/263.02	   mark(U15(x0, x1))
744.20/263.02	   mark(U16(x0))
744.20/263.02	   mark(U21(x0, x1))
744.20/263.02	   mark(U22(x0, x1))
744.20/263.02	   mark(U23(x0))
744.20/263.02	   mark(U31(x0, x1, x2))
744.20/263.02	   mark(U32(x0, x1, x2))
744.20/263.02	   mark(U33(x0, x1, x2))
744.20/263.02	   mark(U34(x0, x1, x2))
744.20/263.02	   mark(U35(x0, x1))
744.20/263.02	   mark(U36(x0))
744.20/263.02	   mark(U41(x0, x1))
744.20/263.02	   mark(U42(x0))
744.20/263.02	   mark(U51(x0))
744.20/263.02	   mark(U61(x0, x1))
744.20/263.02	   mark(U62(x0))
744.20/263.02	   mark(U71(x0, x1))
744.20/263.02	   mark(U72(x0, x1))
744.20/263.02	   mark(U81(x0, x1, x2))
744.20/263.02	   mark(U82(x0, x1, x2))
744.20/263.02	   mark(U83(x0, x1, x2))
744.20/263.02	   mark(U84(x0, x1, x2))
744.20/263.02	   mark(s(x0))
744.20/263.02	   mark(U91(x0, x1))
744.20/263.02	   mark(U92(x0))
744.20/263.02	   mark(0)
744.20/263.02	   U101(mark(x0), x1, x2)
744.20/263.02	   U101(x0, mark(x1), x2)
744.20/263.02	   U101(x0, x1, mark(x2))
744.20/263.02	   U101(active(x0), x1, x2)
744.20/263.02	   U101(x0, active(x1), x2)
744.20/263.02	   U101(x0, x1, active(x2))
744.20/263.02	   U102(mark(x0), x1, x2)
744.20/263.02	   U102(x0, mark(x1), x2)
744.20/263.02	   U102(x0, x1, mark(x2))
744.20/263.02	   U102(active(x0), x1, x2)
744.20/263.02	   U102(x0, active(x1), x2)
744.20/263.02	   U102(x0, x1, active(x2))
744.20/263.02	   isNatKind(mark(x0))
744.20/263.02	   isNatKind(active(x0))
744.20/263.02	   U103(mark(x0), x1, x2)
744.20/263.02	   U103(x0, mark(x1), x2)
744.20/263.02	   U103(x0, x1, mark(x2))
744.20/263.02	   U103(active(x0), x1, x2)
744.20/263.02	   U103(x0, active(x1), x2)
744.20/263.02	   U103(x0, x1, active(x2))
744.20/263.02	   isNat(mark(x0))
744.20/263.02	   isNat(active(x0))
744.20/263.02	   U104(mark(x0), x1, x2)
744.20/263.02	   U104(x0, mark(x1), x2)
744.20/263.02	   U104(x0, x1, mark(x2))
744.20/263.02	   U104(active(x0), x1, x2)
744.20/263.02	   U104(x0, active(x1), x2)
744.20/263.02	   U104(x0, x1, active(x2))
744.20/263.02	   plus(mark(x0), x1)
744.20/263.02	   plus(x0, mark(x1))
744.20/263.02	   plus(active(x0), x1)
744.20/263.02	   plus(x0, active(x1))
744.20/263.02	   x(mark(x0), x1)
744.20/263.02	   x(x0, mark(x1))
744.20/263.02	   x(active(x0), x1)
744.20/263.02	   x(x0, active(x1))
744.20/263.02	   U11(mark(x0), x1, x2)
744.20/263.02	   U11(x0, mark(x1), x2)
744.20/263.02	   U11(x0, x1, mark(x2))
744.20/263.02	   U11(active(x0), x1, x2)
744.20/263.02	   U11(x0, active(x1), x2)
744.20/263.02	   U11(x0, x1, active(x2))
744.20/263.02	   U12(mark(x0), x1, x2)
744.20/263.02	   U12(x0, mark(x1), x2)
744.20/263.02	   U12(x0, x1, mark(x2))
744.20/263.02	   U12(active(x0), x1, x2)
744.20/263.02	   U12(x0, active(x1), x2)
744.20/263.02	   U12(x0, x1, active(x2))
744.20/263.02	   U13(mark(x0), x1, x2)
744.20/263.02	   U13(x0, mark(x1), x2)
744.20/263.02	   U13(x0, x1, mark(x2))
744.20/263.02	   U13(active(x0), x1, x2)
744.20/263.02	   U13(x0, active(x1), x2)
744.20/263.02	   U13(x0, x1, active(x2))
744.20/263.02	   U14(mark(x0), x1, x2)
744.20/263.02	   U14(x0, mark(x1), x2)
744.20/263.02	   U14(x0, x1, mark(x2))
744.20/263.02	   U14(active(x0), x1, x2)
744.20/263.02	   U14(x0, active(x1), x2)
744.20/263.02	   U14(x0, x1, active(x2))
744.20/263.02	   U15(mark(x0), x1)
744.20/263.02	   U15(x0, mark(x1))
744.20/263.02	   U15(active(x0), x1)
744.20/263.02	   U15(x0, active(x1))
744.20/263.02	   U16(mark(x0))
744.20/263.02	   U16(active(x0))
744.20/263.02	   U21(mark(x0), x1)
744.20/263.02	   U21(x0, mark(x1))
744.20/263.02	   U21(active(x0), x1)
744.20/263.02	   U21(x0, active(x1))
744.20/263.02	   U22(mark(x0), x1)
744.20/263.02	   U22(x0, mark(x1))
744.20/263.02	   U22(active(x0), x1)
744.20/263.02	   U22(x0, active(x1))
744.20/263.02	   U23(mark(x0))
744.20/263.02	   U23(active(x0))
744.20/263.02	   U31(mark(x0), x1, x2)
744.20/263.02	   U31(x0, mark(x1), x2)
744.20/263.02	   U31(x0, x1, mark(x2))
744.20/263.02	   U31(active(x0), x1, x2)
744.20/263.02	   U31(x0, active(x1), x2)
744.20/263.02	   U31(x0, x1, active(x2))
744.20/263.02	   U32(mark(x0), x1, x2)
744.20/263.02	   U32(x0, mark(x1), x2)
744.20/263.02	   U32(x0, x1, mark(x2))
744.20/263.02	   U32(active(x0), x1, x2)
744.20/263.02	   U32(x0, active(x1), x2)
744.20/263.02	   U32(x0, x1, active(x2))
744.20/263.02	   U33(mark(x0), x1, x2)
744.20/263.02	   U33(x0, mark(x1), x2)
744.20/263.02	   U33(x0, x1, mark(x2))
744.20/263.02	   U33(active(x0), x1, x2)
744.20/263.02	   U33(x0, active(x1), x2)
744.20/263.02	   U33(x0, x1, active(x2))
744.20/263.02	   U34(mark(x0), x1, x2)
744.20/263.02	   U34(x0, mark(x1), x2)
744.20/263.02	   U34(x0, x1, mark(x2))
744.20/263.02	   U34(active(x0), x1, x2)
744.20/263.02	   U34(x0, active(x1), x2)
744.20/263.02	   U34(x0, x1, active(x2))
744.20/263.02	   U35(mark(x0), x1)
744.20/263.02	   U35(x0, mark(x1))
744.20/263.02	   U35(active(x0), x1)
744.20/263.02	   U35(x0, active(x1))
744.20/263.02	   U36(mark(x0))
744.20/263.02	   U36(active(x0))
744.20/263.02	   U41(mark(x0), x1)
744.20/263.02	   U41(x0, mark(x1))
744.20/263.02	   U41(active(x0), x1)
744.20/263.02	   U41(x0, active(x1))
744.20/263.02	   U42(mark(x0))
744.20/263.02	   U42(active(x0))
744.20/263.02	   U51(mark(x0))
744.20/263.02	   U51(active(x0))
744.20/263.02	   U61(mark(x0), x1)
744.20/263.02	   U61(x0, mark(x1))
744.20/263.02	   U61(active(x0), x1)
744.20/263.02	   U61(x0, active(x1))
744.20/263.02	   U62(mark(x0))
744.20/263.02	   U62(active(x0))
744.20/263.02	   U71(mark(x0), x1)
744.20/263.02	   U71(x0, mark(x1))
744.20/263.02	   U71(active(x0), x1)
744.20/263.02	   U71(x0, active(x1))
744.20/263.02	   U72(mark(x0), x1)
744.20/263.02	   U72(x0, mark(x1))
744.20/263.02	   U72(active(x0), x1)
744.20/263.02	   U72(x0, active(x1))
744.20/263.02	   U81(mark(x0), x1, x2)
744.20/263.02	   U81(x0, mark(x1), x2)
744.20/263.02	   U81(x0, x1, mark(x2))
744.20/263.02	   U81(active(x0), x1, x2)
744.20/263.02	   U81(x0, active(x1), x2)
744.20/263.02	   U81(x0, x1, active(x2))
744.20/263.02	   U82(mark(x0), x1, x2)
744.20/263.02	   U82(x0, mark(x1), x2)
744.20/263.02	   U82(x0, x1, mark(x2))
744.20/263.02	   U82(active(x0), x1, x2)
744.20/263.02	   U82(x0, active(x1), x2)
744.20/263.02	   U82(x0, x1, active(x2))
744.20/263.02	   U83(mark(x0), x1, x2)
744.20/263.02	   U83(x0, mark(x1), x2)
744.20/263.02	   U83(x0, x1, mark(x2))
744.20/263.02	   U83(active(x0), x1, x2)
744.20/263.02	   U83(x0, active(x1), x2)
744.20/263.02	   U83(x0, x1, active(x2))
744.20/263.02	   U84(mark(x0), x1, x2)
744.20/263.02	   U84(x0, mark(x1), x2)
744.20/263.02	   U84(x0, x1, mark(x2))
744.20/263.02	   U84(active(x0), x1, x2)
744.20/263.02	   U84(x0, active(x1), x2)
744.20/263.02	   U84(x0, x1, active(x2))
744.20/263.02	   s(mark(x0))
744.20/263.02	   s(active(x0))
744.20/263.02	   U91(mark(x0), x1)
744.20/263.02	   U91(x0, mark(x1))
744.20/263.02	   U91(active(x0), x1)
744.20/263.02	   U91(x0, active(x1))
744.20/263.02	   U92(mark(x0))
744.20/263.02	   U92(active(x0))
744.20/263.02	
744.20/263.02	We have to consider all minimal (P,Q,R)-chains.
744.20/263.02	----------------------------------------
744.20/263.02	
744.20/263.02	(295) QDPOrderProof (EQUIVALENT)
744.20/263.02	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.02	
744.20/263.02	
744.20/263.02	The following pairs can be oriented strictly and are deleted.
744.20/263.02	
744.20/263.02	   ACTIVE(U61(tt, V2)) -> MARK(U62(isNatKind(V2)))
744.20/263.02	The remaining pairs can at least be oriented weakly.
744.20/263.02	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(tt) =  	[[0A]]
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U31(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U61(x_1, x_2)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(x(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U102(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U101(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U103(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U104(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(U92(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	   <<<
744.20/263.02	 POL(0) =  	[[0A]]
744.20/263.02	>>>
744.20/263.02	
744.20/263.02	
744.20/263.02	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.02	
744.20/263.02	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.02	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.02	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.02	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.02	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.02	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.02	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.02	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.02	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.02	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.02	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.02	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.02	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.02	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.02	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.02	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.02	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.02	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.02	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.02	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.02	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.02	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.02	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.02	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.02	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.02	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.02	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.02	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.02	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.02	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.02	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.02	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.02	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.02	   active(U72(tt, N)) -> mark(N)
744.20/263.02	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.02	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.02	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.02	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.02	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.02	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.02	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.02	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.02	   mark(s(X)) -> active(s(mark(X)))
744.20/263.02	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.02	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.02	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.02	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.02	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.02	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.02	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.02	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.02	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.02	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.02	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.02	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.02	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.02	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.02	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.02	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.02	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.02	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.02	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.02	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.02	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.02	   mark(isNat(X)) -> active(isNat(X))
744.20/263.02	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.02	   mark(tt) -> active(tt)
744.20/263.02	   mark(0) -> active(0)
744.20/263.02	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.02	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.02	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.02	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.02	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.02	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.02	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.02	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.02	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.02	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.02	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.02	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.02	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.02	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.02	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.02	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.02	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.02	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.02	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.02	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.02	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.02	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.02	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.02	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.02	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.02	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.02	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.02	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.02	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.02	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.02	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.02	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.02	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.02	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.02	   active(U16(tt)) -> mark(tt)
744.20/263.02	   active(U23(tt)) -> mark(tt)
744.20/263.02	   active(U36(tt)) -> mark(tt)
744.20/263.02	   active(U42(tt)) -> mark(tt)
744.20/263.02	   active(U51(tt)) -> mark(tt)
744.20/263.02	   active(U62(tt)) -> mark(tt)
744.20/263.02	   active(U92(tt)) -> mark(0)
744.20/263.02	   active(isNat(0)) -> mark(tt)
744.20/263.02	   active(isNatKind(0)) -> mark(tt)
744.20/263.02	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.02	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.02	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.02	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.02	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.02	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.02	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.02	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.02	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.02	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.02	   U16(active(X)) -> U16(X)
744.20/263.02	   U16(mark(X)) -> U16(X)
744.20/263.02	   U23(active(X)) -> U23(X)
744.20/263.02	   U23(mark(X)) -> U23(X)
744.20/263.02	   U36(active(X)) -> U36(X)
744.20/263.02	   U36(mark(X)) -> U36(X)
744.20/263.02	   U42(active(X)) -> U42(X)
744.20/263.02	   U42(mark(X)) -> U42(X)
744.20/263.02	   U62(active(X)) -> U62(X)
744.20/263.02	   U62(mark(X)) -> U62(X)
744.20/263.02	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.02	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.02	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.02	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.02	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.02	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.03	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.03	   s(active(X)) -> s(X)
744.20/263.03	   s(mark(X)) -> s(X)
744.20/263.03	   U92(active(X)) -> U92(X)
744.20/263.03	   U92(mark(X)) -> U92(X)
744.20/263.03	   U51(active(X)) -> U51(X)
744.20/263.03	   U51(mark(X)) -> U51(X)
744.20/263.03	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.03	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.03	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.03	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.03	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.03	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.03	   x(active(X1), X2) -> x(X1, X2)
744.20/263.03	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.03	
744.20/263.03	
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(296)
744.20/263.03	Obligation:
744.20/263.03	Q DP problem:
744.20/263.03	The TRS P consists of the following rules:
744.20/263.03	
744.20/263.03	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.03	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.03	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.03	   MARK(U16(X)) -> MARK(X)
744.20/263.03	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.03	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.03	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.03	   MARK(U23(X)) -> MARK(X)
744.20/263.03	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.03	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.03	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.03	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.03	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.03	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.03	   MARK(U36(X)) -> MARK(X)
744.20/263.03	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.03	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.03	   MARK(U42(X)) -> MARK(X)
744.20/263.03	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.03	   MARK(U62(X)) -> MARK(X)
744.20/263.03	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.03	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U51(X)) -> MARK(X)
744.20/263.03	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.03	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.03	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.03	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.03	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.03	
744.20/263.03	The TRS R consists of the following rules:
744.20/263.03	
744.20/263.03	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.03	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.03	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.03	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.03	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.03	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.03	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.03	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.03	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.03	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.03	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.03	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.03	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.03	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.03	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.03	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.03	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.03	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.03	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.03	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.03	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.03	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.03	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.03	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.03	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.03	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.03	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.03	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.03	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.03	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.03	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.03	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.03	   active(U72(tt, N)) -> mark(N)
744.20/263.03	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.03	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.03	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.03	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.03	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.03	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.03	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.03	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.03	   mark(s(X)) -> active(s(mark(X)))
744.20/263.03	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.03	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.03	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.03	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.03	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.03	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.03	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.03	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.03	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.03	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.03	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.03	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.03	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.03	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.03	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.03	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.03	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.03	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.03	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.03	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.03	   mark(isNat(X)) -> active(isNat(X))
744.20/263.03	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.03	   mark(tt) -> active(tt)
744.20/263.03	   mark(0) -> active(0)
744.20/263.03	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.03	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.03	   active(U16(tt)) -> mark(tt)
744.20/263.03	   active(U23(tt)) -> mark(tt)
744.20/263.03	   active(U36(tt)) -> mark(tt)
744.20/263.03	   active(U42(tt)) -> mark(tt)
744.20/263.03	   active(U51(tt)) -> mark(tt)
744.20/263.03	   active(U62(tt)) -> mark(tt)
744.20/263.03	   active(U92(tt)) -> mark(0)
744.20/263.03	   active(isNat(0)) -> mark(tt)
744.20/263.03	   active(isNatKind(0)) -> mark(tt)
744.20/263.03	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.03	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.03	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.03	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.03	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.03	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.03	   U16(active(X)) -> U16(X)
744.20/263.03	   U16(mark(X)) -> U16(X)
744.20/263.03	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.03	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.03	   U23(active(X)) -> U23(X)
744.20/263.03	   U23(mark(X)) -> U23(X)
744.20/263.03	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.03	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.03	   U36(active(X)) -> U36(X)
744.20/263.03	   U36(mark(X)) -> U36(X)
744.20/263.03	   U42(active(X)) -> U42(X)
744.20/263.03	   U42(mark(X)) -> U42(X)
744.20/263.03	   U62(active(X)) -> U62(X)
744.20/263.03	   U62(mark(X)) -> U62(X)
744.20/263.03	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.03	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.03	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.03	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.03	   s(active(X)) -> s(X)
744.20/263.03	   s(mark(X)) -> s(X)
744.20/263.03	   U92(active(X)) -> U92(X)
744.20/263.03	   U92(mark(X)) -> U92(X)
744.20/263.03	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.03	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.03	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.03	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.03	   U51(active(X)) -> U51(X)
744.20/263.03	   U51(mark(X)) -> U51(X)
744.20/263.03	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.03	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.03	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.03	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.03	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.03	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.03	   x(active(X1), X2) -> x(X1, X2)
744.20/263.03	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.03	
744.20/263.03	The set Q consists of the following terms:
744.20/263.03	
744.20/263.03	   active(U101(tt, x0, x1))
744.20/263.03	   active(U102(tt, x0, x1))
744.20/263.03	   active(U103(tt, x0, x1))
744.20/263.03	   active(U104(tt, x0, x1))
744.20/263.03	   active(U11(tt, x0, x1))
744.20/263.03	   active(U12(tt, x0, x1))
744.20/263.03	   active(U13(tt, x0, x1))
744.20/263.03	   active(U14(tt, x0, x1))
744.20/263.03	   active(U15(tt, x0))
744.20/263.03	   active(U16(tt))
744.20/263.03	   active(U21(tt, x0))
744.20/263.03	   active(U22(tt, x0))
744.20/263.03	   active(U23(tt))
744.20/263.03	   active(U31(tt, x0, x1))
744.20/263.03	   active(U32(tt, x0, x1))
744.20/263.03	   active(U33(tt, x0, x1))
744.20/263.03	   active(U34(tt, x0, x1))
744.20/263.03	   active(U35(tt, x0))
744.20/263.03	   active(U36(tt))
744.20/263.03	   active(U41(tt, x0))
744.20/263.03	   active(U42(tt))
744.20/263.03	   active(U51(tt))
744.20/263.03	   active(U61(tt, x0))
744.20/263.03	   active(U62(tt))
744.20/263.03	   active(U71(tt, x0))
744.20/263.03	   active(U72(tt, x0))
744.20/263.03	   active(U81(tt, x0, x1))
744.20/263.03	   active(U82(tt, x0, x1))
744.20/263.03	   active(U83(tt, x0, x1))
744.20/263.03	   active(U84(tt, x0, x1))
744.20/263.03	   active(U91(tt, x0))
744.20/263.03	   active(U92(tt))
744.20/263.03	   active(isNat(0))
744.20/263.03	   active(isNat(plus(x0, x1)))
744.20/263.03	   active(isNat(s(x0)))
744.20/263.03	   active(isNat(x(x0, x1)))
744.20/263.03	   active(isNatKind(0))
744.20/263.03	   active(isNatKind(plus(x0, x1)))
744.20/263.03	   active(isNatKind(s(x0)))
744.20/263.03	   active(isNatKind(x(x0, x1)))
744.20/263.03	   active(plus(x0, 0))
744.20/263.03	   active(plus(x0, s(x1)))
744.20/263.03	   active(x(x0, 0))
744.20/263.03	   active(x(x0, s(x1)))
744.20/263.03	   mark(U101(x0, x1, x2))
744.20/263.03	   mark(tt)
744.20/263.03	   mark(U102(x0, x1, x2))
744.20/263.03	   mark(isNatKind(x0))
744.20/263.03	   mark(U103(x0, x1, x2))
744.20/263.03	   mark(isNat(x0))
744.20/263.03	   mark(U104(x0, x1, x2))
744.20/263.03	   mark(plus(x0, x1))
744.20/263.03	   mark(x(x0, x1))
744.20/263.03	   mark(U11(x0, x1, x2))
744.20/263.03	   mark(U12(x0, x1, x2))
744.20/263.03	   mark(U13(x0, x1, x2))
744.20/263.03	   mark(U14(x0, x1, x2))
744.20/263.03	   mark(U15(x0, x1))
744.20/263.03	   mark(U16(x0))
744.20/263.03	   mark(U21(x0, x1))
744.20/263.03	   mark(U22(x0, x1))
744.20/263.03	   mark(U23(x0))
744.20/263.03	   mark(U31(x0, x1, x2))
744.20/263.03	   mark(U32(x0, x1, x2))
744.20/263.03	   mark(U33(x0, x1, x2))
744.20/263.03	   mark(U34(x0, x1, x2))
744.20/263.03	   mark(U35(x0, x1))
744.20/263.03	   mark(U36(x0))
744.20/263.03	   mark(U41(x0, x1))
744.20/263.03	   mark(U42(x0))
744.20/263.03	   mark(U51(x0))
744.20/263.03	   mark(U61(x0, x1))
744.20/263.03	   mark(U62(x0))
744.20/263.03	   mark(U71(x0, x1))
744.20/263.03	   mark(U72(x0, x1))
744.20/263.03	   mark(U81(x0, x1, x2))
744.20/263.03	   mark(U82(x0, x1, x2))
744.20/263.03	   mark(U83(x0, x1, x2))
744.20/263.03	   mark(U84(x0, x1, x2))
744.20/263.03	   mark(s(x0))
744.20/263.03	   mark(U91(x0, x1))
744.20/263.03	   mark(U92(x0))
744.20/263.03	   mark(0)
744.20/263.03	   U101(mark(x0), x1, x2)
744.20/263.03	   U101(x0, mark(x1), x2)
744.20/263.03	   U101(x0, x1, mark(x2))
744.20/263.03	   U101(active(x0), x1, x2)
744.20/263.03	   U101(x0, active(x1), x2)
744.20/263.03	   U101(x0, x1, active(x2))
744.20/263.03	   U102(mark(x0), x1, x2)
744.20/263.03	   U102(x0, mark(x1), x2)
744.20/263.03	   U102(x0, x1, mark(x2))
744.20/263.03	   U102(active(x0), x1, x2)
744.20/263.03	   U102(x0, active(x1), x2)
744.20/263.03	   U102(x0, x1, active(x2))
744.20/263.03	   isNatKind(mark(x0))
744.20/263.03	   isNatKind(active(x0))
744.20/263.03	   U103(mark(x0), x1, x2)
744.20/263.03	   U103(x0, mark(x1), x2)
744.20/263.03	   U103(x0, x1, mark(x2))
744.20/263.03	   U103(active(x0), x1, x2)
744.20/263.03	   U103(x0, active(x1), x2)
744.20/263.03	   U103(x0, x1, active(x2))
744.20/263.03	   isNat(mark(x0))
744.20/263.03	   isNat(active(x0))
744.20/263.03	   U104(mark(x0), x1, x2)
744.20/263.03	   U104(x0, mark(x1), x2)
744.20/263.03	   U104(x0, x1, mark(x2))
744.20/263.03	   U104(active(x0), x1, x2)
744.20/263.03	   U104(x0, active(x1), x2)
744.20/263.03	   U104(x0, x1, active(x2))
744.20/263.03	   plus(mark(x0), x1)
744.20/263.03	   plus(x0, mark(x1))
744.20/263.03	   plus(active(x0), x1)
744.20/263.03	   plus(x0, active(x1))
744.20/263.03	   x(mark(x0), x1)
744.20/263.03	   x(x0, mark(x1))
744.20/263.03	   x(active(x0), x1)
744.20/263.03	   x(x0, active(x1))
744.20/263.03	   U11(mark(x0), x1, x2)
744.20/263.03	   U11(x0, mark(x1), x2)
744.20/263.03	   U11(x0, x1, mark(x2))
744.20/263.03	   U11(active(x0), x1, x2)
744.20/263.03	   U11(x0, active(x1), x2)
744.20/263.03	   U11(x0, x1, active(x2))
744.20/263.03	   U12(mark(x0), x1, x2)
744.20/263.03	   U12(x0, mark(x1), x2)
744.20/263.03	   U12(x0, x1, mark(x2))
744.20/263.03	   U12(active(x0), x1, x2)
744.20/263.03	   U12(x0, active(x1), x2)
744.20/263.03	   U12(x0, x1, active(x2))
744.20/263.03	   U13(mark(x0), x1, x2)
744.20/263.03	   U13(x0, mark(x1), x2)
744.20/263.03	   U13(x0, x1, mark(x2))
744.20/263.03	   U13(active(x0), x1, x2)
744.20/263.03	   U13(x0, active(x1), x2)
744.20/263.03	   U13(x0, x1, active(x2))
744.20/263.03	   U14(mark(x0), x1, x2)
744.20/263.03	   U14(x0, mark(x1), x2)
744.20/263.03	   U14(x0, x1, mark(x2))
744.20/263.03	   U14(active(x0), x1, x2)
744.20/263.03	   U14(x0, active(x1), x2)
744.20/263.03	   U14(x0, x1, active(x2))
744.20/263.03	   U15(mark(x0), x1)
744.20/263.03	   U15(x0, mark(x1))
744.20/263.03	   U15(active(x0), x1)
744.20/263.03	   U15(x0, active(x1))
744.20/263.03	   U16(mark(x0))
744.20/263.03	   U16(active(x0))
744.20/263.03	   U21(mark(x0), x1)
744.20/263.03	   U21(x0, mark(x1))
744.20/263.03	   U21(active(x0), x1)
744.20/263.03	   U21(x0, active(x1))
744.20/263.03	   U22(mark(x0), x1)
744.20/263.03	   U22(x0, mark(x1))
744.20/263.03	   U22(active(x0), x1)
744.20/263.03	   U22(x0, active(x1))
744.20/263.03	   U23(mark(x0))
744.20/263.03	   U23(active(x0))
744.20/263.03	   U31(mark(x0), x1, x2)
744.20/263.03	   U31(x0, mark(x1), x2)
744.20/263.03	   U31(x0, x1, mark(x2))
744.20/263.03	   U31(active(x0), x1, x2)
744.20/263.03	   U31(x0, active(x1), x2)
744.20/263.03	   U31(x0, x1, active(x2))
744.20/263.03	   U32(mark(x0), x1, x2)
744.20/263.03	   U32(x0, mark(x1), x2)
744.20/263.03	   U32(x0, x1, mark(x2))
744.20/263.03	   U32(active(x0), x1, x2)
744.20/263.03	   U32(x0, active(x1), x2)
744.20/263.03	   U32(x0, x1, active(x2))
744.20/263.03	   U33(mark(x0), x1, x2)
744.20/263.03	   U33(x0, mark(x1), x2)
744.20/263.03	   U33(x0, x1, mark(x2))
744.20/263.03	   U33(active(x0), x1, x2)
744.20/263.03	   U33(x0, active(x1), x2)
744.20/263.03	   U33(x0, x1, active(x2))
744.20/263.03	   U34(mark(x0), x1, x2)
744.20/263.03	   U34(x0, mark(x1), x2)
744.20/263.03	   U34(x0, x1, mark(x2))
744.20/263.03	   U34(active(x0), x1, x2)
744.20/263.03	   U34(x0, active(x1), x2)
744.20/263.03	   U34(x0, x1, active(x2))
744.20/263.03	   U35(mark(x0), x1)
744.20/263.03	   U35(x0, mark(x1))
744.20/263.03	   U35(active(x0), x1)
744.20/263.03	   U35(x0, active(x1))
744.20/263.03	   U36(mark(x0))
744.20/263.03	   U36(active(x0))
744.20/263.03	   U41(mark(x0), x1)
744.20/263.03	   U41(x0, mark(x1))
744.20/263.03	   U41(active(x0), x1)
744.20/263.03	   U41(x0, active(x1))
744.20/263.03	   U42(mark(x0))
744.20/263.03	   U42(active(x0))
744.20/263.03	   U51(mark(x0))
744.20/263.03	   U51(active(x0))
744.20/263.03	   U61(mark(x0), x1)
744.20/263.03	   U61(x0, mark(x1))
744.20/263.03	   U61(active(x0), x1)
744.20/263.03	   U61(x0, active(x1))
744.20/263.03	   U62(mark(x0))
744.20/263.03	   U62(active(x0))
744.20/263.03	   U71(mark(x0), x1)
744.20/263.03	   U71(x0, mark(x1))
744.20/263.03	   U71(active(x0), x1)
744.20/263.03	   U71(x0, active(x1))
744.20/263.03	   U72(mark(x0), x1)
744.20/263.03	   U72(x0, mark(x1))
744.20/263.03	   U72(active(x0), x1)
744.20/263.03	   U72(x0, active(x1))
744.20/263.03	   U81(mark(x0), x1, x2)
744.20/263.03	   U81(x0, mark(x1), x2)
744.20/263.03	   U81(x0, x1, mark(x2))
744.20/263.03	   U81(active(x0), x1, x2)
744.20/263.03	   U81(x0, active(x1), x2)
744.20/263.03	   U81(x0, x1, active(x2))
744.20/263.03	   U82(mark(x0), x1, x2)
744.20/263.03	   U82(x0, mark(x1), x2)
744.20/263.03	   U82(x0, x1, mark(x2))
744.20/263.03	   U82(active(x0), x1, x2)
744.20/263.03	   U82(x0, active(x1), x2)
744.20/263.03	   U82(x0, x1, active(x2))
744.20/263.03	   U83(mark(x0), x1, x2)
744.20/263.03	   U83(x0, mark(x1), x2)
744.20/263.03	   U83(x0, x1, mark(x2))
744.20/263.03	   U83(active(x0), x1, x2)
744.20/263.03	   U83(x0, active(x1), x2)
744.20/263.03	   U83(x0, x1, active(x2))
744.20/263.03	   U84(mark(x0), x1, x2)
744.20/263.03	   U84(x0, mark(x1), x2)
744.20/263.03	   U84(x0, x1, mark(x2))
744.20/263.03	   U84(active(x0), x1, x2)
744.20/263.03	   U84(x0, active(x1), x2)
744.20/263.03	   U84(x0, x1, active(x2))
744.20/263.03	   s(mark(x0))
744.20/263.03	   s(active(x0))
744.20/263.03	   U91(mark(x0), x1)
744.20/263.03	   U91(x0, mark(x1))
744.20/263.03	   U91(active(x0), x1)
744.20/263.03	   U91(x0, active(x1))
744.20/263.03	   U92(mark(x0))
744.20/263.03	   U92(active(x0))
744.20/263.03	
744.20/263.03	We have to consider all minimal (P,Q,R)-chains.
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(297) QDPOrderProof (EQUIVALENT)
744.20/263.03	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.03	
744.20/263.03	
744.20/263.03	The following pairs can be oriented strictly and are deleted.
744.20/263.03	
744.20/263.03	   MARK(U61(X1, X2)) -> ACTIVE(U61(mark(X1), X2))
744.20/263.03	The remaining pairs can at least be oriented weakly.
744.20/263.03	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.03	
744.20/263.03	POL( ACTIVE_1(x_1) ) = max{0, 2x_1 - 1}
744.20/263.03	POL( U11_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U12_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U13_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U14_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U15_2(x_1, x_2) ) = 1
744.20/263.03	POL( U21_2(x_1, x_2) ) = 1
744.20/263.03	POL( U22_2(x_1, x_2) ) = 1
744.20/263.03	POL( U31_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U32_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U33_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U34_3(x_1, ..., x_3) ) = 1
744.20/263.03	POL( U35_2(x_1, x_2) ) = 1
744.20/263.03	POL( U41_2(x_1, x_2) ) = 1
744.20/263.03	POL( U61_2(x_1, x_2) ) = max{0, -2}
744.20/263.03	POL( mark_1(x_1) ) = max{0, -2}
744.20/263.03	POL( U102_3(x_1, ..., x_3) ) = max{0, x_2 + x_3 - 2}
744.20/263.03	POL( active_1(x_1) ) = x_1 + 2
744.20/263.03	POL( U101_3(x_1, ..., x_3) ) = x_2 + 2
744.20/263.03	POL( tt ) = 0
744.20/263.03	POL( isNatKind_1(x_1) ) = 1
744.20/263.03	POL( U103_3(x_1, ..., x_3) ) = x_2 + x_3 + 2
744.20/263.03	POL( isNat_1(x_1) ) = 1
744.20/263.03	POL( U104_3(x_1, ..., x_3) ) = 2
744.20/263.03	POL( plus_2(x_1, x_2) ) = 2
744.20/263.03	POL( x_2(x_1, x_2) ) = max{0, x_1 - 2}
744.20/263.03	POL( U16_1(x_1) ) = max{0, -2}
744.20/263.03	POL( U23_1(x_1) ) = max{0, -2}
744.20/263.03	POL( U36_1(x_1) ) = max{0, x_1 - 2}
744.20/263.03	POL( U42_1(x_1) ) = max{0, x_1 - 2}
744.20/263.03	POL( U62_1(x_1) ) = 2
744.20/263.03	POL( U71_2(x_1, x_2) ) = 2
744.20/263.03	POL( U72_2(x_1, x_2) ) = x_1 + 2
744.20/263.03	POL( U81_3(x_1, ..., x_3) ) = 2
744.20/263.03	POL( U82_3(x_1, ..., x_3) ) = max{0, x_2 + 2x_3 - 2}
744.20/263.03	POL( U83_3(x_1, ..., x_3) ) = 2x_1 + 2x_2 + 2
744.20/263.03	POL( U84_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.20/263.03	POL( s_1(x_1) ) = 2
744.20/263.03	POL( U91_2(x_1, x_2) ) = x_2 + 2
744.20/263.03	POL( U92_1(x_1) ) = 0
744.20/263.03	POL( U51_1(x_1) ) = max{0, -2}
744.20/263.03	POL( 0 ) = 0
744.20/263.03	POL( MARK_1(x_1) ) = 1
744.20/263.03	
744.20/263.03	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.03	
744.20/263.03	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.03	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.03	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.03	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.03	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.03	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.03	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.03	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.03	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.03	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.03	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.03	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.03	
744.20/263.03	
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(298)
744.20/263.03	Obligation:
744.20/263.03	Q DP problem:
744.20/263.03	The TRS P consists of the following rules:
744.20/263.03	
744.20/263.03	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.03	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.03	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.03	   MARK(U16(X)) -> MARK(X)
744.20/263.03	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.03	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.03	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.03	   MARK(U23(X)) -> MARK(X)
744.20/263.03	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.03	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.03	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.03	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.03	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.03	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.03	   MARK(U36(X)) -> MARK(X)
744.20/263.03	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.03	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.03	   MARK(U42(X)) -> MARK(X)
744.20/263.03	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.03	   MARK(U62(X)) -> MARK(X)
744.20/263.03	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.03	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U51(X)) -> MARK(X)
744.20/263.03	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.03	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.03	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.03	   ACTIVE(isNatKind(x(V1, V2))) -> MARK(U61(isNatKind(V1), V2))
744.20/263.03	
744.20/263.03	The TRS R consists of the following rules:
744.20/263.03	
744.20/263.03	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.03	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.03	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.03	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.03	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.03	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.03	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.03	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.03	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.03	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.03	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.03	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.03	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.03	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.03	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.03	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.03	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.03	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.03	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.03	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.03	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.03	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.03	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.03	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.03	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.03	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.03	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.03	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.03	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.03	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.03	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.03	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.03	   active(U72(tt, N)) -> mark(N)
744.20/263.03	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.03	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.03	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.03	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.03	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.03	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.03	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.03	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.03	   mark(s(X)) -> active(s(mark(X)))
744.20/263.03	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.03	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.03	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.03	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.03	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.03	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.03	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.03	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.03	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.03	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.03	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.03	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.03	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.03	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.03	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.03	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.03	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.03	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.03	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.03	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.03	   mark(isNat(X)) -> active(isNat(X))
744.20/263.03	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.03	   mark(tt) -> active(tt)
744.20/263.03	   mark(0) -> active(0)
744.20/263.03	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.03	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.03	   active(U16(tt)) -> mark(tt)
744.20/263.03	   active(U23(tt)) -> mark(tt)
744.20/263.03	   active(U36(tt)) -> mark(tt)
744.20/263.03	   active(U42(tt)) -> mark(tt)
744.20/263.03	   active(U51(tt)) -> mark(tt)
744.20/263.03	   active(U62(tt)) -> mark(tt)
744.20/263.03	   active(U92(tt)) -> mark(0)
744.20/263.03	   active(isNat(0)) -> mark(tt)
744.20/263.03	   active(isNatKind(0)) -> mark(tt)
744.20/263.03	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.03	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.03	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.03	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.03	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.03	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.03	   U16(active(X)) -> U16(X)
744.20/263.03	   U16(mark(X)) -> U16(X)
744.20/263.03	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.03	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.03	   U23(active(X)) -> U23(X)
744.20/263.03	   U23(mark(X)) -> U23(X)
744.20/263.03	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.03	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.03	   U36(active(X)) -> U36(X)
744.20/263.03	   U36(mark(X)) -> U36(X)
744.20/263.03	   U42(active(X)) -> U42(X)
744.20/263.03	   U42(mark(X)) -> U42(X)
744.20/263.03	   U62(active(X)) -> U62(X)
744.20/263.03	   U62(mark(X)) -> U62(X)
744.20/263.03	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.03	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.03	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.03	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.03	   s(active(X)) -> s(X)
744.20/263.03	   s(mark(X)) -> s(X)
744.20/263.03	   U92(active(X)) -> U92(X)
744.20/263.03	   U92(mark(X)) -> U92(X)
744.20/263.03	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.03	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.03	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.03	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.03	   U51(active(X)) -> U51(X)
744.20/263.03	   U51(mark(X)) -> U51(X)
744.20/263.03	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.03	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.03	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.03	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.03	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.03	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.03	   x(active(X1), X2) -> x(X1, X2)
744.20/263.03	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.03	
744.20/263.03	The set Q consists of the following terms:
744.20/263.03	
744.20/263.03	   active(U101(tt, x0, x1))
744.20/263.03	   active(U102(tt, x0, x1))
744.20/263.03	   active(U103(tt, x0, x1))
744.20/263.03	   active(U104(tt, x0, x1))
744.20/263.03	   active(U11(tt, x0, x1))
744.20/263.03	   active(U12(tt, x0, x1))
744.20/263.03	   active(U13(tt, x0, x1))
744.20/263.03	   active(U14(tt, x0, x1))
744.20/263.03	   active(U15(tt, x0))
744.20/263.03	   active(U16(tt))
744.20/263.03	   active(U21(tt, x0))
744.20/263.03	   active(U22(tt, x0))
744.20/263.03	   active(U23(tt))
744.20/263.03	   active(U31(tt, x0, x1))
744.20/263.03	   active(U32(tt, x0, x1))
744.20/263.03	   active(U33(tt, x0, x1))
744.20/263.03	   active(U34(tt, x0, x1))
744.20/263.03	   active(U35(tt, x0))
744.20/263.03	   active(U36(tt))
744.20/263.03	   active(U41(tt, x0))
744.20/263.03	   active(U42(tt))
744.20/263.03	   active(U51(tt))
744.20/263.03	   active(U61(tt, x0))
744.20/263.03	   active(U62(tt))
744.20/263.03	   active(U71(tt, x0))
744.20/263.03	   active(U72(tt, x0))
744.20/263.03	   active(U81(tt, x0, x1))
744.20/263.03	   active(U82(tt, x0, x1))
744.20/263.03	   active(U83(tt, x0, x1))
744.20/263.03	   active(U84(tt, x0, x1))
744.20/263.03	   active(U91(tt, x0))
744.20/263.03	   active(U92(tt))
744.20/263.03	   active(isNat(0))
744.20/263.03	   active(isNat(plus(x0, x1)))
744.20/263.03	   active(isNat(s(x0)))
744.20/263.03	   active(isNat(x(x0, x1)))
744.20/263.03	   active(isNatKind(0))
744.20/263.03	   active(isNatKind(plus(x0, x1)))
744.20/263.03	   active(isNatKind(s(x0)))
744.20/263.03	   active(isNatKind(x(x0, x1)))
744.20/263.03	   active(plus(x0, 0))
744.20/263.03	   active(plus(x0, s(x1)))
744.20/263.03	   active(x(x0, 0))
744.20/263.03	   active(x(x0, s(x1)))
744.20/263.03	   mark(U101(x0, x1, x2))
744.20/263.03	   mark(tt)
744.20/263.03	   mark(U102(x0, x1, x2))
744.20/263.03	   mark(isNatKind(x0))
744.20/263.03	   mark(U103(x0, x1, x2))
744.20/263.03	   mark(isNat(x0))
744.20/263.03	   mark(U104(x0, x1, x2))
744.20/263.03	   mark(plus(x0, x1))
744.20/263.03	   mark(x(x0, x1))
744.20/263.03	   mark(U11(x0, x1, x2))
744.20/263.03	   mark(U12(x0, x1, x2))
744.20/263.03	   mark(U13(x0, x1, x2))
744.20/263.03	   mark(U14(x0, x1, x2))
744.20/263.03	   mark(U15(x0, x1))
744.20/263.03	   mark(U16(x0))
744.20/263.03	   mark(U21(x0, x1))
744.20/263.03	   mark(U22(x0, x1))
744.20/263.03	   mark(U23(x0))
744.20/263.03	   mark(U31(x0, x1, x2))
744.20/263.03	   mark(U32(x0, x1, x2))
744.20/263.03	   mark(U33(x0, x1, x2))
744.20/263.03	   mark(U34(x0, x1, x2))
744.20/263.03	   mark(U35(x0, x1))
744.20/263.03	   mark(U36(x0))
744.20/263.03	   mark(U41(x0, x1))
744.20/263.03	   mark(U42(x0))
744.20/263.03	   mark(U51(x0))
744.20/263.03	   mark(U61(x0, x1))
744.20/263.03	   mark(U62(x0))
744.20/263.03	   mark(U71(x0, x1))
744.20/263.03	   mark(U72(x0, x1))
744.20/263.03	   mark(U81(x0, x1, x2))
744.20/263.03	   mark(U82(x0, x1, x2))
744.20/263.03	   mark(U83(x0, x1, x2))
744.20/263.03	   mark(U84(x0, x1, x2))
744.20/263.03	   mark(s(x0))
744.20/263.03	   mark(U91(x0, x1))
744.20/263.03	   mark(U92(x0))
744.20/263.03	   mark(0)
744.20/263.03	   U101(mark(x0), x1, x2)
744.20/263.03	   U101(x0, mark(x1), x2)
744.20/263.03	   U101(x0, x1, mark(x2))
744.20/263.03	   U101(active(x0), x1, x2)
744.20/263.03	   U101(x0, active(x1), x2)
744.20/263.03	   U101(x0, x1, active(x2))
744.20/263.03	   U102(mark(x0), x1, x2)
744.20/263.03	   U102(x0, mark(x1), x2)
744.20/263.03	   U102(x0, x1, mark(x2))
744.20/263.03	   U102(active(x0), x1, x2)
744.20/263.03	   U102(x0, active(x1), x2)
744.20/263.03	   U102(x0, x1, active(x2))
744.20/263.03	   isNatKind(mark(x0))
744.20/263.03	   isNatKind(active(x0))
744.20/263.03	   U103(mark(x0), x1, x2)
744.20/263.03	   U103(x0, mark(x1), x2)
744.20/263.03	   U103(x0, x1, mark(x2))
744.20/263.03	   U103(active(x0), x1, x2)
744.20/263.03	   U103(x0, active(x1), x2)
744.20/263.03	   U103(x0, x1, active(x2))
744.20/263.03	   isNat(mark(x0))
744.20/263.03	   isNat(active(x0))
744.20/263.03	   U104(mark(x0), x1, x2)
744.20/263.03	   U104(x0, mark(x1), x2)
744.20/263.03	   U104(x0, x1, mark(x2))
744.20/263.03	   U104(active(x0), x1, x2)
744.20/263.03	   U104(x0, active(x1), x2)
744.20/263.03	   U104(x0, x1, active(x2))
744.20/263.03	   plus(mark(x0), x1)
744.20/263.03	   plus(x0, mark(x1))
744.20/263.03	   plus(active(x0), x1)
744.20/263.03	   plus(x0, active(x1))
744.20/263.03	   x(mark(x0), x1)
744.20/263.03	   x(x0, mark(x1))
744.20/263.03	   x(active(x0), x1)
744.20/263.03	   x(x0, active(x1))
744.20/263.03	   U11(mark(x0), x1, x2)
744.20/263.03	   U11(x0, mark(x1), x2)
744.20/263.03	   U11(x0, x1, mark(x2))
744.20/263.03	   U11(active(x0), x1, x2)
744.20/263.03	   U11(x0, active(x1), x2)
744.20/263.03	   U11(x0, x1, active(x2))
744.20/263.03	   U12(mark(x0), x1, x2)
744.20/263.03	   U12(x0, mark(x1), x2)
744.20/263.03	   U12(x0, x1, mark(x2))
744.20/263.03	   U12(active(x0), x1, x2)
744.20/263.03	   U12(x0, active(x1), x2)
744.20/263.03	   U12(x0, x1, active(x2))
744.20/263.03	   U13(mark(x0), x1, x2)
744.20/263.03	   U13(x0, mark(x1), x2)
744.20/263.03	   U13(x0, x1, mark(x2))
744.20/263.03	   U13(active(x0), x1, x2)
744.20/263.03	   U13(x0, active(x1), x2)
744.20/263.03	   U13(x0, x1, active(x2))
744.20/263.03	   U14(mark(x0), x1, x2)
744.20/263.03	   U14(x0, mark(x1), x2)
744.20/263.03	   U14(x0, x1, mark(x2))
744.20/263.03	   U14(active(x0), x1, x2)
744.20/263.03	   U14(x0, active(x1), x2)
744.20/263.03	   U14(x0, x1, active(x2))
744.20/263.03	   U15(mark(x0), x1)
744.20/263.03	   U15(x0, mark(x1))
744.20/263.03	   U15(active(x0), x1)
744.20/263.03	   U15(x0, active(x1))
744.20/263.03	   U16(mark(x0))
744.20/263.03	   U16(active(x0))
744.20/263.03	   U21(mark(x0), x1)
744.20/263.03	   U21(x0, mark(x1))
744.20/263.03	   U21(active(x0), x1)
744.20/263.03	   U21(x0, active(x1))
744.20/263.03	   U22(mark(x0), x1)
744.20/263.03	   U22(x0, mark(x1))
744.20/263.03	   U22(active(x0), x1)
744.20/263.03	   U22(x0, active(x1))
744.20/263.03	   U23(mark(x0))
744.20/263.03	   U23(active(x0))
744.20/263.03	   U31(mark(x0), x1, x2)
744.20/263.03	   U31(x0, mark(x1), x2)
744.20/263.03	   U31(x0, x1, mark(x2))
744.20/263.03	   U31(active(x0), x1, x2)
744.20/263.03	   U31(x0, active(x1), x2)
744.20/263.03	   U31(x0, x1, active(x2))
744.20/263.03	   U32(mark(x0), x1, x2)
744.20/263.03	   U32(x0, mark(x1), x2)
744.20/263.03	   U32(x0, x1, mark(x2))
744.20/263.03	   U32(active(x0), x1, x2)
744.20/263.03	   U32(x0, active(x1), x2)
744.20/263.03	   U32(x0, x1, active(x2))
744.20/263.03	   U33(mark(x0), x1, x2)
744.20/263.03	   U33(x0, mark(x1), x2)
744.20/263.03	   U33(x0, x1, mark(x2))
744.20/263.03	   U33(active(x0), x1, x2)
744.20/263.03	   U33(x0, active(x1), x2)
744.20/263.03	   U33(x0, x1, active(x2))
744.20/263.03	   U34(mark(x0), x1, x2)
744.20/263.03	   U34(x0, mark(x1), x2)
744.20/263.03	   U34(x0, x1, mark(x2))
744.20/263.03	   U34(active(x0), x1, x2)
744.20/263.03	   U34(x0, active(x1), x2)
744.20/263.03	   U34(x0, x1, active(x2))
744.20/263.03	   U35(mark(x0), x1)
744.20/263.03	   U35(x0, mark(x1))
744.20/263.03	   U35(active(x0), x1)
744.20/263.03	   U35(x0, active(x1))
744.20/263.03	   U36(mark(x0))
744.20/263.03	   U36(active(x0))
744.20/263.03	   U41(mark(x0), x1)
744.20/263.03	   U41(x0, mark(x1))
744.20/263.03	   U41(active(x0), x1)
744.20/263.03	   U41(x0, active(x1))
744.20/263.03	   U42(mark(x0))
744.20/263.03	   U42(active(x0))
744.20/263.03	   U51(mark(x0))
744.20/263.03	   U51(active(x0))
744.20/263.03	   U61(mark(x0), x1)
744.20/263.03	   U61(x0, mark(x1))
744.20/263.03	   U61(active(x0), x1)
744.20/263.03	   U61(x0, active(x1))
744.20/263.03	   U62(mark(x0))
744.20/263.03	   U62(active(x0))
744.20/263.03	   U71(mark(x0), x1)
744.20/263.03	   U71(x0, mark(x1))
744.20/263.03	   U71(active(x0), x1)
744.20/263.03	   U71(x0, active(x1))
744.20/263.03	   U72(mark(x0), x1)
744.20/263.03	   U72(x0, mark(x1))
744.20/263.03	   U72(active(x0), x1)
744.20/263.03	   U72(x0, active(x1))
744.20/263.03	   U81(mark(x0), x1, x2)
744.20/263.03	   U81(x0, mark(x1), x2)
744.20/263.03	   U81(x0, x1, mark(x2))
744.20/263.03	   U81(active(x0), x1, x2)
744.20/263.03	   U81(x0, active(x1), x2)
744.20/263.03	   U81(x0, x1, active(x2))
744.20/263.03	   U82(mark(x0), x1, x2)
744.20/263.03	   U82(x0, mark(x1), x2)
744.20/263.03	   U82(x0, x1, mark(x2))
744.20/263.03	   U82(active(x0), x1, x2)
744.20/263.03	   U82(x0, active(x1), x2)
744.20/263.03	   U82(x0, x1, active(x2))
744.20/263.03	   U83(mark(x0), x1, x2)
744.20/263.03	   U83(x0, mark(x1), x2)
744.20/263.03	   U83(x0, x1, mark(x2))
744.20/263.03	   U83(active(x0), x1, x2)
744.20/263.03	   U83(x0, active(x1), x2)
744.20/263.03	   U83(x0, x1, active(x2))
744.20/263.03	   U84(mark(x0), x1, x2)
744.20/263.03	   U84(x0, mark(x1), x2)
744.20/263.03	   U84(x0, x1, mark(x2))
744.20/263.03	   U84(active(x0), x1, x2)
744.20/263.03	   U84(x0, active(x1), x2)
744.20/263.03	   U84(x0, x1, active(x2))
744.20/263.03	   s(mark(x0))
744.20/263.03	   s(active(x0))
744.20/263.03	   U91(mark(x0), x1)
744.20/263.03	   U91(x0, mark(x1))
744.20/263.03	   U91(active(x0), x1)
744.20/263.03	   U91(x0, active(x1))
744.20/263.03	   U92(mark(x0))
744.20/263.03	   U92(active(x0))
744.20/263.03	
744.20/263.03	We have to consider all minimal (P,Q,R)-chains.
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(299) DependencyGraphProof (EQUIVALENT)
744.20/263.03	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(300)
744.20/263.03	Obligation:
744.20/263.03	Q DP problem:
744.20/263.03	The TRS P consists of the following rules:
744.20/263.03	
744.20/263.03	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.03	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.03	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.03	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.03	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.03	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.03	   MARK(U16(X)) -> MARK(X)
744.20/263.03	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.03	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.03	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.03	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.03	   MARK(U23(X)) -> MARK(X)
744.20/263.03	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.03	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.03	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.03	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.03	   MARK(U36(X)) -> MARK(X)
744.20/263.03	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.03	   MARK(U42(X)) -> MARK(X)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U51(X)) -> MARK(X)
744.20/263.03	   MARK(U62(X)) -> MARK(X)
744.20/263.03	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.03	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.03	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.03	
744.20/263.03	The TRS R consists of the following rules:
744.20/263.03	
744.20/263.03	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.03	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.03	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.03	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.03	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.03	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.03	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.03	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.03	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.03	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.03	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.03	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.03	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.03	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.03	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.03	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.03	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.03	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.03	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.03	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.03	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.03	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.03	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.03	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.03	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.03	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.03	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.03	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.03	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.03	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.03	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.03	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.03	   active(U72(tt, N)) -> mark(N)
744.20/263.03	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.03	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.03	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.03	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.03	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.03	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.03	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.03	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.03	   mark(s(X)) -> active(s(mark(X)))
744.20/263.03	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.03	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.03	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.03	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.03	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.03	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.03	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.03	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.03	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.03	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.03	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.03	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.03	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.03	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.03	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.03	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.03	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.03	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.03	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.03	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.03	   mark(isNat(X)) -> active(isNat(X))
744.20/263.03	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.03	   mark(tt) -> active(tt)
744.20/263.03	   mark(0) -> active(0)
744.20/263.03	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.03	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.03	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.03	   active(U16(tt)) -> mark(tt)
744.20/263.03	   active(U23(tt)) -> mark(tt)
744.20/263.03	   active(U36(tt)) -> mark(tt)
744.20/263.03	   active(U42(tt)) -> mark(tt)
744.20/263.03	   active(U51(tt)) -> mark(tt)
744.20/263.03	   active(U62(tt)) -> mark(tt)
744.20/263.03	   active(U92(tt)) -> mark(0)
744.20/263.03	   active(isNat(0)) -> mark(tt)
744.20/263.03	   active(isNatKind(0)) -> mark(tt)
744.20/263.03	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.03	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.03	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.03	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.03	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.03	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.03	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.03	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.03	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.03	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.03	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.03	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.03	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.03	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.03	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.03	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.03	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.03	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.03	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.03	   U16(active(X)) -> U16(X)
744.20/263.03	   U16(mark(X)) -> U16(X)
744.20/263.03	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.03	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.03	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.03	   U23(active(X)) -> U23(X)
744.20/263.03	   U23(mark(X)) -> U23(X)
744.20/263.03	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.03	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.03	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.03	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.03	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.03	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.03	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.03	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.03	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.03	   U36(active(X)) -> U36(X)
744.20/263.03	   U36(mark(X)) -> U36(X)
744.20/263.03	   U42(active(X)) -> U42(X)
744.20/263.03	   U42(mark(X)) -> U42(X)
744.20/263.03	   U62(active(X)) -> U62(X)
744.20/263.03	   U62(mark(X)) -> U62(X)
744.20/263.03	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.03	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.03	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.03	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.03	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.03	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.03	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.03	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.03	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.03	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.03	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.03	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.03	   s(active(X)) -> s(X)
744.20/263.03	   s(mark(X)) -> s(X)
744.20/263.03	   U92(active(X)) -> U92(X)
744.20/263.03	   U92(mark(X)) -> U92(X)
744.20/263.03	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.03	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.03	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.03	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.03	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.03	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.03	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.03	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.03	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.03	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.03	   U51(active(X)) -> U51(X)
744.20/263.03	   U51(mark(X)) -> U51(X)
744.20/263.03	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.03	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.03	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.03	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.03	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.03	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.03	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.03	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.03	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.03	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.03	   x(active(X1), X2) -> x(X1, X2)
744.20/263.03	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.03	
744.20/263.03	The set Q consists of the following terms:
744.20/263.03	
744.20/263.03	   active(U101(tt, x0, x1))
744.20/263.03	   active(U102(tt, x0, x1))
744.20/263.03	   active(U103(tt, x0, x1))
744.20/263.03	   active(U104(tt, x0, x1))
744.20/263.03	   active(U11(tt, x0, x1))
744.20/263.03	   active(U12(tt, x0, x1))
744.20/263.03	   active(U13(tt, x0, x1))
744.20/263.03	   active(U14(tt, x0, x1))
744.20/263.03	   active(U15(tt, x0))
744.20/263.03	   active(U16(tt))
744.20/263.03	   active(U21(tt, x0))
744.20/263.03	   active(U22(tt, x0))
744.20/263.03	   active(U23(tt))
744.20/263.03	   active(U31(tt, x0, x1))
744.20/263.03	   active(U32(tt, x0, x1))
744.20/263.03	   active(U33(tt, x0, x1))
744.20/263.03	   active(U34(tt, x0, x1))
744.20/263.03	   active(U35(tt, x0))
744.20/263.03	   active(U36(tt))
744.20/263.03	   active(U41(tt, x0))
744.20/263.03	   active(U42(tt))
744.20/263.03	   active(U51(tt))
744.20/263.03	   active(U61(tt, x0))
744.20/263.03	   active(U62(tt))
744.20/263.03	   active(U71(tt, x0))
744.20/263.03	   active(U72(tt, x0))
744.20/263.03	   active(U81(tt, x0, x1))
744.20/263.03	   active(U82(tt, x0, x1))
744.20/263.03	   active(U83(tt, x0, x1))
744.20/263.03	   active(U84(tt, x0, x1))
744.20/263.03	   active(U91(tt, x0))
744.20/263.03	   active(U92(tt))
744.20/263.03	   active(isNat(0))
744.20/263.03	   active(isNat(plus(x0, x1)))
744.20/263.03	   active(isNat(s(x0)))
744.20/263.03	   active(isNat(x(x0, x1)))
744.20/263.03	   active(isNatKind(0))
744.20/263.03	   active(isNatKind(plus(x0, x1)))
744.20/263.03	   active(isNatKind(s(x0)))
744.20/263.03	   active(isNatKind(x(x0, x1)))
744.20/263.03	   active(plus(x0, 0))
744.20/263.03	   active(plus(x0, s(x1)))
744.20/263.03	   active(x(x0, 0))
744.20/263.03	   active(x(x0, s(x1)))
744.20/263.03	   mark(U101(x0, x1, x2))
744.20/263.03	   mark(tt)
744.20/263.03	   mark(U102(x0, x1, x2))
744.20/263.03	   mark(isNatKind(x0))
744.20/263.03	   mark(U103(x0, x1, x2))
744.20/263.03	   mark(isNat(x0))
744.20/263.03	   mark(U104(x0, x1, x2))
744.20/263.03	   mark(plus(x0, x1))
744.20/263.03	   mark(x(x0, x1))
744.20/263.03	   mark(U11(x0, x1, x2))
744.20/263.03	   mark(U12(x0, x1, x2))
744.20/263.03	   mark(U13(x0, x1, x2))
744.20/263.03	   mark(U14(x0, x1, x2))
744.20/263.03	   mark(U15(x0, x1))
744.20/263.03	   mark(U16(x0))
744.20/263.03	   mark(U21(x0, x1))
744.20/263.03	   mark(U22(x0, x1))
744.20/263.03	   mark(U23(x0))
744.20/263.03	   mark(U31(x0, x1, x2))
744.20/263.03	   mark(U32(x0, x1, x2))
744.20/263.03	   mark(U33(x0, x1, x2))
744.20/263.03	   mark(U34(x0, x1, x2))
744.20/263.03	   mark(U35(x0, x1))
744.20/263.03	   mark(U36(x0))
744.20/263.03	   mark(U41(x0, x1))
744.20/263.03	   mark(U42(x0))
744.20/263.03	   mark(U51(x0))
744.20/263.03	   mark(U61(x0, x1))
744.20/263.03	   mark(U62(x0))
744.20/263.03	   mark(U71(x0, x1))
744.20/263.03	   mark(U72(x0, x1))
744.20/263.03	   mark(U81(x0, x1, x2))
744.20/263.03	   mark(U82(x0, x1, x2))
744.20/263.03	   mark(U83(x0, x1, x2))
744.20/263.03	   mark(U84(x0, x1, x2))
744.20/263.03	   mark(s(x0))
744.20/263.03	   mark(U91(x0, x1))
744.20/263.03	   mark(U92(x0))
744.20/263.03	   mark(0)
744.20/263.03	   U101(mark(x0), x1, x2)
744.20/263.03	   U101(x0, mark(x1), x2)
744.20/263.03	   U101(x0, x1, mark(x2))
744.20/263.03	   U101(active(x0), x1, x2)
744.20/263.03	   U101(x0, active(x1), x2)
744.20/263.03	   U101(x0, x1, active(x2))
744.20/263.03	   U102(mark(x0), x1, x2)
744.20/263.03	   U102(x0, mark(x1), x2)
744.20/263.03	   U102(x0, x1, mark(x2))
744.20/263.03	   U102(active(x0), x1, x2)
744.20/263.03	   U102(x0, active(x1), x2)
744.20/263.03	   U102(x0, x1, active(x2))
744.20/263.03	   isNatKind(mark(x0))
744.20/263.03	   isNatKind(active(x0))
744.20/263.03	   U103(mark(x0), x1, x2)
744.20/263.03	   U103(x0, mark(x1), x2)
744.20/263.03	   U103(x0, x1, mark(x2))
744.20/263.03	   U103(active(x0), x1, x2)
744.20/263.03	   U103(x0, active(x1), x2)
744.20/263.03	   U103(x0, x1, active(x2))
744.20/263.03	   isNat(mark(x0))
744.20/263.03	   isNat(active(x0))
744.20/263.03	   U104(mark(x0), x1, x2)
744.20/263.03	   U104(x0, mark(x1), x2)
744.20/263.03	   U104(x0, x1, mark(x2))
744.20/263.03	   U104(active(x0), x1, x2)
744.20/263.03	   U104(x0, active(x1), x2)
744.20/263.03	   U104(x0, x1, active(x2))
744.20/263.03	   plus(mark(x0), x1)
744.20/263.03	   plus(x0, mark(x1))
744.20/263.03	   plus(active(x0), x1)
744.20/263.03	   plus(x0, active(x1))
744.20/263.03	   x(mark(x0), x1)
744.20/263.03	   x(x0, mark(x1))
744.20/263.03	   x(active(x0), x1)
744.20/263.03	   x(x0, active(x1))
744.20/263.03	   U11(mark(x0), x1, x2)
744.20/263.03	   U11(x0, mark(x1), x2)
744.20/263.03	   U11(x0, x1, mark(x2))
744.20/263.03	   U11(active(x0), x1, x2)
744.20/263.03	   U11(x0, active(x1), x2)
744.20/263.03	   U11(x0, x1, active(x2))
744.20/263.03	   U12(mark(x0), x1, x2)
744.20/263.03	   U12(x0, mark(x1), x2)
744.20/263.03	   U12(x0, x1, mark(x2))
744.20/263.03	   U12(active(x0), x1, x2)
744.20/263.03	   U12(x0, active(x1), x2)
744.20/263.03	   U12(x0, x1, active(x2))
744.20/263.03	   U13(mark(x0), x1, x2)
744.20/263.03	   U13(x0, mark(x1), x2)
744.20/263.03	   U13(x0, x1, mark(x2))
744.20/263.03	   U13(active(x0), x1, x2)
744.20/263.03	   U13(x0, active(x1), x2)
744.20/263.03	   U13(x0, x1, active(x2))
744.20/263.03	   U14(mark(x0), x1, x2)
744.20/263.03	   U14(x0, mark(x1), x2)
744.20/263.03	   U14(x0, x1, mark(x2))
744.20/263.03	   U14(active(x0), x1, x2)
744.20/263.03	   U14(x0, active(x1), x2)
744.20/263.03	   U14(x0, x1, active(x2))
744.20/263.03	   U15(mark(x0), x1)
744.20/263.03	   U15(x0, mark(x1))
744.20/263.03	   U15(active(x0), x1)
744.20/263.03	   U15(x0, active(x1))
744.20/263.03	   U16(mark(x0))
744.20/263.03	   U16(active(x0))
744.20/263.03	   U21(mark(x0), x1)
744.20/263.03	   U21(x0, mark(x1))
744.20/263.03	   U21(active(x0), x1)
744.20/263.03	   U21(x0, active(x1))
744.20/263.03	   U22(mark(x0), x1)
744.20/263.03	   U22(x0, mark(x1))
744.20/263.03	   U22(active(x0), x1)
744.20/263.03	   U22(x0, active(x1))
744.20/263.03	   U23(mark(x0))
744.20/263.03	   U23(active(x0))
744.20/263.03	   U31(mark(x0), x1, x2)
744.20/263.03	   U31(x0, mark(x1), x2)
744.20/263.03	   U31(x0, x1, mark(x2))
744.20/263.03	   U31(active(x0), x1, x2)
744.20/263.03	   U31(x0, active(x1), x2)
744.20/263.03	   U31(x0, x1, active(x2))
744.20/263.03	   U32(mark(x0), x1, x2)
744.20/263.03	   U32(x0, mark(x1), x2)
744.20/263.03	   U32(x0, x1, mark(x2))
744.20/263.03	   U32(active(x0), x1, x2)
744.20/263.03	   U32(x0, active(x1), x2)
744.20/263.03	   U32(x0, x1, active(x2))
744.20/263.03	   U33(mark(x0), x1, x2)
744.20/263.03	   U33(x0, mark(x1), x2)
744.20/263.03	   U33(x0, x1, mark(x2))
744.20/263.03	   U33(active(x0), x1, x2)
744.20/263.03	   U33(x0, active(x1), x2)
744.20/263.03	   U33(x0, x1, active(x2))
744.20/263.03	   U34(mark(x0), x1, x2)
744.20/263.03	   U34(x0, mark(x1), x2)
744.20/263.03	   U34(x0, x1, mark(x2))
744.20/263.03	   U34(active(x0), x1, x2)
744.20/263.03	   U34(x0, active(x1), x2)
744.20/263.03	   U34(x0, x1, active(x2))
744.20/263.03	   U35(mark(x0), x1)
744.20/263.03	   U35(x0, mark(x1))
744.20/263.03	   U35(active(x0), x1)
744.20/263.03	   U35(x0, active(x1))
744.20/263.03	   U36(mark(x0))
744.20/263.03	   U36(active(x0))
744.20/263.03	   U41(mark(x0), x1)
744.20/263.03	   U41(x0, mark(x1))
744.20/263.03	   U41(active(x0), x1)
744.20/263.03	   U41(x0, active(x1))
744.20/263.03	   U42(mark(x0))
744.20/263.03	   U42(active(x0))
744.20/263.03	   U51(mark(x0))
744.20/263.03	   U51(active(x0))
744.20/263.03	   U61(mark(x0), x1)
744.20/263.03	   U61(x0, mark(x1))
744.20/263.03	   U61(active(x0), x1)
744.20/263.03	   U61(x0, active(x1))
744.20/263.03	   U62(mark(x0))
744.20/263.03	   U62(active(x0))
744.20/263.03	   U71(mark(x0), x1)
744.20/263.03	   U71(x0, mark(x1))
744.20/263.03	   U71(active(x0), x1)
744.20/263.03	   U71(x0, active(x1))
744.20/263.03	   U72(mark(x0), x1)
744.20/263.03	   U72(x0, mark(x1))
744.20/263.03	   U72(active(x0), x1)
744.20/263.03	   U72(x0, active(x1))
744.20/263.03	   U81(mark(x0), x1, x2)
744.20/263.03	   U81(x0, mark(x1), x2)
744.20/263.03	   U81(x0, x1, mark(x2))
744.20/263.03	   U81(active(x0), x1, x2)
744.20/263.03	   U81(x0, active(x1), x2)
744.20/263.03	   U81(x0, x1, active(x2))
744.20/263.03	   U82(mark(x0), x1, x2)
744.20/263.03	   U82(x0, mark(x1), x2)
744.20/263.03	   U82(x0, x1, mark(x2))
744.20/263.03	   U82(active(x0), x1, x2)
744.20/263.03	   U82(x0, active(x1), x2)
744.20/263.03	   U82(x0, x1, active(x2))
744.20/263.03	   U83(mark(x0), x1, x2)
744.20/263.03	   U83(x0, mark(x1), x2)
744.20/263.03	   U83(x0, x1, mark(x2))
744.20/263.03	   U83(active(x0), x1, x2)
744.20/263.03	   U83(x0, active(x1), x2)
744.20/263.03	   U83(x0, x1, active(x2))
744.20/263.03	   U84(mark(x0), x1, x2)
744.20/263.03	   U84(x0, mark(x1), x2)
744.20/263.03	   U84(x0, x1, mark(x2))
744.20/263.03	   U84(active(x0), x1, x2)
744.20/263.03	   U84(x0, active(x1), x2)
744.20/263.03	   U84(x0, x1, active(x2))
744.20/263.03	   s(mark(x0))
744.20/263.03	   s(active(x0))
744.20/263.03	   U91(mark(x0), x1)
744.20/263.03	   U91(x0, mark(x1))
744.20/263.03	   U91(active(x0), x1)
744.20/263.03	   U91(x0, active(x1))
744.20/263.03	   U92(mark(x0))
744.20/263.03	   U92(active(x0))
744.20/263.03	
744.20/263.03	We have to consider all minimal (P,Q,R)-chains.
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(301) QDPOrderProof (EQUIVALENT)
744.20/263.03	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.03	
744.20/263.03	
744.20/263.03	The following pairs can be oriented strictly and are deleted.
744.20/263.03	
744.20/263.03	   MARK(U62(X)) -> MARK(X)
744.20/263.03	The remaining pairs can at least be oriented weakly.
744.20/263.03	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.20/263.03	
744.20/263.03	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.20/263.03	POL( U11_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U12_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U13_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U14_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.03	POL( U21_2(x_1, x_2) ) = 2x_1 + 1
744.20/263.03	POL( U22_2(x_1, x_2) ) = x_1 + 1
744.20/263.03	POL( U31_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U32_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U33_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U34_3(x_1, ..., x_3) ) = 2x_1 + 1
744.20/263.03	POL( U35_2(x_1, x_2) ) = x_1 + 1
744.20/263.03	POL( U41_2(x_1, x_2) ) = x_1 + 1
744.20/263.03	POL( mark_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.03	POL( U102_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.20/263.03	POL( active_1(x_1) ) = 2x_1 + 2
744.20/263.03	POL( U101_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.20/263.03	POL( tt ) = 0
744.20/263.03	POL( isNatKind_1(x_1) ) = 0
744.20/263.03	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.20/263.03	POL( isNat_1(x_1) ) = 0
744.20/263.03	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.20/263.03	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.20/263.03	POL( x_2(x_1, x_2) ) = 0
744.20/263.03	POL( U16_1(x_1) ) = x_1 + 1
744.20/263.03	POL( U23_1(x_1) ) = 2x_1 + 1
744.20/263.03	POL( U36_1(x_1) ) = 2x_1 + 1
744.20/263.03	POL( U42_1(x_1) ) = x_1 + 1
744.20/263.03	POL( U61_2(x_1, x_2) ) = 2
744.20/263.03	POL( U62_1(x_1) ) = x_1 + 2
744.20/263.03	POL( U71_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.20/263.03	POL( U72_2(x_1, x_2) ) = max{0, x_1 - 2}
744.20/263.03	POL( U81_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.20/263.03	POL( U82_3(x_1, ..., x_3) ) = 2x_2 + x_3 + 2
744.20/263.03	POL( U83_3(x_1, ..., x_3) ) = 2
744.20/263.03	POL( U84_3(x_1, ..., x_3) ) = x_3 + 2
744.20/263.03	POL( s_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.03	POL( U91_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.20/263.03	POL( U92_1(x_1) ) = 2
744.20/263.03	POL( U51_1(x_1) ) = x_1 + 1
744.20/263.03	POL( 0 ) = 2
744.20/263.03	POL( MARK_1(x_1) ) = max{0, 2x_1 - 2}
744.20/263.03	
744.20/263.03	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.03	none
744.20/263.03	
744.20/263.03	
744.20/263.03	----------------------------------------
744.20/263.03	
744.20/263.03	(302)
744.20/263.03	Obligation:
744.20/263.03	Q DP problem:
744.20/263.03	The TRS P consists of the following rules:
744.20/263.03	
744.20/263.03	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.03	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.03	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.03	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.03	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.03	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.03	   MARK(U16(X)) -> MARK(X)
744.20/263.03	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.03	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.03	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.03	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.03	   MARK(U23(X)) -> MARK(X)
744.20/263.03	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.03	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.03	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.03	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.03	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.03	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.03	   MARK(U36(X)) -> MARK(X)
744.20/263.03	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.03	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.03	   MARK(U42(X)) -> MARK(X)
744.20/263.03	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.03	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.03	   MARK(U51(X)) -> MARK(X)
744.20/263.03	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.03	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.03	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.03	
744.20/263.03	The TRS R consists of the following rules:
744.20/263.03	
744.20/263.03	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.03	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.03	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.03	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.03	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.03	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.03	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.03	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.03	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.03	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.03	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.03	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.03	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.03	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.03	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.03	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.03	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.03	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.03	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.03	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.03	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.03	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.03	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.03	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.03	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.03	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.03	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.03	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.03	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.03	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.03	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.03	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.03	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.03	   active(U72(tt, N)) -> mark(N)
744.20/263.03	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.03	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.03	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.03	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.03	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.03	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.03	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.03	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.03	   mark(s(X)) -> active(s(mark(X)))
744.20/263.03	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.03	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.03	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.03	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.03	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.03	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.03	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.03	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.03	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.03	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.03	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.03	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.03	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.03	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.03	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.03	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.03	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.03	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.03	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.03	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.03	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.03	   mark(isNat(X)) -> active(isNat(X))
744.20/263.03	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.03	   mark(tt) -> active(tt)
744.20/263.03	   mark(0) -> active(0)
744.20/263.04	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.04	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.04	   active(U16(tt)) -> mark(tt)
744.20/263.04	   active(U23(tt)) -> mark(tt)
744.20/263.04	   active(U36(tt)) -> mark(tt)
744.20/263.04	   active(U42(tt)) -> mark(tt)
744.20/263.04	   active(U51(tt)) -> mark(tt)
744.20/263.04	   active(U62(tt)) -> mark(tt)
744.20/263.04	   active(U92(tt)) -> mark(0)
744.20/263.04	   active(isNat(0)) -> mark(tt)
744.20/263.04	   active(isNatKind(0)) -> mark(tt)
744.20/263.04	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.04	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.04	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.04	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.04	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.04	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.04	   U16(active(X)) -> U16(X)
744.20/263.04	   U16(mark(X)) -> U16(X)
744.20/263.04	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.04	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.04	   U23(active(X)) -> U23(X)
744.20/263.04	   U23(mark(X)) -> U23(X)
744.20/263.04	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.04	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.04	   U36(active(X)) -> U36(X)
744.20/263.04	   U36(mark(X)) -> U36(X)
744.20/263.04	   U42(active(X)) -> U42(X)
744.20/263.04	   U42(mark(X)) -> U42(X)
744.20/263.04	   U62(active(X)) -> U62(X)
744.20/263.04	   U62(mark(X)) -> U62(X)
744.20/263.04	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.04	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.04	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.04	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.04	   s(active(X)) -> s(X)
744.20/263.04	   s(mark(X)) -> s(X)
744.20/263.04	   U92(active(X)) -> U92(X)
744.20/263.04	   U92(mark(X)) -> U92(X)
744.20/263.04	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.04	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.04	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.04	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.04	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.04	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.04	   U51(active(X)) -> U51(X)
744.20/263.04	   U51(mark(X)) -> U51(X)
744.20/263.04	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.04	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.04	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.04	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.04	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.04	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.04	   x(active(X1), X2) -> x(X1, X2)
744.20/263.04	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.04	
744.20/263.04	The set Q consists of the following terms:
744.20/263.04	
744.20/263.04	   active(U101(tt, x0, x1))
744.20/263.04	   active(U102(tt, x0, x1))
744.20/263.04	   active(U103(tt, x0, x1))
744.20/263.04	   active(U104(tt, x0, x1))
744.20/263.04	   active(U11(tt, x0, x1))
744.20/263.04	   active(U12(tt, x0, x1))
744.20/263.04	   active(U13(tt, x0, x1))
744.20/263.04	   active(U14(tt, x0, x1))
744.20/263.04	   active(U15(tt, x0))
744.20/263.04	   active(U16(tt))
744.20/263.04	   active(U21(tt, x0))
744.20/263.04	   active(U22(tt, x0))
744.20/263.04	   active(U23(tt))
744.20/263.04	   active(U31(tt, x0, x1))
744.20/263.04	   active(U32(tt, x0, x1))
744.20/263.04	   active(U33(tt, x0, x1))
744.20/263.04	   active(U34(tt, x0, x1))
744.20/263.04	   active(U35(tt, x0))
744.20/263.04	   active(U36(tt))
744.20/263.04	   active(U41(tt, x0))
744.20/263.04	   active(U42(tt))
744.20/263.04	   active(U51(tt))
744.20/263.04	   active(U61(tt, x0))
744.20/263.04	   active(U62(tt))
744.20/263.04	   active(U71(tt, x0))
744.20/263.04	   active(U72(tt, x0))
744.20/263.04	   active(U81(tt, x0, x1))
744.20/263.04	   active(U82(tt, x0, x1))
744.20/263.04	   active(U83(tt, x0, x1))
744.20/263.04	   active(U84(tt, x0, x1))
744.20/263.04	   active(U91(tt, x0))
744.20/263.04	   active(U92(tt))
744.20/263.04	   active(isNat(0))
744.20/263.04	   active(isNat(plus(x0, x1)))
744.20/263.04	   active(isNat(s(x0)))
744.20/263.04	   active(isNat(x(x0, x1)))
744.20/263.04	   active(isNatKind(0))
744.20/263.04	   active(isNatKind(plus(x0, x1)))
744.20/263.04	   active(isNatKind(s(x0)))
744.20/263.04	   active(isNatKind(x(x0, x1)))
744.20/263.04	   active(plus(x0, 0))
744.20/263.04	   active(plus(x0, s(x1)))
744.20/263.04	   active(x(x0, 0))
744.20/263.04	   active(x(x0, s(x1)))
744.20/263.04	   mark(U101(x0, x1, x2))
744.20/263.04	   mark(tt)
744.20/263.04	   mark(U102(x0, x1, x2))
744.20/263.04	   mark(isNatKind(x0))
744.20/263.04	   mark(U103(x0, x1, x2))
744.20/263.04	   mark(isNat(x0))
744.20/263.04	   mark(U104(x0, x1, x2))
744.20/263.04	   mark(plus(x0, x1))
744.20/263.04	   mark(x(x0, x1))
744.20/263.04	   mark(U11(x0, x1, x2))
744.20/263.04	   mark(U12(x0, x1, x2))
744.20/263.04	   mark(U13(x0, x1, x2))
744.20/263.04	   mark(U14(x0, x1, x2))
744.20/263.04	   mark(U15(x0, x1))
744.20/263.04	   mark(U16(x0))
744.20/263.04	   mark(U21(x0, x1))
744.20/263.04	   mark(U22(x0, x1))
744.20/263.04	   mark(U23(x0))
744.20/263.04	   mark(U31(x0, x1, x2))
744.20/263.04	   mark(U32(x0, x1, x2))
744.20/263.04	   mark(U33(x0, x1, x2))
744.20/263.04	   mark(U34(x0, x1, x2))
744.20/263.04	   mark(U35(x0, x1))
744.20/263.04	   mark(U36(x0))
744.20/263.04	   mark(U41(x0, x1))
744.20/263.04	   mark(U42(x0))
744.20/263.04	   mark(U51(x0))
744.20/263.04	   mark(U61(x0, x1))
744.20/263.04	   mark(U62(x0))
744.20/263.04	   mark(U71(x0, x1))
744.20/263.04	   mark(U72(x0, x1))
744.20/263.04	   mark(U81(x0, x1, x2))
744.20/263.04	   mark(U82(x0, x1, x2))
744.20/263.04	   mark(U83(x0, x1, x2))
744.20/263.04	   mark(U84(x0, x1, x2))
744.20/263.04	   mark(s(x0))
744.20/263.04	   mark(U91(x0, x1))
744.20/263.04	   mark(U92(x0))
744.20/263.04	   mark(0)
744.20/263.04	   U101(mark(x0), x1, x2)
744.20/263.04	   U101(x0, mark(x1), x2)
744.20/263.04	   U101(x0, x1, mark(x2))
744.20/263.04	   U101(active(x0), x1, x2)
744.20/263.04	   U101(x0, active(x1), x2)
744.20/263.04	   U101(x0, x1, active(x2))
744.20/263.04	   U102(mark(x0), x1, x2)
744.20/263.04	   U102(x0, mark(x1), x2)
744.20/263.04	   U102(x0, x1, mark(x2))
744.20/263.04	   U102(active(x0), x1, x2)
744.20/263.04	   U102(x0, active(x1), x2)
744.20/263.04	   U102(x0, x1, active(x2))
744.20/263.04	   isNatKind(mark(x0))
744.20/263.04	   isNatKind(active(x0))
744.20/263.04	   U103(mark(x0), x1, x2)
744.20/263.04	   U103(x0, mark(x1), x2)
744.20/263.04	   U103(x0, x1, mark(x2))
744.20/263.04	   U103(active(x0), x1, x2)
744.20/263.04	   U103(x0, active(x1), x2)
744.20/263.04	   U103(x0, x1, active(x2))
744.20/263.04	   isNat(mark(x0))
744.20/263.04	   isNat(active(x0))
744.20/263.04	   U104(mark(x0), x1, x2)
744.20/263.04	   U104(x0, mark(x1), x2)
744.20/263.04	   U104(x0, x1, mark(x2))
744.20/263.04	   U104(active(x0), x1, x2)
744.20/263.04	   U104(x0, active(x1), x2)
744.20/263.04	   U104(x0, x1, active(x2))
744.20/263.04	   plus(mark(x0), x1)
744.20/263.04	   plus(x0, mark(x1))
744.20/263.04	   plus(active(x0), x1)
744.20/263.04	   plus(x0, active(x1))
744.20/263.04	   x(mark(x0), x1)
744.20/263.04	   x(x0, mark(x1))
744.20/263.04	   x(active(x0), x1)
744.20/263.04	   x(x0, active(x1))
744.20/263.04	   U11(mark(x0), x1, x2)
744.20/263.04	   U11(x0, mark(x1), x2)
744.20/263.04	   U11(x0, x1, mark(x2))
744.20/263.04	   U11(active(x0), x1, x2)
744.20/263.04	   U11(x0, active(x1), x2)
744.20/263.04	   U11(x0, x1, active(x2))
744.20/263.04	   U12(mark(x0), x1, x2)
744.20/263.04	   U12(x0, mark(x1), x2)
744.20/263.04	   U12(x0, x1, mark(x2))
744.20/263.04	   U12(active(x0), x1, x2)
744.20/263.04	   U12(x0, active(x1), x2)
744.20/263.04	   U12(x0, x1, active(x2))
744.20/263.04	   U13(mark(x0), x1, x2)
744.20/263.04	   U13(x0, mark(x1), x2)
744.20/263.04	   U13(x0, x1, mark(x2))
744.20/263.04	   U13(active(x0), x1, x2)
744.20/263.04	   U13(x0, active(x1), x2)
744.20/263.04	   U13(x0, x1, active(x2))
744.20/263.04	   U14(mark(x0), x1, x2)
744.20/263.04	   U14(x0, mark(x1), x2)
744.20/263.04	   U14(x0, x1, mark(x2))
744.20/263.04	   U14(active(x0), x1, x2)
744.20/263.04	   U14(x0, active(x1), x2)
744.20/263.04	   U14(x0, x1, active(x2))
744.20/263.04	   U15(mark(x0), x1)
744.20/263.04	   U15(x0, mark(x1))
744.20/263.04	   U15(active(x0), x1)
744.20/263.04	   U15(x0, active(x1))
744.20/263.04	   U16(mark(x0))
744.20/263.04	   U16(active(x0))
744.20/263.04	   U21(mark(x0), x1)
744.20/263.04	   U21(x0, mark(x1))
744.20/263.04	   U21(active(x0), x1)
744.20/263.04	   U21(x0, active(x1))
744.20/263.04	   U22(mark(x0), x1)
744.20/263.04	   U22(x0, mark(x1))
744.20/263.04	   U22(active(x0), x1)
744.20/263.04	   U22(x0, active(x1))
744.20/263.04	   U23(mark(x0))
744.20/263.04	   U23(active(x0))
744.20/263.04	   U31(mark(x0), x1, x2)
744.20/263.04	   U31(x0, mark(x1), x2)
744.20/263.04	   U31(x0, x1, mark(x2))
744.20/263.04	   U31(active(x0), x1, x2)
744.20/263.04	   U31(x0, active(x1), x2)
744.20/263.04	   U31(x0, x1, active(x2))
744.20/263.04	   U32(mark(x0), x1, x2)
744.20/263.04	   U32(x0, mark(x1), x2)
744.20/263.04	   U32(x0, x1, mark(x2))
744.20/263.04	   U32(active(x0), x1, x2)
744.20/263.04	   U32(x0, active(x1), x2)
744.20/263.04	   U32(x0, x1, active(x2))
744.20/263.04	   U33(mark(x0), x1, x2)
744.20/263.04	   U33(x0, mark(x1), x2)
744.20/263.04	   U33(x0, x1, mark(x2))
744.20/263.04	   U33(active(x0), x1, x2)
744.20/263.04	   U33(x0, active(x1), x2)
744.20/263.04	   U33(x0, x1, active(x2))
744.20/263.04	   U34(mark(x0), x1, x2)
744.20/263.04	   U34(x0, mark(x1), x2)
744.20/263.04	   U34(x0, x1, mark(x2))
744.20/263.04	   U34(active(x0), x1, x2)
744.20/263.04	   U34(x0, active(x1), x2)
744.20/263.04	   U34(x0, x1, active(x2))
744.20/263.04	   U35(mark(x0), x1)
744.20/263.04	   U35(x0, mark(x1))
744.20/263.04	   U35(active(x0), x1)
744.20/263.04	   U35(x0, active(x1))
744.20/263.04	   U36(mark(x0))
744.20/263.04	   U36(active(x0))
744.20/263.04	   U41(mark(x0), x1)
744.20/263.04	   U41(x0, mark(x1))
744.20/263.04	   U41(active(x0), x1)
744.20/263.04	   U41(x0, active(x1))
744.20/263.04	   U42(mark(x0))
744.20/263.04	   U42(active(x0))
744.20/263.04	   U51(mark(x0))
744.20/263.04	   U51(active(x0))
744.20/263.04	   U61(mark(x0), x1)
744.20/263.04	   U61(x0, mark(x1))
744.20/263.04	   U61(active(x0), x1)
744.20/263.04	   U61(x0, active(x1))
744.20/263.04	   U62(mark(x0))
744.20/263.04	   U62(active(x0))
744.20/263.04	   U71(mark(x0), x1)
744.20/263.04	   U71(x0, mark(x1))
744.20/263.04	   U71(active(x0), x1)
744.20/263.04	   U71(x0, active(x1))
744.20/263.04	   U72(mark(x0), x1)
744.20/263.04	   U72(x0, mark(x1))
744.20/263.04	   U72(active(x0), x1)
744.20/263.04	   U72(x0, active(x1))
744.20/263.04	   U81(mark(x0), x1, x2)
744.20/263.04	   U81(x0, mark(x1), x2)
744.20/263.04	   U81(x0, x1, mark(x2))
744.20/263.04	   U81(active(x0), x1, x2)
744.20/263.04	   U81(x0, active(x1), x2)
744.20/263.04	   U81(x0, x1, active(x2))
744.20/263.04	   U82(mark(x0), x1, x2)
744.20/263.04	   U82(x0, mark(x1), x2)
744.20/263.04	   U82(x0, x1, mark(x2))
744.20/263.04	   U82(active(x0), x1, x2)
744.20/263.04	   U82(x0, active(x1), x2)
744.20/263.04	   U82(x0, x1, active(x2))
744.20/263.04	   U83(mark(x0), x1, x2)
744.20/263.04	   U83(x0, mark(x1), x2)
744.20/263.04	   U83(x0, x1, mark(x2))
744.20/263.04	   U83(active(x0), x1, x2)
744.20/263.04	   U83(x0, active(x1), x2)
744.20/263.04	   U83(x0, x1, active(x2))
744.20/263.04	   U84(mark(x0), x1, x2)
744.20/263.04	   U84(x0, mark(x1), x2)
744.20/263.04	   U84(x0, x1, mark(x2))
744.20/263.04	   U84(active(x0), x1, x2)
744.20/263.04	   U84(x0, active(x1), x2)
744.20/263.04	   U84(x0, x1, active(x2))
744.20/263.04	   s(mark(x0))
744.20/263.04	   s(active(x0))
744.20/263.04	   U91(mark(x0), x1)
744.20/263.04	   U91(x0, mark(x1))
744.20/263.04	   U91(active(x0), x1)
744.20/263.04	   U91(x0, active(x1))
744.20/263.04	   U92(mark(x0))
744.20/263.04	   U92(active(x0))
744.20/263.04	
744.20/263.04	We have to consider all minimal (P,Q,R)-chains.
744.20/263.04	----------------------------------------
744.20/263.04	
744.20/263.04	(303) QDPOrderProof (EQUIVALENT)
744.20/263.04	We use the reduction pair processor [LPAR04,JAR06].
744.20/263.04	
744.20/263.04	
744.20/263.04	The following pairs can be oriented strictly and are deleted.
744.20/263.04	
744.20/263.04	   MARK(U31(X1, X2, X3)) -> MARK(X1)
744.20/263.04	The remaining pairs can at least be oriented weakly.
744.20/263.04	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(tt) =  	[[0A]]
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U31(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U36(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U51(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(s(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(x(x_1, x_2)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U102(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U101(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U103(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U104(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U62(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U71(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	   <<<
744.20/263.04	 POL(0) =  	[[0A]]
744.20/263.04	>>>
744.20/263.04	
744.20/263.04	
744.20/263.04	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.20/263.04	
744.20/263.04	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.04	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.04	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.04	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.04	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.04	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.04	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.04	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.04	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.04	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.04	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.04	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.04	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.04	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.04	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.04	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.04	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.04	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.04	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.04	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.04	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.04	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.04	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.04	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.04	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.04	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.04	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.04	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.04	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.04	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.04	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.04	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.04	   active(U72(tt, N)) -> mark(N)
744.20/263.04	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.04	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.04	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.04	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.04	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.04	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.04	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.04	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.04	   mark(s(X)) -> active(s(mark(X)))
744.20/263.04	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.04	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.04	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.04	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.04	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.04	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.04	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.04	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.04	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.04	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.04	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.04	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.04	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.04	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.04	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.04	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.04	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.04	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.04	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.04	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.04	   mark(isNat(X)) -> active(isNat(X))
744.20/263.04	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.04	   mark(tt) -> active(tt)
744.20/263.04	   mark(0) -> active(0)
744.20/263.04	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.04	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.04	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.04	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.04	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.04	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.04	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.04	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.04	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.04	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.04	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.04	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.04	   active(U16(tt)) -> mark(tt)
744.20/263.04	   active(U23(tt)) -> mark(tt)
744.20/263.04	   active(U36(tt)) -> mark(tt)
744.20/263.04	   active(U42(tt)) -> mark(tt)
744.20/263.04	   active(U51(tt)) -> mark(tt)
744.20/263.04	   active(U62(tt)) -> mark(tt)
744.20/263.04	   active(U92(tt)) -> mark(0)
744.20/263.04	   active(isNat(0)) -> mark(tt)
744.20/263.04	   active(isNatKind(0)) -> mark(tt)
744.20/263.04	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.04	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.04	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.04	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.04	   U16(active(X)) -> U16(X)
744.20/263.04	   U16(mark(X)) -> U16(X)
744.20/263.04	   U23(active(X)) -> U23(X)
744.20/263.04	   U23(mark(X)) -> U23(X)
744.20/263.04	   U36(active(X)) -> U36(X)
744.20/263.04	   U36(mark(X)) -> U36(X)
744.20/263.04	   U42(active(X)) -> U42(X)
744.20/263.04	   U42(mark(X)) -> U42(X)
744.20/263.04	   U62(active(X)) -> U62(X)
744.20/263.04	   U62(mark(X)) -> U62(X)
744.20/263.04	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.04	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.04	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.04	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.04	   s(active(X)) -> s(X)
744.20/263.04	   s(mark(X)) -> s(X)
744.20/263.04	   U92(active(X)) -> U92(X)
744.20/263.04	   U92(mark(X)) -> U92(X)
744.20/263.04	   U51(active(X)) -> U51(X)
744.20/263.04	   U51(mark(X)) -> U51(X)
744.20/263.04	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.04	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.04	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.04	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.04	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.04	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.04	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.04	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.04	   x(active(X1), X2) -> x(X1, X2)
744.20/263.04	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.04	
744.20/263.04	
744.20/263.04	----------------------------------------
744.20/263.04	
744.20/263.04	(304)
744.20/263.04	Obligation:
744.20/263.04	Q DP problem:
744.20/263.04	The TRS P consists of the following rules:
744.20/263.04	
744.20/263.04	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.20/263.04	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.20/263.04	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.20/263.04	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.20/263.04	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.20/263.04	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.20/263.04	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.20/263.04	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.20/263.04	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.20/263.04	   MARK(U16(X)) -> MARK(X)
744.20/263.04	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.20/263.04	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.20/263.04	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.20/263.04	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.20/263.04	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.20/263.04	   MARK(U23(X)) -> MARK(X)
744.20/263.04	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U15(X1, X2)) -> MARK(X1)
744.20/263.04	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.20/263.04	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.20/263.04	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.20/263.04	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.20/263.04	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.20/263.04	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.20/263.04	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.20/263.04	   MARK(U36(X)) -> MARK(X)
744.20/263.04	   MARK(U21(X1, X2)) -> MARK(X1)
744.20/263.04	   MARK(U22(X1, X2)) -> MARK(X1)
744.20/263.04	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.20/263.04	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.20/263.04	   MARK(U42(X)) -> MARK(X)
744.20/263.04	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.20/263.04	   MARK(U35(X1, X2)) -> MARK(X1)
744.20/263.04	   MARK(U41(X1, X2)) -> MARK(X1)
744.20/263.04	   MARK(U51(X)) -> MARK(X)
744.20/263.04	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.20/263.04	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.20/263.04	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.20/263.04	
744.20/263.04	The TRS R consists of the following rules:
744.20/263.04	
744.20/263.04	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.20/263.04	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.20/263.04	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.20/263.04	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.20/263.04	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.20/263.04	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.20/263.04	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.20/263.04	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.20/263.04	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.20/263.04	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.20/263.04	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.20/263.04	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.20/263.04	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.20/263.04	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.20/263.04	   mark(U16(X)) -> active(U16(mark(X)))
744.20/263.04	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.20/263.04	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.20/263.04	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.20/263.04	   mark(U23(X)) -> active(U23(mark(X)))
744.20/263.04	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.20/263.04	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.20/263.04	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.20/263.04	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.20/263.04	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.20/263.04	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.20/263.04	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.20/263.04	   mark(U36(X)) -> active(U36(mark(X)))
744.20/263.04	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.20/263.04	   mark(U42(X)) -> active(U42(mark(X)))
744.20/263.04	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.20/263.04	   mark(U62(X)) -> active(U62(mark(X)))
744.20/263.04	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.20/263.04	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.20/263.04	   active(U72(tt, N)) -> mark(N)
744.20/263.04	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.20/263.04	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.20/263.04	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.20/263.04	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.20/263.04	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.20/263.04	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.20/263.04	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.20/263.04	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.20/263.04	   mark(s(X)) -> active(s(mark(X)))
744.20/263.04	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.20/263.04	   mark(U92(X)) -> active(U92(mark(X)))
744.20/263.04	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.20/263.04	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.20/263.04	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.20/263.04	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.20/263.04	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.20/263.04	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.20/263.04	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.20/263.04	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.20/263.04	   mark(U51(X)) -> active(U51(mark(X)))
744.20/263.04	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.20/263.04	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.20/263.04	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.20/263.04	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.20/263.04	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.20/263.04	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.20/263.04	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.20/263.04	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.20/263.04	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.20/263.04	   mark(isNatKind(X)) -> active(isNatKind(X))
744.20/263.04	   mark(isNat(X)) -> active(isNat(X))
744.20/263.04	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.20/263.04	   mark(tt) -> active(tt)
744.20/263.04	   mark(0) -> active(0)
744.20/263.04	   U61(X1, mark(X2)) -> U61(X1, X2)
744.20/263.04	   U61(mark(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(active(X1), X2) -> U61(X1, X2)
744.20/263.04	   U61(X1, active(X2)) -> U61(X1, X2)
744.20/263.04	   active(U16(tt)) -> mark(tt)
744.20/263.04	   active(U23(tt)) -> mark(tt)
744.20/263.04	   active(U36(tt)) -> mark(tt)
744.20/263.04	   active(U42(tt)) -> mark(tt)
744.20/263.04	   active(U51(tt)) -> mark(tt)
744.20/263.04	   active(U62(tt)) -> mark(tt)
744.20/263.04	   active(U92(tt)) -> mark(0)
744.20/263.04	   active(isNat(0)) -> mark(tt)
744.20/263.04	   active(isNatKind(0)) -> mark(tt)
744.20/263.04	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.20/263.04	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.20/263.04	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.20/263.04	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.20/263.04	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.20/263.04	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.20/263.04	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.20/263.04	   plus(X1, mark(X2)) -> plus(X1, X2)
744.20/263.04	   plus(mark(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(active(X1), X2) -> plus(X1, X2)
744.20/263.04	   plus(X1, active(X2)) -> plus(X1, X2)
744.20/263.04	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.20/263.04	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.20/263.04	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.20/263.04	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.20/263.04	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.20/263.04	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.20/263.04	   U15(X1, mark(X2)) -> U15(X1, X2)
744.20/263.04	   U15(mark(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(active(X1), X2) -> U15(X1, X2)
744.20/263.04	   U15(X1, active(X2)) -> U15(X1, X2)
744.20/263.04	   U16(active(X)) -> U16(X)
744.20/263.04	   U16(mark(X)) -> U16(X)
744.20/263.04	   U22(X1, mark(X2)) -> U22(X1, X2)
744.20/263.04	   U22(mark(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(active(X1), X2) -> U22(X1, X2)
744.20/263.04	   U22(X1, active(X2)) -> U22(X1, X2)
744.20/263.04	   U23(active(X)) -> U23(X)
744.20/263.04	   U23(mark(X)) -> U23(X)
744.20/263.04	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.20/263.04	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.20/263.04	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.20/263.04	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.20/263.04	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.20/263.04	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.20/263.04	   U35(X1, mark(X2)) -> U35(X1, X2)
744.20/263.04	   U35(mark(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(active(X1), X2) -> U35(X1, X2)
744.20/263.04	   U35(X1, active(X2)) -> U35(X1, X2)
744.20/263.04	   U36(active(X)) -> U36(X)
744.20/263.04	   U36(mark(X)) -> U36(X)
744.20/263.04	   U42(active(X)) -> U42(X)
744.20/263.04	   U42(mark(X)) -> U42(X)
744.20/263.04	   U62(active(X)) -> U62(X)
744.20/263.04	   U62(mark(X)) -> U62(X)
744.20/263.04	   U72(X1, mark(X2)) -> U72(X1, X2)
744.20/263.04	   U72(mark(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(active(X1), X2) -> U72(X1, X2)
744.20/263.04	   U72(X1, active(X2)) -> U72(X1, X2)
744.20/263.04	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.20/263.04	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.20/263.04	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.20/263.04	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.20/263.04	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.20/263.04	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.20/263.04	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.20/263.04	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.20/263.04	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.20/263.04	   s(active(X)) -> s(X)
744.20/263.04	   s(mark(X)) -> s(X)
744.20/263.04	   U92(active(X)) -> U92(X)
744.20/263.04	   U92(mark(X)) -> U92(X)
744.20/263.04	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.20/263.04	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.20/263.04	   U21(X1, mark(X2)) -> U21(X1, X2)
744.20/263.04	   U21(mark(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(active(X1), X2) -> U21(X1, X2)
744.20/263.04	   U21(X1, active(X2)) -> U21(X1, X2)
744.20/263.04	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.20/263.04	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.20/263.04	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.20/263.04	   U41(X1, mark(X2)) -> U41(X1, X2)
744.20/263.04	   U41(mark(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(active(X1), X2) -> U41(X1, X2)
744.20/263.04	   U41(X1, active(X2)) -> U41(X1, X2)
744.20/263.04	   U51(active(X)) -> U51(X)
744.20/263.04	   U51(mark(X)) -> U51(X)
744.20/263.04	   U71(X1, mark(X2)) -> U71(X1, X2)
744.20/263.04	   U71(mark(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(active(X1), X2) -> U71(X1, X2)
744.20/263.04	   U71(X1, active(X2)) -> U71(X1, X2)
744.20/263.04	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.20/263.04	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.20/263.04	   U91(X1, mark(X2)) -> U91(X1, X2)
744.20/263.04	   U91(mark(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(active(X1), X2) -> U91(X1, X2)
744.20/263.04	   U91(X1, active(X2)) -> U91(X1, X2)
744.20/263.04	   x(X1, mark(X2)) -> x(X1, X2)
744.20/263.04	   x(mark(X1), X2) -> x(X1, X2)
744.20/263.04	   x(active(X1), X2) -> x(X1, X2)
744.20/263.04	   x(X1, active(X2)) -> x(X1, X2)
744.20/263.04	
744.20/263.04	The set Q consists of the following terms:
744.20/263.04	
744.20/263.04	   active(U101(tt, x0, x1))
744.20/263.04	   active(U102(tt, x0, x1))
744.20/263.04	   active(U103(tt, x0, x1))
744.20/263.04	   active(U104(tt, x0, x1))
744.20/263.04	   active(U11(tt, x0, x1))
744.20/263.04	   active(U12(tt, x0, x1))
744.20/263.04	   active(U13(tt, x0, x1))
744.20/263.04	   active(U14(tt, x0, x1))
744.20/263.04	   active(U15(tt, x0))
744.20/263.04	   active(U16(tt))
744.20/263.04	   active(U21(tt, x0))
744.20/263.04	   active(U22(tt, x0))
744.20/263.04	   active(U23(tt))
744.20/263.04	   active(U31(tt, x0, x1))
744.20/263.04	   active(U32(tt, x0, x1))
744.20/263.04	   active(U33(tt, x0, x1))
744.20/263.04	   active(U34(tt, x0, x1))
744.20/263.04	   active(U35(tt, x0))
744.20/263.04	   active(U36(tt))
744.20/263.04	   active(U41(tt, x0))
744.20/263.04	   active(U42(tt))
744.20/263.04	   active(U51(tt))
744.20/263.04	   active(U61(tt, x0))
744.20/263.04	   active(U62(tt))
744.20/263.04	   active(U71(tt, x0))
744.20/263.04	   active(U72(tt, x0))
744.20/263.04	   active(U81(tt, x0, x1))
744.20/263.04	   active(U82(tt, x0, x1))
744.20/263.04	   active(U83(tt, x0, x1))
744.20/263.04	   active(U84(tt, x0, x1))
744.20/263.04	   active(U91(tt, x0))
744.20/263.04	   active(U92(tt))
744.20/263.04	   active(isNat(0))
744.20/263.04	   active(isNat(plus(x0, x1)))
744.20/263.04	   active(isNat(s(x0)))
744.20/263.04	   active(isNat(x(x0, x1)))
744.20/263.04	   active(isNatKind(0))
744.20/263.04	   active(isNatKind(plus(x0, x1)))
744.20/263.04	   active(isNatKind(s(x0)))
744.20/263.04	   active(isNatKind(x(x0, x1)))
744.20/263.04	   active(plus(x0, 0))
744.20/263.04	   active(plus(x0, s(x1)))
744.20/263.04	   active(x(x0, 0))
744.20/263.04	   active(x(x0, s(x1)))
744.20/263.04	   mark(U101(x0, x1, x2))
744.20/263.04	   mark(tt)
744.20/263.04	   mark(U102(x0, x1, x2))
744.20/263.04	   mark(isNatKind(x0))
744.20/263.04	   mark(U103(x0, x1, x2))
744.20/263.04	   mark(isNat(x0))
744.20/263.04	   mark(U104(x0, x1, x2))
744.20/263.04	   mark(plus(x0, x1))
744.20/263.04	   mark(x(x0, x1))
744.20/263.04	   mark(U11(x0, x1, x2))
744.20/263.04	   mark(U12(x0, x1, x2))
744.20/263.04	   mark(U13(x0, x1, x2))
744.20/263.04	   mark(U14(x0, x1, x2))
744.20/263.04	   mark(U15(x0, x1))
744.20/263.04	   mark(U16(x0))
744.20/263.04	   mark(U21(x0, x1))
744.20/263.04	   mark(U22(x0, x1))
744.20/263.04	   mark(U23(x0))
744.20/263.04	   mark(U31(x0, x1, x2))
744.20/263.04	   mark(U32(x0, x1, x2))
744.20/263.04	   mark(U33(x0, x1, x2))
744.20/263.04	   mark(U34(x0, x1, x2))
744.20/263.04	   mark(U35(x0, x1))
744.20/263.04	   mark(U36(x0))
744.20/263.04	   mark(U41(x0, x1))
744.20/263.04	   mark(U42(x0))
744.20/263.04	   mark(U51(x0))
744.20/263.04	   mark(U61(x0, x1))
744.20/263.04	   mark(U62(x0))
744.20/263.04	   mark(U71(x0, x1))
744.20/263.04	   mark(U72(x0, x1))
744.20/263.04	   mark(U81(x0, x1, x2))
744.20/263.04	   mark(U82(x0, x1, x2))
744.20/263.04	   mark(U83(x0, x1, x2))
744.20/263.04	   mark(U84(x0, x1, x2))
744.20/263.04	   mark(s(x0))
744.20/263.04	   mark(U91(x0, x1))
744.20/263.04	   mark(U92(x0))
744.20/263.04	   mark(0)
744.20/263.04	   U101(mark(x0), x1, x2)
744.20/263.04	   U101(x0, mark(x1), x2)
744.20/263.04	   U101(x0, x1, mark(x2))
744.20/263.04	   U101(active(x0), x1, x2)
744.20/263.04	   U101(x0, active(x1), x2)
744.20/263.04	   U101(x0, x1, active(x2))
744.20/263.04	   U102(mark(x0), x1, x2)
744.20/263.04	   U102(x0, mark(x1), x2)
744.20/263.04	   U102(x0, x1, mark(x2))
744.20/263.04	   U102(active(x0), x1, x2)
744.20/263.04	   U102(x0, active(x1), x2)
744.20/263.04	   U102(x0, x1, active(x2))
744.20/263.04	   isNatKind(mark(x0))
744.20/263.04	   isNatKind(active(x0))
744.20/263.04	   U103(mark(x0), x1, x2)
744.20/263.04	   U103(x0, mark(x1), x2)
744.20/263.04	   U103(x0, x1, mark(x2))
744.20/263.04	   U103(active(x0), x1, x2)
744.20/263.04	   U103(x0, active(x1), x2)
744.20/263.04	   U103(x0, x1, active(x2))
744.20/263.04	   isNat(mark(x0))
744.20/263.04	   isNat(active(x0))
744.20/263.04	   U104(mark(x0), x1, x2)
744.20/263.04	   U104(x0, mark(x1), x2)
744.30/263.04	   U104(x0, x1, mark(x2))
744.30/263.04	   U104(active(x0), x1, x2)
744.30/263.04	   U104(x0, active(x1), x2)
744.30/263.04	   U104(x0, x1, active(x2))
744.30/263.04	   plus(mark(x0), x1)
744.30/263.04	   plus(x0, mark(x1))
744.30/263.04	   plus(active(x0), x1)
744.30/263.04	   plus(x0, active(x1))
744.30/263.04	   x(mark(x0), x1)
744.30/263.04	   x(x0, mark(x1))
744.30/263.04	   x(active(x0), x1)
744.30/263.04	   x(x0, active(x1))
744.30/263.04	   U11(mark(x0), x1, x2)
744.30/263.04	   U11(x0, mark(x1), x2)
744.30/263.04	   U11(x0, x1, mark(x2))
744.30/263.04	   U11(active(x0), x1, x2)
744.30/263.04	   U11(x0, active(x1), x2)
744.30/263.04	   U11(x0, x1, active(x2))
744.30/263.04	   U12(mark(x0), x1, x2)
744.30/263.04	   U12(x0, mark(x1), x2)
744.30/263.04	   U12(x0, x1, mark(x2))
744.30/263.04	   U12(active(x0), x1, x2)
744.30/263.04	   U12(x0, active(x1), x2)
744.30/263.04	   U12(x0, x1, active(x2))
744.30/263.04	   U13(mark(x0), x1, x2)
744.30/263.04	   U13(x0, mark(x1), x2)
744.30/263.04	   U13(x0, x1, mark(x2))
744.30/263.04	   U13(active(x0), x1, x2)
744.30/263.04	   U13(x0, active(x1), x2)
744.30/263.04	   U13(x0, x1, active(x2))
744.30/263.04	   U14(mark(x0), x1, x2)
744.30/263.04	   U14(x0, mark(x1), x2)
744.30/263.04	   U14(x0, x1, mark(x2))
744.30/263.04	   U14(active(x0), x1, x2)
744.30/263.04	   U14(x0, active(x1), x2)
744.30/263.04	   U14(x0, x1, active(x2))
744.30/263.04	   U15(mark(x0), x1)
744.30/263.04	   U15(x0, mark(x1))
744.30/263.04	   U15(active(x0), x1)
744.30/263.04	   U15(x0, active(x1))
744.30/263.04	   U16(mark(x0))
744.30/263.04	   U16(active(x0))
744.30/263.04	   U21(mark(x0), x1)
744.30/263.04	   U21(x0, mark(x1))
744.30/263.04	   U21(active(x0), x1)
744.30/263.04	   U21(x0, active(x1))
744.30/263.04	   U22(mark(x0), x1)
744.30/263.04	   U22(x0, mark(x1))
744.30/263.04	   U22(active(x0), x1)
744.30/263.04	   U22(x0, active(x1))
744.30/263.04	   U23(mark(x0))
744.30/263.04	   U23(active(x0))
744.30/263.04	   U31(mark(x0), x1, x2)
744.30/263.04	   U31(x0, mark(x1), x2)
744.30/263.04	   U31(x0, x1, mark(x2))
744.30/263.04	   U31(active(x0), x1, x2)
744.30/263.04	   U31(x0, active(x1), x2)
744.30/263.04	   U31(x0, x1, active(x2))
744.30/263.04	   U32(mark(x0), x1, x2)
744.30/263.04	   U32(x0, mark(x1), x2)
744.30/263.04	   U32(x0, x1, mark(x2))
744.30/263.04	   U32(active(x0), x1, x2)
744.30/263.04	   U32(x0, active(x1), x2)
744.30/263.04	   U32(x0, x1, active(x2))
744.30/263.04	   U33(mark(x0), x1, x2)
744.30/263.04	   U33(x0, mark(x1), x2)
744.30/263.04	   U33(x0, x1, mark(x2))
744.30/263.04	   U33(active(x0), x1, x2)
744.30/263.04	   U33(x0, active(x1), x2)
744.30/263.04	   U33(x0, x1, active(x2))
744.30/263.04	   U34(mark(x0), x1, x2)
744.30/263.04	   U34(x0, mark(x1), x2)
744.30/263.04	   U34(x0, x1, mark(x2))
744.30/263.04	   U34(active(x0), x1, x2)
744.30/263.04	   U34(x0, active(x1), x2)
744.30/263.04	   U34(x0, x1, active(x2))
744.30/263.04	   U35(mark(x0), x1)
744.30/263.04	   U35(x0, mark(x1))
744.30/263.04	   U35(active(x0), x1)
744.30/263.04	   U35(x0, active(x1))
744.30/263.04	   U36(mark(x0))
744.30/263.04	   U36(active(x0))
744.30/263.04	   U41(mark(x0), x1)
744.30/263.04	   U41(x0, mark(x1))
744.30/263.04	   U41(active(x0), x1)
744.30/263.04	   U41(x0, active(x1))
744.30/263.04	   U42(mark(x0))
744.30/263.04	   U42(active(x0))
744.30/263.04	   U51(mark(x0))
744.30/263.04	   U51(active(x0))
744.30/263.04	   U61(mark(x0), x1)
744.30/263.04	   U61(x0, mark(x1))
744.30/263.04	   U61(active(x0), x1)
744.30/263.04	   U61(x0, active(x1))
744.30/263.04	   U62(mark(x0))
744.30/263.04	   U62(active(x0))
744.30/263.04	   U71(mark(x0), x1)
744.30/263.04	   U71(x0, mark(x1))
744.30/263.04	   U71(active(x0), x1)
744.30/263.04	   U71(x0, active(x1))
744.30/263.04	   U72(mark(x0), x1)
744.30/263.04	   U72(x0, mark(x1))
744.30/263.04	   U72(active(x0), x1)
744.30/263.04	   U72(x0, active(x1))
744.30/263.04	   U81(mark(x0), x1, x2)
744.30/263.04	   U81(x0, mark(x1), x2)
744.30/263.04	   U81(x0, x1, mark(x2))
744.30/263.04	   U81(active(x0), x1, x2)
744.30/263.04	   U81(x0, active(x1), x2)
744.30/263.04	   U81(x0, x1, active(x2))
744.30/263.04	   U82(mark(x0), x1, x2)
744.30/263.04	   U82(x0, mark(x1), x2)
744.30/263.04	   U82(x0, x1, mark(x2))
744.30/263.04	   U82(active(x0), x1, x2)
744.30/263.04	   U82(x0, active(x1), x2)
744.30/263.04	   U82(x0, x1, active(x2))
744.30/263.04	   U83(mark(x0), x1, x2)
744.30/263.04	   U83(x0, mark(x1), x2)
744.30/263.04	   U83(x0, x1, mark(x2))
744.30/263.04	   U83(active(x0), x1, x2)
744.30/263.04	   U83(x0, active(x1), x2)
744.30/263.04	   U83(x0, x1, active(x2))
744.30/263.04	   U84(mark(x0), x1, x2)
744.30/263.04	   U84(x0, mark(x1), x2)
744.30/263.04	   U84(x0, x1, mark(x2))
744.30/263.04	   U84(active(x0), x1, x2)
744.30/263.04	   U84(x0, active(x1), x2)
744.30/263.04	   U84(x0, x1, active(x2))
744.30/263.04	   s(mark(x0))
744.30/263.04	   s(active(x0))
744.30/263.04	   U91(mark(x0), x1)
744.30/263.04	   U91(x0, mark(x1))
744.30/263.04	   U91(active(x0), x1)
744.30/263.04	   U91(x0, active(x1))
744.30/263.04	   U92(mark(x0))
744.30/263.04	   U92(active(x0))
744.30/263.04	
744.30/263.04	We have to consider all minimal (P,Q,R)-chains.
744.30/263.04	----------------------------------------
744.30/263.04	
744.30/263.04	(305) QDPOrderProof (EQUIVALENT)
744.30/263.04	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.04	
744.30/263.04	
744.30/263.04	The following pairs can be oriented strictly and are deleted.
744.30/263.04	
744.30/263.04	   MARK(U32(X1, X2, X3)) -> MARK(X1)
744.30/263.04	The remaining pairs can at least be oriented weakly.
744.30/263.04	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(tt) =  	[[0A]]
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(plus(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U15(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U31(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U34(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U36(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U101(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U91(x_1, x_2)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	   <<<
744.30/263.04	 POL(0) =  	[[0A]]
744.30/263.04	>>>
744.30/263.04	
744.30/263.04	
744.30/263.04	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.04	
744.30/263.04	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.04	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.04	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.04	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.04	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.04	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.04	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.04	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.04	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.04	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.04	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.04	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.04	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.04	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.04	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.04	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.04	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.04	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.04	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.04	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.04	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.04	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.04	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.04	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.04	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.04	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.04	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.04	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.04	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.04	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.04	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.04	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.04	   active(U72(tt, N)) -> mark(N)
744.30/263.04	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.04	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.04	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.04	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.04	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.04	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.04	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.04	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.04	   mark(s(X)) -> active(s(mark(X)))
744.30/263.04	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.04	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.04	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.04	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.04	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.04	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.04	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.04	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.04	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.04	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.04	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.04	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.04	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.04	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.04	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.04	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.04	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.04	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.04	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.04	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.04	   mark(isNat(X)) -> active(isNat(X))
744.30/263.04	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.04	   mark(tt) -> active(tt)
744.30/263.04	   mark(0) -> active(0)
744.30/263.04	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.04	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.04	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.04	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.04	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.04	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.04	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.04	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.04	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.04	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.04	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.04	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.04	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.04	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.04	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.04	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.04	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.04	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.04	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.04	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.04	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.04	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.04	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.04	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.04	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.04	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.04	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.04	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.04	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.04	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.04	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.04	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.04	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.04	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.04	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.04	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.04	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.04	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.04	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.04	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.04	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.04	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.04	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.04	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.04	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.04	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.04	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.04	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.04	   active(U16(tt)) -> mark(tt)
744.30/263.04	   active(U23(tt)) -> mark(tt)
744.30/263.04	   active(U36(tt)) -> mark(tt)
744.30/263.04	   active(U42(tt)) -> mark(tt)
744.30/263.04	   active(U51(tt)) -> mark(tt)
744.30/263.04	   active(U62(tt)) -> mark(tt)
744.30/263.04	   active(U92(tt)) -> mark(0)
744.30/263.04	   active(isNat(0)) -> mark(tt)
744.30/263.04	   active(isNatKind(0)) -> mark(tt)
744.30/263.04	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.04	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.04	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.04	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.04	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.04	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.04	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.04	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.04	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.04	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.04	   U16(active(X)) -> U16(X)
744.30/263.04	   U16(mark(X)) -> U16(X)
744.30/263.04	   U23(active(X)) -> U23(X)
744.30/263.04	   U23(mark(X)) -> U23(X)
744.30/263.04	   U36(active(X)) -> U36(X)
744.30/263.04	   U36(mark(X)) -> U36(X)
744.30/263.04	   U42(active(X)) -> U42(X)
744.30/263.04	   U42(mark(X)) -> U42(X)
744.30/263.04	   U62(active(X)) -> U62(X)
744.30/263.04	   U62(mark(X)) -> U62(X)
744.30/263.04	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.04	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.04	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.04	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.04	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.04	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.04	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.04	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.04	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.04	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.04	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.04	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.04	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.04	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.04	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.04	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.04	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.04	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.04	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.04	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.04	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.04	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.04	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.04	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.04	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.04	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.04	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.04	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.04	   s(active(X)) -> s(X)
744.30/263.04	   s(mark(X)) -> s(X)
744.30/263.04	   U92(active(X)) -> U92(X)
744.30/263.04	   U92(mark(X)) -> U92(X)
744.30/263.04	   U51(active(X)) -> U51(X)
744.30/263.04	   U51(mark(X)) -> U51(X)
744.30/263.04	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.04	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.04	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.04	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.04	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.04	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.04	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.04	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.04	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.04	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.04	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.04	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.04	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.04	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.04	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.04	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.04	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.04	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.04	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.04	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.04	   x(active(X1), X2) -> x(X1, X2)
744.30/263.04	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.04	
744.30/263.04	
744.30/263.04	----------------------------------------
744.30/263.04	
744.30/263.04	(306)
744.30/263.04	Obligation:
744.30/263.04	Q DP problem:
744.30/263.04	The TRS P consists of the following rules:
744.30/263.04	
744.30/263.04	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.04	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.04	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.04	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.04	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.04	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.04	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.04	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.04	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.04	   MARK(U16(X)) -> MARK(X)
744.30/263.04	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.04	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.04	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.04	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.04	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.04	   MARK(U23(X)) -> MARK(X)
744.30/263.04	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.04	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.04	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.04	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.04	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.04	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.04	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.30/263.04	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.30/263.04	   MARK(U36(X)) -> MARK(X)
744.30/263.04	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.04	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.04	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.04	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.04	   MARK(U42(X)) -> MARK(X)
744.30/263.04	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.04	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.04	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.04	   MARK(U51(X)) -> MARK(X)
744.30/263.04	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.04	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.04	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.04	
744.30/263.04	The TRS R consists of the following rules:
744.30/263.04	
744.30/263.04	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.04	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.04	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.04	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.04	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.04	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.04	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.04	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.04	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.04	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.04	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.04	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.04	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.04	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.04	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.04	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.04	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.04	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.04	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.04	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.04	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.04	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.04	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.04	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.04	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.04	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.04	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.04	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.04	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.04	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.04	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.04	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.04	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.04	   active(U72(tt, N)) -> mark(N)
744.30/263.04	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.04	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.04	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.04	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.04	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.04	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.04	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.04	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.04	   mark(s(X)) -> active(s(mark(X)))
744.30/263.04	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.04	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.04	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.04	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.04	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.04	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.04	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.04	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.04	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.04	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.04	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.04	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.04	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.04	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.04	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.04	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.04	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.04	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.04	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.04	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.04	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.04	   mark(isNat(X)) -> active(isNat(X))
744.30/263.04	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.04	   mark(tt) -> active(tt)
744.30/263.04	   mark(0) -> active(0)
744.30/263.04	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.04	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.04	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.04	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.04	   active(U16(tt)) -> mark(tt)
744.30/263.04	   active(U23(tt)) -> mark(tt)
744.30/263.04	   active(U36(tt)) -> mark(tt)
744.30/263.04	   active(U42(tt)) -> mark(tt)
744.30/263.04	   active(U51(tt)) -> mark(tt)
744.30/263.04	   active(U62(tt)) -> mark(tt)
744.30/263.04	   active(U92(tt)) -> mark(0)
744.30/263.04	   active(isNat(0)) -> mark(tt)
744.30/263.04	   active(isNatKind(0)) -> mark(tt)
744.30/263.04	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.04	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.04	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.04	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.04	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.04	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.04	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.04	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.04	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.04	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.04	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.04	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.04	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.04	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.04	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.04	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.04	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.04	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.04	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.04	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.04	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.04	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.04	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.04	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.04	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.04	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.04	   U16(active(X)) -> U16(X)
744.30/263.04	   U16(mark(X)) -> U16(X)
744.30/263.04	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.04	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.04	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.04	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.04	   U23(active(X)) -> U23(X)
744.30/263.04	   U23(mark(X)) -> U23(X)
744.30/263.04	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.04	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.04	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.04	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.04	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.04	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.04	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.04	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.05	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.05	   U36(active(X)) -> U36(X)
744.30/263.05	   U36(mark(X)) -> U36(X)
744.30/263.05	   U42(active(X)) -> U42(X)
744.30/263.05	   U42(mark(X)) -> U42(X)
744.30/263.05	   U62(active(X)) -> U62(X)
744.30/263.05	   U62(mark(X)) -> U62(X)
744.30/263.05	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.05	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.05	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.05	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.05	   s(active(X)) -> s(X)
744.30/263.05	   s(mark(X)) -> s(X)
744.30/263.05	   U92(active(X)) -> U92(X)
744.30/263.05	   U92(mark(X)) -> U92(X)
744.30/263.05	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.05	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.05	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.05	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.05	   U51(active(X)) -> U51(X)
744.30/263.05	   U51(mark(X)) -> U51(X)
744.30/263.05	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.05	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.05	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.05	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.05	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.05	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.05	   x(active(X1), X2) -> x(X1, X2)
744.30/263.05	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.05	
744.30/263.05	The set Q consists of the following terms:
744.30/263.05	
744.30/263.05	   active(U101(tt, x0, x1))
744.30/263.05	   active(U102(tt, x0, x1))
744.30/263.05	   active(U103(tt, x0, x1))
744.30/263.05	   active(U104(tt, x0, x1))
744.30/263.05	   active(U11(tt, x0, x1))
744.30/263.05	   active(U12(tt, x0, x1))
744.30/263.05	   active(U13(tt, x0, x1))
744.30/263.05	   active(U14(tt, x0, x1))
744.30/263.05	   active(U15(tt, x0))
744.30/263.05	   active(U16(tt))
744.30/263.05	   active(U21(tt, x0))
744.30/263.05	   active(U22(tt, x0))
744.30/263.05	   active(U23(tt))
744.30/263.05	   active(U31(tt, x0, x1))
744.30/263.05	   active(U32(tt, x0, x1))
744.30/263.05	   active(U33(tt, x0, x1))
744.30/263.05	   active(U34(tt, x0, x1))
744.30/263.05	   active(U35(tt, x0))
744.30/263.05	   active(U36(tt))
744.30/263.05	   active(U41(tt, x0))
744.30/263.05	   active(U42(tt))
744.30/263.05	   active(U51(tt))
744.30/263.05	   active(U61(tt, x0))
744.30/263.05	   active(U62(tt))
744.30/263.05	   active(U71(tt, x0))
744.30/263.05	   active(U72(tt, x0))
744.30/263.05	   active(U81(tt, x0, x1))
744.30/263.05	   active(U82(tt, x0, x1))
744.30/263.05	   active(U83(tt, x0, x1))
744.30/263.05	   active(U84(tt, x0, x1))
744.30/263.05	   active(U91(tt, x0))
744.30/263.05	   active(U92(tt))
744.30/263.05	   active(isNat(0))
744.30/263.05	   active(isNat(plus(x0, x1)))
744.30/263.05	   active(isNat(s(x0)))
744.30/263.05	   active(isNat(x(x0, x1)))
744.30/263.05	   active(isNatKind(0))
744.30/263.05	   active(isNatKind(plus(x0, x1)))
744.30/263.05	   active(isNatKind(s(x0)))
744.30/263.05	   active(isNatKind(x(x0, x1)))
744.30/263.05	   active(plus(x0, 0))
744.30/263.05	   active(plus(x0, s(x1)))
744.30/263.05	   active(x(x0, 0))
744.30/263.05	   active(x(x0, s(x1)))
744.30/263.05	   mark(U101(x0, x1, x2))
744.30/263.05	   mark(tt)
744.30/263.05	   mark(U102(x0, x1, x2))
744.30/263.05	   mark(isNatKind(x0))
744.30/263.05	   mark(U103(x0, x1, x2))
744.30/263.05	   mark(isNat(x0))
744.30/263.05	   mark(U104(x0, x1, x2))
744.30/263.05	   mark(plus(x0, x1))
744.30/263.05	   mark(x(x0, x1))
744.30/263.05	   mark(U11(x0, x1, x2))
744.30/263.05	   mark(U12(x0, x1, x2))
744.30/263.05	   mark(U13(x0, x1, x2))
744.30/263.05	   mark(U14(x0, x1, x2))
744.30/263.05	   mark(U15(x0, x1))
744.30/263.05	   mark(U16(x0))
744.30/263.05	   mark(U21(x0, x1))
744.30/263.05	   mark(U22(x0, x1))
744.30/263.05	   mark(U23(x0))
744.30/263.05	   mark(U31(x0, x1, x2))
744.30/263.05	   mark(U32(x0, x1, x2))
744.30/263.05	   mark(U33(x0, x1, x2))
744.30/263.05	   mark(U34(x0, x1, x2))
744.30/263.05	   mark(U35(x0, x1))
744.30/263.05	   mark(U36(x0))
744.30/263.05	   mark(U41(x0, x1))
744.30/263.05	   mark(U42(x0))
744.30/263.05	   mark(U51(x0))
744.30/263.05	   mark(U61(x0, x1))
744.30/263.05	   mark(U62(x0))
744.30/263.05	   mark(U71(x0, x1))
744.30/263.05	   mark(U72(x0, x1))
744.30/263.05	   mark(U81(x0, x1, x2))
744.30/263.05	   mark(U82(x0, x1, x2))
744.30/263.05	   mark(U83(x0, x1, x2))
744.30/263.05	   mark(U84(x0, x1, x2))
744.30/263.05	   mark(s(x0))
744.30/263.05	   mark(U91(x0, x1))
744.30/263.05	   mark(U92(x0))
744.30/263.05	   mark(0)
744.30/263.05	   U101(mark(x0), x1, x2)
744.30/263.05	   U101(x0, mark(x1), x2)
744.30/263.05	   U101(x0, x1, mark(x2))
744.30/263.05	   U101(active(x0), x1, x2)
744.30/263.05	   U101(x0, active(x1), x2)
744.30/263.05	   U101(x0, x1, active(x2))
744.30/263.05	   U102(mark(x0), x1, x2)
744.30/263.05	   U102(x0, mark(x1), x2)
744.30/263.05	   U102(x0, x1, mark(x2))
744.30/263.05	   U102(active(x0), x1, x2)
744.30/263.05	   U102(x0, active(x1), x2)
744.30/263.05	   U102(x0, x1, active(x2))
744.30/263.05	   isNatKind(mark(x0))
744.30/263.05	   isNatKind(active(x0))
744.30/263.05	   U103(mark(x0), x1, x2)
744.30/263.05	   U103(x0, mark(x1), x2)
744.30/263.05	   U103(x0, x1, mark(x2))
744.30/263.05	   U103(active(x0), x1, x2)
744.30/263.05	   U103(x0, active(x1), x2)
744.30/263.05	   U103(x0, x1, active(x2))
744.30/263.05	   isNat(mark(x0))
744.30/263.05	   isNat(active(x0))
744.30/263.05	   U104(mark(x0), x1, x2)
744.30/263.05	   U104(x0, mark(x1), x2)
744.30/263.05	   U104(x0, x1, mark(x2))
744.30/263.05	   U104(active(x0), x1, x2)
744.30/263.05	   U104(x0, active(x1), x2)
744.30/263.05	   U104(x0, x1, active(x2))
744.30/263.05	   plus(mark(x0), x1)
744.30/263.05	   plus(x0, mark(x1))
744.30/263.05	   plus(active(x0), x1)
744.30/263.05	   plus(x0, active(x1))
744.30/263.05	   x(mark(x0), x1)
744.30/263.05	   x(x0, mark(x1))
744.30/263.05	   x(active(x0), x1)
744.30/263.05	   x(x0, active(x1))
744.30/263.05	   U11(mark(x0), x1, x2)
744.30/263.05	   U11(x0, mark(x1), x2)
744.30/263.05	   U11(x0, x1, mark(x2))
744.30/263.05	   U11(active(x0), x1, x2)
744.30/263.05	   U11(x0, active(x1), x2)
744.30/263.05	   U11(x0, x1, active(x2))
744.30/263.05	   U12(mark(x0), x1, x2)
744.30/263.05	   U12(x0, mark(x1), x2)
744.30/263.05	   U12(x0, x1, mark(x2))
744.30/263.05	   U12(active(x0), x1, x2)
744.30/263.05	   U12(x0, active(x1), x2)
744.30/263.05	   U12(x0, x1, active(x2))
744.30/263.05	   U13(mark(x0), x1, x2)
744.30/263.05	   U13(x0, mark(x1), x2)
744.30/263.05	   U13(x0, x1, mark(x2))
744.30/263.05	   U13(active(x0), x1, x2)
744.30/263.05	   U13(x0, active(x1), x2)
744.30/263.05	   U13(x0, x1, active(x2))
744.30/263.05	   U14(mark(x0), x1, x2)
744.30/263.05	   U14(x0, mark(x1), x2)
744.30/263.05	   U14(x0, x1, mark(x2))
744.30/263.05	   U14(active(x0), x1, x2)
744.30/263.05	   U14(x0, active(x1), x2)
744.30/263.05	   U14(x0, x1, active(x2))
744.30/263.05	   U15(mark(x0), x1)
744.30/263.05	   U15(x0, mark(x1))
744.30/263.05	   U15(active(x0), x1)
744.30/263.05	   U15(x0, active(x1))
744.30/263.05	   U16(mark(x0))
744.30/263.05	   U16(active(x0))
744.30/263.05	   U21(mark(x0), x1)
744.30/263.05	   U21(x0, mark(x1))
744.30/263.05	   U21(active(x0), x1)
744.30/263.05	   U21(x0, active(x1))
744.30/263.05	   U22(mark(x0), x1)
744.30/263.05	   U22(x0, mark(x1))
744.30/263.05	   U22(active(x0), x1)
744.30/263.05	   U22(x0, active(x1))
744.30/263.05	   U23(mark(x0))
744.30/263.05	   U23(active(x0))
744.30/263.05	   U31(mark(x0), x1, x2)
744.30/263.05	   U31(x0, mark(x1), x2)
744.30/263.05	   U31(x0, x1, mark(x2))
744.30/263.05	   U31(active(x0), x1, x2)
744.30/263.05	   U31(x0, active(x1), x2)
744.30/263.05	   U31(x0, x1, active(x2))
744.30/263.05	   U32(mark(x0), x1, x2)
744.30/263.05	   U32(x0, mark(x1), x2)
744.30/263.05	   U32(x0, x1, mark(x2))
744.30/263.05	   U32(active(x0), x1, x2)
744.30/263.05	   U32(x0, active(x1), x2)
744.30/263.05	   U32(x0, x1, active(x2))
744.30/263.05	   U33(mark(x0), x1, x2)
744.30/263.05	   U33(x0, mark(x1), x2)
744.30/263.05	   U33(x0, x1, mark(x2))
744.30/263.05	   U33(active(x0), x1, x2)
744.30/263.05	   U33(x0, active(x1), x2)
744.30/263.05	   U33(x0, x1, active(x2))
744.30/263.05	   U34(mark(x0), x1, x2)
744.30/263.05	   U34(x0, mark(x1), x2)
744.30/263.05	   U34(x0, x1, mark(x2))
744.30/263.05	   U34(active(x0), x1, x2)
744.30/263.05	   U34(x0, active(x1), x2)
744.30/263.05	   U34(x0, x1, active(x2))
744.30/263.05	   U35(mark(x0), x1)
744.30/263.05	   U35(x0, mark(x1))
744.30/263.05	   U35(active(x0), x1)
744.30/263.05	   U35(x0, active(x1))
744.30/263.05	   U36(mark(x0))
744.30/263.05	   U36(active(x0))
744.30/263.05	   U41(mark(x0), x1)
744.30/263.05	   U41(x0, mark(x1))
744.30/263.05	   U41(active(x0), x1)
744.30/263.05	   U41(x0, active(x1))
744.30/263.05	   U42(mark(x0))
744.30/263.05	   U42(active(x0))
744.30/263.05	   U51(mark(x0))
744.30/263.05	   U51(active(x0))
744.30/263.05	   U61(mark(x0), x1)
744.30/263.05	   U61(x0, mark(x1))
744.30/263.05	   U61(active(x0), x1)
744.30/263.05	   U61(x0, active(x1))
744.30/263.05	   U62(mark(x0))
744.30/263.05	   U62(active(x0))
744.30/263.05	   U71(mark(x0), x1)
744.30/263.05	   U71(x0, mark(x1))
744.30/263.05	   U71(active(x0), x1)
744.30/263.05	   U71(x0, active(x1))
744.30/263.05	   U72(mark(x0), x1)
744.30/263.05	   U72(x0, mark(x1))
744.30/263.05	   U72(active(x0), x1)
744.30/263.05	   U72(x0, active(x1))
744.30/263.05	   U81(mark(x0), x1, x2)
744.30/263.05	   U81(x0, mark(x1), x2)
744.30/263.05	   U81(x0, x1, mark(x2))
744.30/263.05	   U81(active(x0), x1, x2)
744.30/263.05	   U81(x0, active(x1), x2)
744.30/263.05	   U81(x0, x1, active(x2))
744.30/263.05	   U82(mark(x0), x1, x2)
744.30/263.05	   U82(x0, mark(x1), x2)
744.30/263.05	   U82(x0, x1, mark(x2))
744.30/263.05	   U82(active(x0), x1, x2)
744.30/263.05	   U82(x0, active(x1), x2)
744.30/263.05	   U82(x0, x1, active(x2))
744.30/263.05	   U83(mark(x0), x1, x2)
744.30/263.05	   U83(x0, mark(x1), x2)
744.30/263.05	   U83(x0, x1, mark(x2))
744.30/263.05	   U83(active(x0), x1, x2)
744.30/263.05	   U83(x0, active(x1), x2)
744.30/263.05	   U83(x0, x1, active(x2))
744.30/263.05	   U84(mark(x0), x1, x2)
744.30/263.05	   U84(x0, mark(x1), x2)
744.30/263.05	   U84(x0, x1, mark(x2))
744.30/263.05	   U84(active(x0), x1, x2)
744.30/263.05	   U84(x0, active(x1), x2)
744.30/263.05	   U84(x0, x1, active(x2))
744.30/263.05	   s(mark(x0))
744.30/263.05	   s(active(x0))
744.30/263.05	   U91(mark(x0), x1)
744.30/263.05	   U91(x0, mark(x1))
744.30/263.05	   U91(active(x0), x1)
744.30/263.05	   U91(x0, active(x1))
744.30/263.05	   U92(mark(x0))
744.30/263.05	   U92(active(x0))
744.30/263.05	
744.30/263.05	We have to consider all minimal (P,Q,R)-chains.
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(307) QDPOrderProof (EQUIVALENT)
744.30/263.05	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.05	
744.30/263.05	
744.30/263.05	The following pairs can be oriented strictly and are deleted.
744.30/263.05	
744.30/263.05	   ACTIVE(U35(tt, V2)) -> MARK(U36(isNat(V2)))
744.30/263.05	The remaining pairs can at least be oriented weakly.
744.30/263.05	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(tt) =  	[[0A]]
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U13(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U31(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U34(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U35(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U36(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U42(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(s(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(x(x_1, x_2)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U101(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U71(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U91(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	   <<<
744.30/263.05	 POL(0) =  	[[0A]]
744.30/263.05	>>>
744.30/263.05	
744.30/263.05	
744.30/263.05	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.05	
744.30/263.05	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.05	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.05	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.05	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.05	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.05	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.05	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.05	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.05	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.05	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.05	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.05	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.05	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.05	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.05	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.05	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.05	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.05	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.05	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.05	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.05	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.05	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.05	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.05	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.05	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.05	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.05	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.05	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.05	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.05	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.05	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.05	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.05	   active(U72(tt, N)) -> mark(N)
744.30/263.05	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.05	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.05	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.05	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.05	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.05	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.05	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.05	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.05	   mark(s(X)) -> active(s(mark(X)))
744.30/263.05	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.05	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.05	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.05	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.05	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.05	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.05	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.05	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.05	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.05	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.05	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.05	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.05	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.05	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.05	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.05	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.05	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.05	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.05	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.05	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.05	   mark(isNat(X)) -> active(isNat(X))
744.30/263.05	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.05	   mark(tt) -> active(tt)
744.30/263.05	   mark(0) -> active(0)
744.30/263.05	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.05	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.05	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.05	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.05	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.05	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.05	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.05	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.05	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.05	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.05	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.05	   active(U16(tt)) -> mark(tt)
744.30/263.05	   active(U23(tt)) -> mark(tt)
744.30/263.05	   active(U36(tt)) -> mark(tt)
744.30/263.05	   active(U42(tt)) -> mark(tt)
744.30/263.05	   active(U51(tt)) -> mark(tt)
744.30/263.05	   active(U62(tt)) -> mark(tt)
744.30/263.05	   active(U92(tt)) -> mark(0)
744.30/263.05	   active(isNat(0)) -> mark(tt)
744.30/263.05	   active(isNatKind(0)) -> mark(tt)
744.30/263.05	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.05	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.05	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.05	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.05	   U16(active(X)) -> U16(X)
744.30/263.05	   U16(mark(X)) -> U16(X)
744.30/263.05	   U23(active(X)) -> U23(X)
744.30/263.05	   U23(mark(X)) -> U23(X)
744.30/263.05	   U36(active(X)) -> U36(X)
744.30/263.05	   U36(mark(X)) -> U36(X)
744.30/263.05	   U42(active(X)) -> U42(X)
744.30/263.05	   U42(mark(X)) -> U42(X)
744.30/263.05	   U62(active(X)) -> U62(X)
744.30/263.05	   U62(mark(X)) -> U62(X)
744.30/263.05	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.05	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.05	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.05	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.05	   s(active(X)) -> s(X)
744.30/263.05	   s(mark(X)) -> s(X)
744.30/263.05	   U92(active(X)) -> U92(X)
744.30/263.05	   U92(mark(X)) -> U92(X)
744.30/263.05	   U51(active(X)) -> U51(X)
744.30/263.05	   U51(mark(X)) -> U51(X)
744.30/263.05	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.05	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.05	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.05	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.05	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.05	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.05	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.05	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.05	   x(active(X1), X2) -> x(X1, X2)
744.30/263.05	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.05	
744.30/263.05	
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(308)
744.30/263.05	Obligation:
744.30/263.05	Q DP problem:
744.30/263.05	The TRS P consists of the following rules:
744.30/263.05	
744.30/263.05	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.05	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.05	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.05	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.05	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.05	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.05	   MARK(U16(X)) -> MARK(X)
744.30/263.05	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.05	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.05	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.05	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.05	   MARK(U23(X)) -> MARK(X)
744.30/263.05	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.05	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.05	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.30/263.05	   MARK(U36(X)) -> MARK(X)
744.30/263.05	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.05	   MARK(U42(X)) -> MARK(X)
744.30/263.05	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U51(X)) -> MARK(X)
744.30/263.05	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.05	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.05	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.05	
744.30/263.05	The TRS R consists of the following rules:
744.30/263.05	
744.30/263.05	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.05	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.05	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.05	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.05	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.05	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.05	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.05	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.05	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.05	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.05	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.05	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.05	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.05	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.05	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.05	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.05	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.05	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.05	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.05	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.05	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.05	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.05	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.05	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.05	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.05	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.05	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.05	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.05	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.05	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.05	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.05	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.05	   active(U72(tt, N)) -> mark(N)
744.30/263.05	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.05	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.05	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.05	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.05	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.05	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.05	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.05	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.05	   mark(s(X)) -> active(s(mark(X)))
744.30/263.05	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.05	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.05	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.05	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.05	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.05	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.05	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.05	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.05	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.05	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.05	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.05	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.05	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.05	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.05	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.05	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.05	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.05	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.05	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.05	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.05	   mark(isNat(X)) -> active(isNat(X))
744.30/263.05	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.05	   mark(tt) -> active(tt)
744.30/263.05	   mark(0) -> active(0)
744.30/263.05	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.05	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.05	   active(U16(tt)) -> mark(tt)
744.30/263.05	   active(U23(tt)) -> mark(tt)
744.30/263.05	   active(U36(tt)) -> mark(tt)
744.30/263.05	   active(U42(tt)) -> mark(tt)
744.30/263.05	   active(U51(tt)) -> mark(tt)
744.30/263.05	   active(U62(tt)) -> mark(tt)
744.30/263.05	   active(U92(tt)) -> mark(0)
744.30/263.05	   active(isNat(0)) -> mark(tt)
744.30/263.05	   active(isNatKind(0)) -> mark(tt)
744.30/263.05	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.05	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.05	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.05	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.05	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.05	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.05	   U16(active(X)) -> U16(X)
744.30/263.05	   U16(mark(X)) -> U16(X)
744.30/263.05	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.05	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.05	   U23(active(X)) -> U23(X)
744.30/263.05	   U23(mark(X)) -> U23(X)
744.30/263.05	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.05	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.05	   U36(active(X)) -> U36(X)
744.30/263.05	   U36(mark(X)) -> U36(X)
744.30/263.05	   U42(active(X)) -> U42(X)
744.30/263.05	   U42(mark(X)) -> U42(X)
744.30/263.05	   U62(active(X)) -> U62(X)
744.30/263.05	   U62(mark(X)) -> U62(X)
744.30/263.05	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.05	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.05	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.05	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.05	   s(active(X)) -> s(X)
744.30/263.05	   s(mark(X)) -> s(X)
744.30/263.05	   U92(active(X)) -> U92(X)
744.30/263.05	   U92(mark(X)) -> U92(X)
744.30/263.05	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.05	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.05	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.05	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.05	   U51(active(X)) -> U51(X)
744.30/263.05	   U51(mark(X)) -> U51(X)
744.30/263.05	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.05	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.05	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.05	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.05	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.05	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.05	   x(active(X1), X2) -> x(X1, X2)
744.30/263.05	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.05	
744.30/263.05	The set Q consists of the following terms:
744.30/263.05	
744.30/263.05	   active(U101(tt, x0, x1))
744.30/263.05	   active(U102(tt, x0, x1))
744.30/263.05	   active(U103(tt, x0, x1))
744.30/263.05	   active(U104(tt, x0, x1))
744.30/263.05	   active(U11(tt, x0, x1))
744.30/263.05	   active(U12(tt, x0, x1))
744.30/263.05	   active(U13(tt, x0, x1))
744.30/263.05	   active(U14(tt, x0, x1))
744.30/263.05	   active(U15(tt, x0))
744.30/263.05	   active(U16(tt))
744.30/263.05	   active(U21(tt, x0))
744.30/263.05	   active(U22(tt, x0))
744.30/263.05	   active(U23(tt))
744.30/263.05	   active(U31(tt, x0, x1))
744.30/263.05	   active(U32(tt, x0, x1))
744.30/263.05	   active(U33(tt, x0, x1))
744.30/263.05	   active(U34(tt, x0, x1))
744.30/263.05	   active(U35(tt, x0))
744.30/263.05	   active(U36(tt))
744.30/263.05	   active(U41(tt, x0))
744.30/263.05	   active(U42(tt))
744.30/263.05	   active(U51(tt))
744.30/263.05	   active(U61(tt, x0))
744.30/263.05	   active(U62(tt))
744.30/263.05	   active(U71(tt, x0))
744.30/263.05	   active(U72(tt, x0))
744.30/263.05	   active(U81(tt, x0, x1))
744.30/263.05	   active(U82(tt, x0, x1))
744.30/263.05	   active(U83(tt, x0, x1))
744.30/263.05	   active(U84(tt, x0, x1))
744.30/263.05	   active(U91(tt, x0))
744.30/263.05	   active(U92(tt))
744.30/263.05	   active(isNat(0))
744.30/263.05	   active(isNat(plus(x0, x1)))
744.30/263.05	   active(isNat(s(x0)))
744.30/263.05	   active(isNat(x(x0, x1)))
744.30/263.05	   active(isNatKind(0))
744.30/263.05	   active(isNatKind(plus(x0, x1)))
744.30/263.05	   active(isNatKind(s(x0)))
744.30/263.05	   active(isNatKind(x(x0, x1)))
744.30/263.05	   active(plus(x0, 0))
744.30/263.05	   active(plus(x0, s(x1)))
744.30/263.05	   active(x(x0, 0))
744.30/263.05	   active(x(x0, s(x1)))
744.30/263.05	   mark(U101(x0, x1, x2))
744.30/263.05	   mark(tt)
744.30/263.05	   mark(U102(x0, x1, x2))
744.30/263.05	   mark(isNatKind(x0))
744.30/263.05	   mark(U103(x0, x1, x2))
744.30/263.05	   mark(isNat(x0))
744.30/263.05	   mark(U104(x0, x1, x2))
744.30/263.05	   mark(plus(x0, x1))
744.30/263.05	   mark(x(x0, x1))
744.30/263.05	   mark(U11(x0, x1, x2))
744.30/263.05	   mark(U12(x0, x1, x2))
744.30/263.05	   mark(U13(x0, x1, x2))
744.30/263.05	   mark(U14(x0, x1, x2))
744.30/263.05	   mark(U15(x0, x1))
744.30/263.05	   mark(U16(x0))
744.30/263.05	   mark(U21(x0, x1))
744.30/263.05	   mark(U22(x0, x1))
744.30/263.05	   mark(U23(x0))
744.30/263.05	   mark(U31(x0, x1, x2))
744.30/263.05	   mark(U32(x0, x1, x2))
744.30/263.05	   mark(U33(x0, x1, x2))
744.30/263.05	   mark(U34(x0, x1, x2))
744.30/263.05	   mark(U35(x0, x1))
744.30/263.05	   mark(U36(x0))
744.30/263.05	   mark(U41(x0, x1))
744.30/263.05	   mark(U42(x0))
744.30/263.05	   mark(U51(x0))
744.30/263.05	   mark(U61(x0, x1))
744.30/263.05	   mark(U62(x0))
744.30/263.05	   mark(U71(x0, x1))
744.30/263.05	   mark(U72(x0, x1))
744.30/263.05	   mark(U81(x0, x1, x2))
744.30/263.05	   mark(U82(x0, x1, x2))
744.30/263.05	   mark(U83(x0, x1, x2))
744.30/263.05	   mark(U84(x0, x1, x2))
744.30/263.05	   mark(s(x0))
744.30/263.05	   mark(U91(x0, x1))
744.30/263.05	   mark(U92(x0))
744.30/263.05	   mark(0)
744.30/263.05	   U101(mark(x0), x1, x2)
744.30/263.05	   U101(x0, mark(x1), x2)
744.30/263.05	   U101(x0, x1, mark(x2))
744.30/263.05	   U101(active(x0), x1, x2)
744.30/263.05	   U101(x0, active(x1), x2)
744.30/263.05	   U101(x0, x1, active(x2))
744.30/263.05	   U102(mark(x0), x1, x2)
744.30/263.05	   U102(x0, mark(x1), x2)
744.30/263.05	   U102(x0, x1, mark(x2))
744.30/263.05	   U102(active(x0), x1, x2)
744.30/263.05	   U102(x0, active(x1), x2)
744.30/263.05	   U102(x0, x1, active(x2))
744.30/263.05	   isNatKind(mark(x0))
744.30/263.05	   isNatKind(active(x0))
744.30/263.05	   U103(mark(x0), x1, x2)
744.30/263.05	   U103(x0, mark(x1), x2)
744.30/263.05	   U103(x0, x1, mark(x2))
744.30/263.05	   U103(active(x0), x1, x2)
744.30/263.05	   U103(x0, active(x1), x2)
744.30/263.05	   U103(x0, x1, active(x2))
744.30/263.05	   isNat(mark(x0))
744.30/263.05	   isNat(active(x0))
744.30/263.05	   U104(mark(x0), x1, x2)
744.30/263.05	   U104(x0, mark(x1), x2)
744.30/263.05	   U104(x0, x1, mark(x2))
744.30/263.05	   U104(active(x0), x1, x2)
744.30/263.05	   U104(x0, active(x1), x2)
744.30/263.05	   U104(x0, x1, active(x2))
744.30/263.05	   plus(mark(x0), x1)
744.30/263.05	   plus(x0, mark(x1))
744.30/263.05	   plus(active(x0), x1)
744.30/263.05	   plus(x0, active(x1))
744.30/263.05	   x(mark(x0), x1)
744.30/263.05	   x(x0, mark(x1))
744.30/263.05	   x(active(x0), x1)
744.30/263.05	   x(x0, active(x1))
744.30/263.05	   U11(mark(x0), x1, x2)
744.30/263.05	   U11(x0, mark(x1), x2)
744.30/263.05	   U11(x0, x1, mark(x2))
744.30/263.05	   U11(active(x0), x1, x2)
744.30/263.05	   U11(x0, active(x1), x2)
744.30/263.05	   U11(x0, x1, active(x2))
744.30/263.05	   U12(mark(x0), x1, x2)
744.30/263.05	   U12(x0, mark(x1), x2)
744.30/263.05	   U12(x0, x1, mark(x2))
744.30/263.05	   U12(active(x0), x1, x2)
744.30/263.05	   U12(x0, active(x1), x2)
744.30/263.05	   U12(x0, x1, active(x2))
744.30/263.05	   U13(mark(x0), x1, x2)
744.30/263.05	   U13(x0, mark(x1), x2)
744.30/263.05	   U13(x0, x1, mark(x2))
744.30/263.05	   U13(active(x0), x1, x2)
744.30/263.05	   U13(x0, active(x1), x2)
744.30/263.05	   U13(x0, x1, active(x2))
744.30/263.05	   U14(mark(x0), x1, x2)
744.30/263.05	   U14(x0, mark(x1), x2)
744.30/263.05	   U14(x0, x1, mark(x2))
744.30/263.05	   U14(active(x0), x1, x2)
744.30/263.05	   U14(x0, active(x1), x2)
744.30/263.05	   U14(x0, x1, active(x2))
744.30/263.05	   U15(mark(x0), x1)
744.30/263.05	   U15(x0, mark(x1))
744.30/263.05	   U15(active(x0), x1)
744.30/263.05	   U15(x0, active(x1))
744.30/263.05	   U16(mark(x0))
744.30/263.05	   U16(active(x0))
744.30/263.05	   U21(mark(x0), x1)
744.30/263.05	   U21(x0, mark(x1))
744.30/263.05	   U21(active(x0), x1)
744.30/263.05	   U21(x0, active(x1))
744.30/263.05	   U22(mark(x0), x1)
744.30/263.05	   U22(x0, mark(x1))
744.30/263.05	   U22(active(x0), x1)
744.30/263.05	   U22(x0, active(x1))
744.30/263.05	   U23(mark(x0))
744.30/263.05	   U23(active(x0))
744.30/263.05	   U31(mark(x0), x1, x2)
744.30/263.05	   U31(x0, mark(x1), x2)
744.30/263.05	   U31(x0, x1, mark(x2))
744.30/263.05	   U31(active(x0), x1, x2)
744.30/263.05	   U31(x0, active(x1), x2)
744.30/263.05	   U31(x0, x1, active(x2))
744.30/263.05	   U32(mark(x0), x1, x2)
744.30/263.05	   U32(x0, mark(x1), x2)
744.30/263.05	   U32(x0, x1, mark(x2))
744.30/263.05	   U32(active(x0), x1, x2)
744.30/263.05	   U32(x0, active(x1), x2)
744.30/263.05	   U32(x0, x1, active(x2))
744.30/263.05	   U33(mark(x0), x1, x2)
744.30/263.05	   U33(x0, mark(x1), x2)
744.30/263.05	   U33(x0, x1, mark(x2))
744.30/263.05	   U33(active(x0), x1, x2)
744.30/263.05	   U33(x0, active(x1), x2)
744.30/263.05	   U33(x0, x1, active(x2))
744.30/263.05	   U34(mark(x0), x1, x2)
744.30/263.05	   U34(x0, mark(x1), x2)
744.30/263.05	   U34(x0, x1, mark(x2))
744.30/263.05	   U34(active(x0), x1, x2)
744.30/263.05	   U34(x0, active(x1), x2)
744.30/263.05	   U34(x0, x1, active(x2))
744.30/263.05	   U35(mark(x0), x1)
744.30/263.05	   U35(x0, mark(x1))
744.30/263.05	   U35(active(x0), x1)
744.30/263.05	   U35(x0, active(x1))
744.30/263.05	   U36(mark(x0))
744.30/263.05	   U36(active(x0))
744.30/263.05	   U41(mark(x0), x1)
744.30/263.05	   U41(x0, mark(x1))
744.30/263.05	   U41(active(x0), x1)
744.30/263.05	   U41(x0, active(x1))
744.30/263.05	   U42(mark(x0))
744.30/263.05	   U42(active(x0))
744.30/263.05	   U51(mark(x0))
744.30/263.05	   U51(active(x0))
744.30/263.05	   U61(mark(x0), x1)
744.30/263.05	   U61(x0, mark(x1))
744.30/263.05	   U61(active(x0), x1)
744.30/263.05	   U61(x0, active(x1))
744.30/263.05	   U62(mark(x0))
744.30/263.05	   U62(active(x0))
744.30/263.05	   U71(mark(x0), x1)
744.30/263.05	   U71(x0, mark(x1))
744.30/263.05	   U71(active(x0), x1)
744.30/263.05	   U71(x0, active(x1))
744.30/263.05	   U72(mark(x0), x1)
744.30/263.05	   U72(x0, mark(x1))
744.30/263.05	   U72(active(x0), x1)
744.30/263.05	   U72(x0, active(x1))
744.30/263.05	   U81(mark(x0), x1, x2)
744.30/263.05	   U81(x0, mark(x1), x2)
744.30/263.05	   U81(x0, x1, mark(x2))
744.30/263.05	   U81(active(x0), x1, x2)
744.30/263.05	   U81(x0, active(x1), x2)
744.30/263.05	   U81(x0, x1, active(x2))
744.30/263.05	   U82(mark(x0), x1, x2)
744.30/263.05	   U82(x0, mark(x1), x2)
744.30/263.05	   U82(x0, x1, mark(x2))
744.30/263.05	   U82(active(x0), x1, x2)
744.30/263.05	   U82(x0, active(x1), x2)
744.30/263.05	   U82(x0, x1, active(x2))
744.30/263.05	   U83(mark(x0), x1, x2)
744.30/263.05	   U83(x0, mark(x1), x2)
744.30/263.05	   U83(x0, x1, mark(x2))
744.30/263.05	   U83(active(x0), x1, x2)
744.30/263.05	   U83(x0, active(x1), x2)
744.30/263.05	   U83(x0, x1, active(x2))
744.30/263.05	   U84(mark(x0), x1, x2)
744.30/263.05	   U84(x0, mark(x1), x2)
744.30/263.05	   U84(x0, x1, mark(x2))
744.30/263.05	   U84(active(x0), x1, x2)
744.30/263.05	   U84(x0, active(x1), x2)
744.30/263.05	   U84(x0, x1, active(x2))
744.30/263.05	   s(mark(x0))
744.30/263.05	   s(active(x0))
744.30/263.05	   U91(mark(x0), x1)
744.30/263.05	   U91(x0, mark(x1))
744.30/263.05	   U91(active(x0), x1)
744.30/263.05	   U91(x0, active(x1))
744.30/263.05	   U92(mark(x0))
744.30/263.05	   U92(active(x0))
744.30/263.05	
744.30/263.05	We have to consider all minimal (P,Q,R)-chains.
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(309) QDPOrderProof (EQUIVALENT)
744.30/263.05	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.05	
744.30/263.05	
744.30/263.05	The following pairs can be oriented strictly and are deleted.
744.30/263.05	
744.30/263.05	   MARK(U35(X1, X2)) -> ACTIVE(U35(mark(X1), X2))
744.30/263.05	The remaining pairs can at least be oriented weakly.
744.30/263.05	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.30/263.05	
744.30/263.05	POL( ACTIVE_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U11_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U12_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U13_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U14_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U15_2(x_1, x_2) ) = 2
744.30/263.05	POL( U21_2(x_1, x_2) ) = 2
744.30/263.05	POL( U22_2(x_1, x_2) ) = 2
744.30/263.05	POL( U31_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U32_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U33_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U34_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U35_2(x_1, x_2) ) = max{0, -2}
744.30/263.05	POL( U41_2(x_1, x_2) ) = 2
744.30/263.05	POL( mark_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U102_3(x_1, ..., x_3) ) = 2x_1 + 2
744.30/263.05	POL( active_1(x_1) ) = 2
744.30/263.05	POL( U101_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.30/263.05	POL( tt ) = 0
744.30/263.05	POL( isNatKind_1(x_1) ) = 2
744.30/263.05	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.30/263.05	POL( isNat_1(x_1) ) = 2
744.30/263.05	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( plus_2(x_1, x_2) ) = max{0, x_1 - 2}
744.30/263.05	POL( x_2(x_1, x_2) ) = max{0, x_1 - 2}
744.30/263.05	POL( U16_1(x_1) ) = max{0, x_1 - 2}
744.30/263.05	POL( U23_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U36_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U42_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U61_2(x_1, x_2) ) = max{0, x_2 - 1}
744.30/263.05	POL( U62_1(x_1) ) = 2
744.30/263.05	POL( U71_2(x_1, x_2) ) = max{0, x_1 + 2x_2 - 1}
744.30/263.05	POL( U72_2(x_1, x_2) ) = 2x_1 + 2
744.30/263.05	POL( U81_3(x_1, ..., x_3) ) = x_2 + x_3 + 1
744.30/263.05	POL( U82_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.30/263.05	POL( U83_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.30/263.05	POL( U84_3(x_1, ..., x_3) ) = 2x_3 + 2
744.30/263.05	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.30/263.05	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U92_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U51_1(x_1) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( 0 ) = 0
744.30/263.05	POL( MARK_1(x_1) ) = 2
744.30/263.05	
744.30/263.05	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.05	
744.30/263.05	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.05	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.05	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.05	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.05	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.05	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.05	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.05	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.05	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.05	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.05	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.05	
744.30/263.05	
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(310)
744.30/263.05	Obligation:
744.30/263.05	Q DP problem:
744.30/263.05	The TRS P consists of the following rules:
744.30/263.05	
744.30/263.05	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.05	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.05	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.05	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.05	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.05	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.05	   MARK(U16(X)) -> MARK(X)
744.30/263.05	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.05	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.05	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.05	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.05	   MARK(U23(X)) -> MARK(X)
744.30/263.05	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.05	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.05	   MARK(U36(X)) -> MARK(X)
744.30/263.05	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.05	   MARK(U42(X)) -> MARK(X)
744.30/263.05	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.05	   MARK(U51(X)) -> MARK(X)
744.30/263.05	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.05	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.05	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.05	
744.30/263.05	The TRS R consists of the following rules:
744.30/263.05	
744.30/263.05	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.05	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.05	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.05	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.05	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.05	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.05	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.05	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.05	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.05	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.05	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.05	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.05	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.05	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.05	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.05	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.05	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.05	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.05	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.05	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.05	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.05	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.05	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.05	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.05	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.05	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.05	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.05	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.05	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.05	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.05	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.05	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.05	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.05	   active(U72(tt, N)) -> mark(N)
744.30/263.05	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.05	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.05	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.05	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.05	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.05	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.05	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.05	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.05	   mark(s(X)) -> active(s(mark(X)))
744.30/263.05	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.05	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.05	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.05	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.05	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.05	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.05	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.05	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.05	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.05	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.05	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.05	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.05	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.05	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.05	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.05	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.05	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.05	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.05	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.05	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.05	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.05	   mark(isNat(X)) -> active(isNat(X))
744.30/263.05	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.05	   mark(tt) -> active(tt)
744.30/263.05	   mark(0) -> active(0)
744.30/263.05	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.05	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.05	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.05	   active(U16(tt)) -> mark(tt)
744.30/263.05	   active(U23(tt)) -> mark(tt)
744.30/263.05	   active(U36(tt)) -> mark(tt)
744.30/263.05	   active(U42(tt)) -> mark(tt)
744.30/263.05	   active(U51(tt)) -> mark(tt)
744.30/263.05	   active(U62(tt)) -> mark(tt)
744.30/263.05	   active(U92(tt)) -> mark(0)
744.30/263.05	   active(isNat(0)) -> mark(tt)
744.30/263.05	   active(isNatKind(0)) -> mark(tt)
744.30/263.05	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.05	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.05	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.05	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.05	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.05	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.05	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.05	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.05	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.05	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.05	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.05	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.05	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.05	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.05	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.05	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.05	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.05	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.05	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.05	   U16(active(X)) -> U16(X)
744.30/263.05	   U16(mark(X)) -> U16(X)
744.30/263.05	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.05	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.05	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.05	   U23(active(X)) -> U23(X)
744.30/263.05	   U23(mark(X)) -> U23(X)
744.30/263.05	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.05	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.05	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.05	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.05	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.05	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.05	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.05	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.05	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.05	   U36(active(X)) -> U36(X)
744.30/263.05	   U36(mark(X)) -> U36(X)
744.30/263.05	   U42(active(X)) -> U42(X)
744.30/263.05	   U42(mark(X)) -> U42(X)
744.30/263.05	   U62(active(X)) -> U62(X)
744.30/263.05	   U62(mark(X)) -> U62(X)
744.30/263.05	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.05	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.05	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.05	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.05	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.05	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.05	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.05	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.05	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.05	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.05	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.05	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.05	   s(active(X)) -> s(X)
744.30/263.05	   s(mark(X)) -> s(X)
744.30/263.05	   U92(active(X)) -> U92(X)
744.30/263.05	   U92(mark(X)) -> U92(X)
744.30/263.05	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.05	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.05	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.05	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.05	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.05	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.05	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.05	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.05	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.05	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.05	   U51(active(X)) -> U51(X)
744.30/263.05	   U51(mark(X)) -> U51(X)
744.30/263.05	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.05	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.05	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.05	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.05	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.05	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.05	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.05	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.05	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.05	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.05	   x(active(X1), X2) -> x(X1, X2)
744.30/263.05	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.05	
744.30/263.05	The set Q consists of the following terms:
744.30/263.05	
744.30/263.05	   active(U101(tt, x0, x1))
744.30/263.05	   active(U102(tt, x0, x1))
744.30/263.05	   active(U103(tt, x0, x1))
744.30/263.05	   active(U104(tt, x0, x1))
744.30/263.05	   active(U11(tt, x0, x1))
744.30/263.05	   active(U12(tt, x0, x1))
744.30/263.05	   active(U13(tt, x0, x1))
744.30/263.05	   active(U14(tt, x0, x1))
744.30/263.05	   active(U15(tt, x0))
744.30/263.05	   active(U16(tt))
744.30/263.05	   active(U21(tt, x0))
744.30/263.05	   active(U22(tt, x0))
744.30/263.05	   active(U23(tt))
744.30/263.05	   active(U31(tt, x0, x1))
744.30/263.05	   active(U32(tt, x0, x1))
744.30/263.05	   active(U33(tt, x0, x1))
744.30/263.05	   active(U34(tt, x0, x1))
744.30/263.05	   active(U35(tt, x0))
744.30/263.05	   active(U36(tt))
744.30/263.05	   active(U41(tt, x0))
744.30/263.05	   active(U42(tt))
744.30/263.05	   active(U51(tt))
744.30/263.05	   active(U61(tt, x0))
744.30/263.05	   active(U62(tt))
744.30/263.05	   active(U71(tt, x0))
744.30/263.05	   active(U72(tt, x0))
744.30/263.05	   active(U81(tt, x0, x1))
744.30/263.05	   active(U82(tt, x0, x1))
744.30/263.05	   active(U83(tt, x0, x1))
744.30/263.05	   active(U84(tt, x0, x1))
744.30/263.05	   active(U91(tt, x0))
744.30/263.05	   active(U92(tt))
744.30/263.05	   active(isNat(0))
744.30/263.05	   active(isNat(plus(x0, x1)))
744.30/263.05	   active(isNat(s(x0)))
744.30/263.05	   active(isNat(x(x0, x1)))
744.30/263.05	   active(isNatKind(0))
744.30/263.05	   active(isNatKind(plus(x0, x1)))
744.30/263.05	   active(isNatKind(s(x0)))
744.30/263.05	   active(isNatKind(x(x0, x1)))
744.30/263.05	   active(plus(x0, 0))
744.30/263.05	   active(plus(x0, s(x1)))
744.30/263.05	   active(x(x0, 0))
744.30/263.05	   active(x(x0, s(x1)))
744.30/263.05	   mark(U101(x0, x1, x2))
744.30/263.05	   mark(tt)
744.30/263.05	   mark(U102(x0, x1, x2))
744.30/263.05	   mark(isNatKind(x0))
744.30/263.05	   mark(U103(x0, x1, x2))
744.30/263.05	   mark(isNat(x0))
744.30/263.05	   mark(U104(x0, x1, x2))
744.30/263.05	   mark(plus(x0, x1))
744.30/263.05	   mark(x(x0, x1))
744.30/263.05	   mark(U11(x0, x1, x2))
744.30/263.05	   mark(U12(x0, x1, x2))
744.30/263.05	   mark(U13(x0, x1, x2))
744.30/263.05	   mark(U14(x0, x1, x2))
744.30/263.05	   mark(U15(x0, x1))
744.30/263.05	   mark(U16(x0))
744.30/263.05	   mark(U21(x0, x1))
744.30/263.05	   mark(U22(x0, x1))
744.30/263.05	   mark(U23(x0))
744.30/263.05	   mark(U31(x0, x1, x2))
744.30/263.05	   mark(U32(x0, x1, x2))
744.30/263.05	   mark(U33(x0, x1, x2))
744.30/263.05	   mark(U34(x0, x1, x2))
744.30/263.05	   mark(U35(x0, x1))
744.30/263.05	   mark(U36(x0))
744.30/263.05	   mark(U41(x0, x1))
744.30/263.05	   mark(U42(x0))
744.30/263.05	   mark(U51(x0))
744.30/263.05	   mark(U61(x0, x1))
744.30/263.05	   mark(U62(x0))
744.30/263.05	   mark(U71(x0, x1))
744.30/263.05	   mark(U72(x0, x1))
744.30/263.05	   mark(U81(x0, x1, x2))
744.30/263.05	   mark(U82(x0, x1, x2))
744.30/263.05	   mark(U83(x0, x1, x2))
744.30/263.05	   mark(U84(x0, x1, x2))
744.30/263.05	   mark(s(x0))
744.30/263.05	   mark(U91(x0, x1))
744.30/263.05	   mark(U92(x0))
744.30/263.05	   mark(0)
744.30/263.05	   U101(mark(x0), x1, x2)
744.30/263.05	   U101(x0, mark(x1), x2)
744.30/263.05	   U101(x0, x1, mark(x2))
744.30/263.05	   U101(active(x0), x1, x2)
744.30/263.05	   U101(x0, active(x1), x2)
744.30/263.05	   U101(x0, x1, active(x2))
744.30/263.05	   U102(mark(x0), x1, x2)
744.30/263.05	   U102(x0, mark(x1), x2)
744.30/263.05	   U102(x0, x1, mark(x2))
744.30/263.05	   U102(active(x0), x1, x2)
744.30/263.05	   U102(x0, active(x1), x2)
744.30/263.05	   U102(x0, x1, active(x2))
744.30/263.05	   isNatKind(mark(x0))
744.30/263.05	   isNatKind(active(x0))
744.30/263.05	   U103(mark(x0), x1, x2)
744.30/263.05	   U103(x0, mark(x1), x2)
744.30/263.05	   U103(x0, x1, mark(x2))
744.30/263.05	   U103(active(x0), x1, x2)
744.30/263.05	   U103(x0, active(x1), x2)
744.30/263.05	   U103(x0, x1, active(x2))
744.30/263.05	   isNat(mark(x0))
744.30/263.05	   isNat(active(x0))
744.30/263.05	   U104(mark(x0), x1, x2)
744.30/263.05	   U104(x0, mark(x1), x2)
744.30/263.05	   U104(x0, x1, mark(x2))
744.30/263.05	   U104(active(x0), x1, x2)
744.30/263.05	   U104(x0, active(x1), x2)
744.30/263.05	   U104(x0, x1, active(x2))
744.30/263.05	   plus(mark(x0), x1)
744.30/263.05	   plus(x0, mark(x1))
744.30/263.05	   plus(active(x0), x1)
744.30/263.05	   plus(x0, active(x1))
744.30/263.05	   x(mark(x0), x1)
744.30/263.05	   x(x0, mark(x1))
744.30/263.05	   x(active(x0), x1)
744.30/263.05	   x(x0, active(x1))
744.30/263.05	   U11(mark(x0), x1, x2)
744.30/263.05	   U11(x0, mark(x1), x2)
744.30/263.05	   U11(x0, x1, mark(x2))
744.30/263.05	   U11(active(x0), x1, x2)
744.30/263.05	   U11(x0, active(x1), x2)
744.30/263.05	   U11(x0, x1, active(x2))
744.30/263.05	   U12(mark(x0), x1, x2)
744.30/263.05	   U12(x0, mark(x1), x2)
744.30/263.05	   U12(x0, x1, mark(x2))
744.30/263.05	   U12(active(x0), x1, x2)
744.30/263.05	   U12(x0, active(x1), x2)
744.30/263.05	   U12(x0, x1, active(x2))
744.30/263.05	   U13(mark(x0), x1, x2)
744.30/263.05	   U13(x0, mark(x1), x2)
744.30/263.05	   U13(x0, x1, mark(x2))
744.30/263.05	   U13(active(x0), x1, x2)
744.30/263.05	   U13(x0, active(x1), x2)
744.30/263.05	   U13(x0, x1, active(x2))
744.30/263.05	   U14(mark(x0), x1, x2)
744.30/263.05	   U14(x0, mark(x1), x2)
744.30/263.05	   U14(x0, x1, mark(x2))
744.30/263.05	   U14(active(x0), x1, x2)
744.30/263.05	   U14(x0, active(x1), x2)
744.30/263.05	   U14(x0, x1, active(x2))
744.30/263.05	   U15(mark(x0), x1)
744.30/263.05	   U15(x0, mark(x1))
744.30/263.05	   U15(active(x0), x1)
744.30/263.05	   U15(x0, active(x1))
744.30/263.05	   U16(mark(x0))
744.30/263.05	   U16(active(x0))
744.30/263.05	   U21(mark(x0), x1)
744.30/263.05	   U21(x0, mark(x1))
744.30/263.05	   U21(active(x0), x1)
744.30/263.05	   U21(x0, active(x1))
744.30/263.05	   U22(mark(x0), x1)
744.30/263.05	   U22(x0, mark(x1))
744.30/263.05	   U22(active(x0), x1)
744.30/263.05	   U22(x0, active(x1))
744.30/263.05	   U23(mark(x0))
744.30/263.05	   U23(active(x0))
744.30/263.05	   U31(mark(x0), x1, x2)
744.30/263.05	   U31(x0, mark(x1), x2)
744.30/263.05	   U31(x0, x1, mark(x2))
744.30/263.05	   U31(active(x0), x1, x2)
744.30/263.05	   U31(x0, active(x1), x2)
744.30/263.05	   U31(x0, x1, active(x2))
744.30/263.05	   U32(mark(x0), x1, x2)
744.30/263.05	   U32(x0, mark(x1), x2)
744.30/263.05	   U32(x0, x1, mark(x2))
744.30/263.05	   U32(active(x0), x1, x2)
744.30/263.05	   U32(x0, active(x1), x2)
744.30/263.05	   U32(x0, x1, active(x2))
744.30/263.05	   U33(mark(x0), x1, x2)
744.30/263.05	   U33(x0, mark(x1), x2)
744.30/263.05	   U33(x0, x1, mark(x2))
744.30/263.05	   U33(active(x0), x1, x2)
744.30/263.05	   U33(x0, active(x1), x2)
744.30/263.05	   U33(x0, x1, active(x2))
744.30/263.05	   U34(mark(x0), x1, x2)
744.30/263.05	   U34(x0, mark(x1), x2)
744.30/263.05	   U34(x0, x1, mark(x2))
744.30/263.05	   U34(active(x0), x1, x2)
744.30/263.05	   U34(x0, active(x1), x2)
744.30/263.05	   U34(x0, x1, active(x2))
744.30/263.05	   U35(mark(x0), x1)
744.30/263.05	   U35(x0, mark(x1))
744.30/263.05	   U35(active(x0), x1)
744.30/263.05	   U35(x0, active(x1))
744.30/263.05	   U36(mark(x0))
744.30/263.05	   U36(active(x0))
744.30/263.05	   U41(mark(x0), x1)
744.30/263.05	   U41(x0, mark(x1))
744.30/263.05	   U41(active(x0), x1)
744.30/263.05	   U41(x0, active(x1))
744.30/263.05	   U42(mark(x0))
744.30/263.05	   U42(active(x0))
744.30/263.05	   U51(mark(x0))
744.30/263.05	   U51(active(x0))
744.30/263.05	   U61(mark(x0), x1)
744.30/263.05	   U61(x0, mark(x1))
744.30/263.05	   U61(active(x0), x1)
744.30/263.05	   U61(x0, active(x1))
744.30/263.05	   U62(mark(x0))
744.30/263.05	   U62(active(x0))
744.30/263.05	   U71(mark(x0), x1)
744.30/263.05	   U71(x0, mark(x1))
744.30/263.05	   U71(active(x0), x1)
744.30/263.05	   U71(x0, active(x1))
744.30/263.05	   U72(mark(x0), x1)
744.30/263.05	   U72(x0, mark(x1))
744.30/263.05	   U72(active(x0), x1)
744.30/263.05	   U72(x0, active(x1))
744.30/263.05	   U81(mark(x0), x1, x2)
744.30/263.05	   U81(x0, mark(x1), x2)
744.30/263.05	   U81(x0, x1, mark(x2))
744.30/263.05	   U81(active(x0), x1, x2)
744.30/263.05	   U81(x0, active(x1), x2)
744.30/263.05	   U81(x0, x1, active(x2))
744.30/263.05	   U82(mark(x0), x1, x2)
744.30/263.05	   U82(x0, mark(x1), x2)
744.30/263.05	   U82(x0, x1, mark(x2))
744.30/263.05	   U82(active(x0), x1, x2)
744.30/263.05	   U82(x0, active(x1), x2)
744.30/263.05	   U82(x0, x1, active(x2))
744.30/263.05	   U83(mark(x0), x1, x2)
744.30/263.05	   U83(x0, mark(x1), x2)
744.30/263.05	   U83(x0, x1, mark(x2))
744.30/263.05	   U83(active(x0), x1, x2)
744.30/263.05	   U83(x0, active(x1), x2)
744.30/263.05	   U83(x0, x1, active(x2))
744.30/263.05	   U84(mark(x0), x1, x2)
744.30/263.05	   U84(x0, mark(x1), x2)
744.30/263.05	   U84(x0, x1, mark(x2))
744.30/263.05	   U84(active(x0), x1, x2)
744.30/263.05	   U84(x0, active(x1), x2)
744.30/263.05	   U84(x0, x1, active(x2))
744.30/263.05	   s(mark(x0))
744.30/263.05	   s(active(x0))
744.30/263.05	   U91(mark(x0), x1)
744.30/263.05	   U91(x0, mark(x1))
744.30/263.05	   U91(active(x0), x1)
744.30/263.05	   U91(x0, active(x1))
744.30/263.05	   U92(mark(x0))
744.30/263.05	   U92(active(x0))
744.30/263.05	
744.30/263.05	We have to consider all minimal (P,Q,R)-chains.
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(311) QDPOrderProof (EQUIVALENT)
744.30/263.05	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.05	
744.30/263.05	
744.30/263.05	The following pairs can be oriented strictly and are deleted.
744.30/263.05	
744.30/263.05	   MARK(U36(X)) -> MARK(X)
744.30/263.05	The remaining pairs can at least be oriented weakly.
744.30/263.05	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.30/263.05	
744.30/263.05	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.30/263.05	POL( U11_3(x_1, ..., x_3) ) = x_1 + 1
744.30/263.05	POL( U12_3(x_1, ..., x_3) ) = 2x_1 + 1
744.30/263.05	POL( U13_3(x_1, ..., x_3) ) = 2x_1 + 1
744.30/263.05	POL( U14_3(x_1, ..., x_3) ) = x_1 + 1
744.30/263.05	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.30/263.05	POL( U21_2(x_1, x_2) ) = 2x_1 + 1
744.30/263.05	POL( U22_2(x_1, x_2) ) = 2x_1 + 1
744.30/263.05	POL( U31_3(x_1, ..., x_3) ) = max{0, -2}
744.30/263.05	POL( U32_3(x_1, ..., x_3) ) = 1
744.30/263.05	POL( U33_3(x_1, ..., x_3) ) = 2x_1 + 1
744.30/263.05	POL( U34_3(x_1, ..., x_3) ) = 2x_1 + 1
744.30/263.05	POL( U41_2(x_1, x_2) ) = 2x_1 + 1
744.30/263.05	POL( mark_1(x_1) ) = 0
744.30/263.05	POL( U102_3(x_1, ..., x_3) ) = 2x_1 + x_2 + x_3 + 1
744.30/263.05	POL( active_1(x_1) ) = x_1 + 1
744.30/263.05	POL( U101_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.30/263.05	POL( tt ) = 0
744.30/263.05	POL( isNatKind_1(x_1) ) = 0
744.30/263.05	POL( U103_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( isNat_1(x_1) ) = 0
744.30/263.05	POL( U104_3(x_1, ..., x_3) ) = 2x_3 + 2
744.30/263.05	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.30/263.05	POL( x_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.30/263.05	POL( U16_1(x_1) ) = x_1 + 1
744.30/263.05	POL( U23_1(x_1) ) = 2x_1 + 1
744.30/263.05	POL( U35_2(x_1, x_2) ) = 2x_1 + 1
744.30/263.05	POL( U36_1(x_1) ) = 2x_1 + 2
744.30/263.05	POL( U42_1(x_1) ) = x_1 + 1
744.30/263.05	POL( U61_2(x_1, x_2) ) = 2
744.30/263.05	POL( U62_1(x_1) ) = 1
744.30/263.05	POL( U71_2(x_1, x_2) ) = max{0, 2x_2 - 1}
744.30/263.05	POL( U72_2(x_1, x_2) ) = max{0, x_1 - 2}
744.30/263.05	POL( U81_3(x_1, ..., x_3) ) = x_2 + 2x_3 + 2
744.30/263.05	POL( U82_3(x_1, ..., x_3) ) = 2
744.30/263.05	POL( U83_3(x_1, ..., x_3) ) = x_3 + 2
744.30/263.05	POL( U84_3(x_1, ..., x_3) ) = x_2 + 2
744.30/263.05	POL( s_1(x_1) ) = 0
744.30/263.05	POL( U91_2(x_1, x_2) ) = max{0, x_2 - 2}
744.30/263.05	POL( U92_1(x_1) ) = 1
744.30/263.05	POL( U51_1(x_1) ) = 2x_1 + 1
744.30/263.05	POL( 0 ) = 1
744.30/263.05	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.30/263.05	
744.30/263.05	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.05	none
744.30/263.05	
744.30/263.05	
744.30/263.05	----------------------------------------
744.30/263.05	
744.30/263.05	(312)
744.30/263.05	Obligation:
744.30/263.05	Q DP problem:
744.30/263.05	The TRS P consists of the following rules:
744.30/263.05	
744.30/263.05	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.05	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.05	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.05	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.05	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.05	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.05	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.05	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.05	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.05	   MARK(U16(X)) -> MARK(X)
744.30/263.05	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.05	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.05	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.06	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.06	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.06	   MARK(U23(X)) -> MARK(X)
744.30/263.06	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.06	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.06	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.06	   MARK(U42(X)) -> MARK(X)
744.30/263.06	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U51(X)) -> MARK(X)
744.30/263.06	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.06	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.06	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.06	
744.30/263.06	The TRS R consists of the following rules:
744.30/263.06	
744.30/263.06	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.06	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.06	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.06	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.06	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.06	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.06	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.06	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.06	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.06	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.06	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.06	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.06	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.06	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.06	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.06	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.06	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.06	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.06	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.06	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.06	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.06	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.06	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.06	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.06	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.06	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.06	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.06	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.06	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.06	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.06	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.06	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.06	   active(U72(tt, N)) -> mark(N)
744.30/263.06	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.06	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.06	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.06	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.06	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.06	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.06	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.06	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.06	   mark(s(X)) -> active(s(mark(X)))
744.30/263.06	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.06	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.06	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.06	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.06	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.06	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.06	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.06	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.06	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.06	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.06	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.06	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.06	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.06	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.06	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.06	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.06	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.06	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.06	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.06	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.06	   mark(isNat(X)) -> active(isNat(X))
744.30/263.06	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.06	   mark(tt) -> active(tt)
744.30/263.06	   mark(0) -> active(0)
744.30/263.06	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.06	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.06	   active(U16(tt)) -> mark(tt)
744.30/263.06	   active(U23(tt)) -> mark(tt)
744.30/263.06	   active(U36(tt)) -> mark(tt)
744.30/263.06	   active(U42(tt)) -> mark(tt)
744.30/263.06	   active(U51(tt)) -> mark(tt)
744.30/263.06	   active(U62(tt)) -> mark(tt)
744.30/263.06	   active(U92(tt)) -> mark(0)
744.30/263.06	   active(isNat(0)) -> mark(tt)
744.30/263.06	   active(isNatKind(0)) -> mark(tt)
744.30/263.06	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.06	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.06	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.06	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.06	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.06	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.06	   U16(active(X)) -> U16(X)
744.30/263.06	   U16(mark(X)) -> U16(X)
744.30/263.06	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.06	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.06	   U23(active(X)) -> U23(X)
744.30/263.06	   U23(mark(X)) -> U23(X)
744.30/263.06	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.06	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.06	   U36(active(X)) -> U36(X)
744.30/263.06	   U36(mark(X)) -> U36(X)
744.30/263.06	   U42(active(X)) -> U42(X)
744.30/263.06	   U42(mark(X)) -> U42(X)
744.30/263.06	   U62(active(X)) -> U62(X)
744.30/263.06	   U62(mark(X)) -> U62(X)
744.30/263.06	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.06	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.06	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.06	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.06	   s(active(X)) -> s(X)
744.30/263.06	   s(mark(X)) -> s(X)
744.30/263.06	   U92(active(X)) -> U92(X)
744.30/263.06	   U92(mark(X)) -> U92(X)
744.30/263.06	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.06	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.06	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.06	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.06	   U51(active(X)) -> U51(X)
744.30/263.06	   U51(mark(X)) -> U51(X)
744.30/263.06	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.06	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.06	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.06	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.06	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.06	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.06	   x(active(X1), X2) -> x(X1, X2)
744.30/263.06	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.06	
744.30/263.06	The set Q consists of the following terms:
744.30/263.06	
744.30/263.06	   active(U101(tt, x0, x1))
744.30/263.06	   active(U102(tt, x0, x1))
744.30/263.06	   active(U103(tt, x0, x1))
744.30/263.06	   active(U104(tt, x0, x1))
744.30/263.06	   active(U11(tt, x0, x1))
744.30/263.06	   active(U12(tt, x0, x1))
744.30/263.06	   active(U13(tt, x0, x1))
744.30/263.06	   active(U14(tt, x0, x1))
744.30/263.06	   active(U15(tt, x0))
744.30/263.06	   active(U16(tt))
744.30/263.06	   active(U21(tt, x0))
744.30/263.06	   active(U22(tt, x0))
744.30/263.06	   active(U23(tt))
744.30/263.06	   active(U31(tt, x0, x1))
744.30/263.06	   active(U32(tt, x0, x1))
744.30/263.06	   active(U33(tt, x0, x1))
744.30/263.06	   active(U34(tt, x0, x1))
744.30/263.06	   active(U35(tt, x0))
744.30/263.06	   active(U36(tt))
744.30/263.06	   active(U41(tt, x0))
744.30/263.06	   active(U42(tt))
744.30/263.06	   active(U51(tt))
744.30/263.06	   active(U61(tt, x0))
744.30/263.06	   active(U62(tt))
744.30/263.06	   active(U71(tt, x0))
744.30/263.06	   active(U72(tt, x0))
744.30/263.06	   active(U81(tt, x0, x1))
744.30/263.06	   active(U82(tt, x0, x1))
744.30/263.06	   active(U83(tt, x0, x1))
744.30/263.06	   active(U84(tt, x0, x1))
744.30/263.06	   active(U91(tt, x0))
744.30/263.06	   active(U92(tt))
744.30/263.06	   active(isNat(0))
744.30/263.06	   active(isNat(plus(x0, x1)))
744.30/263.06	   active(isNat(s(x0)))
744.30/263.06	   active(isNat(x(x0, x1)))
744.30/263.06	   active(isNatKind(0))
744.30/263.06	   active(isNatKind(plus(x0, x1)))
744.30/263.06	   active(isNatKind(s(x0)))
744.30/263.06	   active(isNatKind(x(x0, x1)))
744.30/263.06	   active(plus(x0, 0))
744.30/263.06	   active(plus(x0, s(x1)))
744.30/263.06	   active(x(x0, 0))
744.30/263.06	   active(x(x0, s(x1)))
744.30/263.06	   mark(U101(x0, x1, x2))
744.30/263.06	   mark(tt)
744.30/263.06	   mark(U102(x0, x1, x2))
744.30/263.06	   mark(isNatKind(x0))
744.30/263.06	   mark(U103(x0, x1, x2))
744.30/263.06	   mark(isNat(x0))
744.30/263.06	   mark(U104(x0, x1, x2))
744.30/263.06	   mark(plus(x0, x1))
744.30/263.06	   mark(x(x0, x1))
744.30/263.06	   mark(U11(x0, x1, x2))
744.30/263.06	   mark(U12(x0, x1, x2))
744.30/263.06	   mark(U13(x0, x1, x2))
744.30/263.06	   mark(U14(x0, x1, x2))
744.30/263.06	   mark(U15(x0, x1))
744.30/263.06	   mark(U16(x0))
744.30/263.06	   mark(U21(x0, x1))
744.30/263.06	   mark(U22(x0, x1))
744.30/263.06	   mark(U23(x0))
744.30/263.06	   mark(U31(x0, x1, x2))
744.30/263.06	   mark(U32(x0, x1, x2))
744.30/263.06	   mark(U33(x0, x1, x2))
744.30/263.06	   mark(U34(x0, x1, x2))
744.30/263.06	   mark(U35(x0, x1))
744.30/263.06	   mark(U36(x0))
744.30/263.06	   mark(U41(x0, x1))
744.30/263.06	   mark(U42(x0))
744.30/263.06	   mark(U51(x0))
744.30/263.06	   mark(U61(x0, x1))
744.30/263.06	   mark(U62(x0))
744.30/263.06	   mark(U71(x0, x1))
744.30/263.06	   mark(U72(x0, x1))
744.30/263.06	   mark(U81(x0, x1, x2))
744.30/263.06	   mark(U82(x0, x1, x2))
744.30/263.06	   mark(U83(x0, x1, x2))
744.30/263.06	   mark(U84(x0, x1, x2))
744.30/263.06	   mark(s(x0))
744.30/263.06	   mark(U91(x0, x1))
744.30/263.06	   mark(U92(x0))
744.30/263.06	   mark(0)
744.30/263.06	   U101(mark(x0), x1, x2)
744.30/263.06	   U101(x0, mark(x1), x2)
744.30/263.06	   U101(x0, x1, mark(x2))
744.30/263.06	   U101(active(x0), x1, x2)
744.30/263.06	   U101(x0, active(x1), x2)
744.30/263.06	   U101(x0, x1, active(x2))
744.30/263.06	   U102(mark(x0), x1, x2)
744.30/263.06	   U102(x0, mark(x1), x2)
744.30/263.06	   U102(x0, x1, mark(x2))
744.30/263.06	   U102(active(x0), x1, x2)
744.30/263.06	   U102(x0, active(x1), x2)
744.30/263.06	   U102(x0, x1, active(x2))
744.30/263.06	   isNatKind(mark(x0))
744.30/263.06	   isNatKind(active(x0))
744.30/263.06	   U103(mark(x0), x1, x2)
744.30/263.06	   U103(x0, mark(x1), x2)
744.30/263.06	   U103(x0, x1, mark(x2))
744.30/263.06	   U103(active(x0), x1, x2)
744.30/263.06	   U103(x0, active(x1), x2)
744.30/263.06	   U103(x0, x1, active(x2))
744.30/263.06	   isNat(mark(x0))
744.30/263.06	   isNat(active(x0))
744.30/263.06	   U104(mark(x0), x1, x2)
744.30/263.06	   U104(x0, mark(x1), x2)
744.30/263.06	   U104(x0, x1, mark(x2))
744.30/263.06	   U104(active(x0), x1, x2)
744.30/263.06	   U104(x0, active(x1), x2)
744.30/263.06	   U104(x0, x1, active(x2))
744.30/263.06	   plus(mark(x0), x1)
744.30/263.06	   plus(x0, mark(x1))
744.30/263.06	   plus(active(x0), x1)
744.30/263.06	   plus(x0, active(x1))
744.30/263.06	   x(mark(x0), x1)
744.30/263.06	   x(x0, mark(x1))
744.30/263.06	   x(active(x0), x1)
744.30/263.06	   x(x0, active(x1))
744.30/263.06	   U11(mark(x0), x1, x2)
744.30/263.06	   U11(x0, mark(x1), x2)
744.30/263.06	   U11(x0, x1, mark(x2))
744.30/263.06	   U11(active(x0), x1, x2)
744.30/263.06	   U11(x0, active(x1), x2)
744.30/263.06	   U11(x0, x1, active(x2))
744.30/263.06	   U12(mark(x0), x1, x2)
744.30/263.06	   U12(x0, mark(x1), x2)
744.30/263.06	   U12(x0, x1, mark(x2))
744.30/263.06	   U12(active(x0), x1, x2)
744.30/263.06	   U12(x0, active(x1), x2)
744.30/263.06	   U12(x0, x1, active(x2))
744.30/263.06	   U13(mark(x0), x1, x2)
744.30/263.06	   U13(x0, mark(x1), x2)
744.30/263.06	   U13(x0, x1, mark(x2))
744.30/263.06	   U13(active(x0), x1, x2)
744.30/263.06	   U13(x0, active(x1), x2)
744.30/263.06	   U13(x0, x1, active(x2))
744.30/263.06	   U14(mark(x0), x1, x2)
744.30/263.06	   U14(x0, mark(x1), x2)
744.30/263.06	   U14(x0, x1, mark(x2))
744.30/263.06	   U14(active(x0), x1, x2)
744.30/263.06	   U14(x0, active(x1), x2)
744.30/263.06	   U14(x0, x1, active(x2))
744.30/263.06	   U15(mark(x0), x1)
744.30/263.06	   U15(x0, mark(x1))
744.30/263.06	   U15(active(x0), x1)
744.30/263.06	   U15(x0, active(x1))
744.30/263.06	   U16(mark(x0))
744.30/263.06	   U16(active(x0))
744.30/263.06	   U21(mark(x0), x1)
744.30/263.06	   U21(x0, mark(x1))
744.30/263.06	   U21(active(x0), x1)
744.30/263.06	   U21(x0, active(x1))
744.30/263.06	   U22(mark(x0), x1)
744.30/263.06	   U22(x0, mark(x1))
744.30/263.06	   U22(active(x0), x1)
744.30/263.06	   U22(x0, active(x1))
744.30/263.06	   U23(mark(x0))
744.30/263.06	   U23(active(x0))
744.30/263.06	   U31(mark(x0), x1, x2)
744.30/263.06	   U31(x0, mark(x1), x2)
744.30/263.06	   U31(x0, x1, mark(x2))
744.30/263.06	   U31(active(x0), x1, x2)
744.30/263.06	   U31(x0, active(x1), x2)
744.30/263.06	   U31(x0, x1, active(x2))
744.30/263.06	   U32(mark(x0), x1, x2)
744.30/263.06	   U32(x0, mark(x1), x2)
744.30/263.06	   U32(x0, x1, mark(x2))
744.30/263.06	   U32(active(x0), x1, x2)
744.30/263.06	   U32(x0, active(x1), x2)
744.30/263.06	   U32(x0, x1, active(x2))
744.30/263.06	   U33(mark(x0), x1, x2)
744.30/263.06	   U33(x0, mark(x1), x2)
744.30/263.06	   U33(x0, x1, mark(x2))
744.30/263.06	   U33(active(x0), x1, x2)
744.30/263.06	   U33(x0, active(x1), x2)
744.30/263.06	   U33(x0, x1, active(x2))
744.30/263.06	   U34(mark(x0), x1, x2)
744.30/263.06	   U34(x0, mark(x1), x2)
744.30/263.06	   U34(x0, x1, mark(x2))
744.30/263.06	   U34(active(x0), x1, x2)
744.30/263.06	   U34(x0, active(x1), x2)
744.30/263.06	   U34(x0, x1, active(x2))
744.30/263.06	   U35(mark(x0), x1)
744.30/263.06	   U35(x0, mark(x1))
744.30/263.06	   U35(active(x0), x1)
744.30/263.06	   U35(x0, active(x1))
744.30/263.06	   U36(mark(x0))
744.30/263.06	   U36(active(x0))
744.30/263.06	   U41(mark(x0), x1)
744.30/263.06	   U41(x0, mark(x1))
744.30/263.06	   U41(active(x0), x1)
744.30/263.06	   U41(x0, active(x1))
744.30/263.06	   U42(mark(x0))
744.30/263.06	   U42(active(x0))
744.30/263.06	   U51(mark(x0))
744.30/263.06	   U51(active(x0))
744.30/263.06	   U61(mark(x0), x1)
744.30/263.06	   U61(x0, mark(x1))
744.30/263.06	   U61(active(x0), x1)
744.30/263.06	   U61(x0, active(x1))
744.30/263.06	   U62(mark(x0))
744.30/263.06	   U62(active(x0))
744.30/263.06	   U71(mark(x0), x1)
744.30/263.06	   U71(x0, mark(x1))
744.30/263.06	   U71(active(x0), x1)
744.30/263.06	   U71(x0, active(x1))
744.30/263.06	   U72(mark(x0), x1)
744.30/263.06	   U72(x0, mark(x1))
744.30/263.06	   U72(active(x0), x1)
744.30/263.06	   U72(x0, active(x1))
744.30/263.06	   U81(mark(x0), x1, x2)
744.30/263.06	   U81(x0, mark(x1), x2)
744.30/263.06	   U81(x0, x1, mark(x2))
744.30/263.06	   U81(active(x0), x1, x2)
744.30/263.06	   U81(x0, active(x1), x2)
744.30/263.06	   U81(x0, x1, active(x2))
744.30/263.06	   U82(mark(x0), x1, x2)
744.30/263.06	   U82(x0, mark(x1), x2)
744.30/263.06	   U82(x0, x1, mark(x2))
744.30/263.06	   U82(active(x0), x1, x2)
744.30/263.06	   U82(x0, active(x1), x2)
744.30/263.06	   U82(x0, x1, active(x2))
744.30/263.06	   U83(mark(x0), x1, x2)
744.30/263.06	   U83(x0, mark(x1), x2)
744.30/263.06	   U83(x0, x1, mark(x2))
744.30/263.06	   U83(active(x0), x1, x2)
744.30/263.06	   U83(x0, active(x1), x2)
744.30/263.06	   U83(x0, x1, active(x2))
744.30/263.06	   U84(mark(x0), x1, x2)
744.30/263.06	   U84(x0, mark(x1), x2)
744.30/263.06	   U84(x0, x1, mark(x2))
744.30/263.06	   U84(active(x0), x1, x2)
744.30/263.06	   U84(x0, active(x1), x2)
744.30/263.06	   U84(x0, x1, active(x2))
744.30/263.06	   s(mark(x0))
744.30/263.06	   s(active(x0))
744.30/263.06	   U91(mark(x0), x1)
744.30/263.06	   U91(x0, mark(x1))
744.30/263.06	   U91(active(x0), x1)
744.30/263.06	   U91(x0, active(x1))
744.30/263.06	   U92(mark(x0))
744.30/263.06	   U92(active(x0))
744.30/263.06	
744.30/263.06	We have to consider all minimal (P,Q,R)-chains.
744.30/263.06	----------------------------------------
744.30/263.06	
744.30/263.06	(313) QDPOrderProof (EQUIVALENT)
744.30/263.06	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.06	
744.30/263.06	
744.30/263.06	The following pairs can be oriented strictly and are deleted.
744.30/263.06	
744.30/263.06	   MARK(U13(X1, X2, X3)) -> MARK(X1)
744.30/263.06	The remaining pairs can at least be oriented weakly.
744.30/263.06	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U12(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U11(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(tt) =  	[[0A]]
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U13(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U14(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U15(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(isNat(x_1)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U21(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U22(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U31(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U33(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U34(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(s(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U103(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U81(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U91(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(0) =  	[[0A]]
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	
744.30/263.06	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.06	
744.30/263.06	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.06	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.06	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.06	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.06	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.06	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.06	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.06	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.06	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.06	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.06	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.06	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.06	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.06	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.06	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.06	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.06	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.06	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.06	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.06	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.06	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.06	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.06	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.06	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.06	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.06	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.06	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.06	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.06	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.06	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.06	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.06	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.06	   active(U72(tt, N)) -> mark(N)
744.30/263.06	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.06	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.06	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.06	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.06	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.06	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.06	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.06	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.06	   mark(s(X)) -> active(s(mark(X)))
744.30/263.06	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.06	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.06	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.06	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.06	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.06	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.06	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.06	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.06	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.06	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.06	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.06	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.06	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.06	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.06	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.06	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.06	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.06	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.06	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.06	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.06	   mark(isNat(X)) -> active(isNat(X))
744.30/263.06	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.06	   mark(tt) -> active(tt)
744.30/263.06	   mark(0) -> active(0)
744.30/263.06	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.06	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.06	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.06	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.06	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.06	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.06	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.06	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.06	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.06	   active(U16(tt)) -> mark(tt)
744.30/263.06	   active(U23(tt)) -> mark(tt)
744.30/263.06	   active(U36(tt)) -> mark(tt)
744.30/263.06	   active(U42(tt)) -> mark(tt)
744.30/263.06	   active(U51(tt)) -> mark(tt)
744.30/263.06	   active(U62(tt)) -> mark(tt)
744.30/263.06	   active(U92(tt)) -> mark(0)
744.30/263.06	   active(isNat(0)) -> mark(tt)
744.30/263.06	   active(isNatKind(0)) -> mark(tt)
744.30/263.06	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.06	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.06	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.06	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.06	   U16(active(X)) -> U16(X)
744.30/263.06	   U16(mark(X)) -> U16(X)
744.30/263.06	   U23(active(X)) -> U23(X)
744.30/263.06	   U23(mark(X)) -> U23(X)
744.30/263.06	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.06	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.06	   U36(active(X)) -> U36(X)
744.30/263.06	   U36(mark(X)) -> U36(X)
744.30/263.06	   U42(active(X)) -> U42(X)
744.30/263.06	   U42(mark(X)) -> U42(X)
744.30/263.06	   U62(active(X)) -> U62(X)
744.30/263.06	   U62(mark(X)) -> U62(X)
744.30/263.06	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.06	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.06	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.06	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.06	   s(active(X)) -> s(X)
744.30/263.06	   s(mark(X)) -> s(X)
744.30/263.06	   U92(active(X)) -> U92(X)
744.30/263.06	   U92(mark(X)) -> U92(X)
744.30/263.06	   U51(active(X)) -> U51(X)
744.30/263.06	   U51(mark(X)) -> U51(X)
744.30/263.06	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.06	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.06	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.06	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.06	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.06	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.06	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.06	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.06	   x(active(X1), X2) -> x(X1, X2)
744.30/263.06	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.06	
744.30/263.06	
744.30/263.06	----------------------------------------
744.30/263.06	
744.30/263.06	(314)
744.30/263.06	Obligation:
744.30/263.06	Q DP problem:
744.30/263.06	The TRS P consists of the following rules:
744.30/263.06	
744.30/263.06	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.06	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.06	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.06	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.06	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.06	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.06	   MARK(U16(X)) -> MARK(X)
744.30/263.06	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.06	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.06	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.06	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.06	   MARK(U23(X)) -> MARK(X)
744.30/263.06	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.06	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.06	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.06	   MARK(U42(X)) -> MARK(X)
744.30/263.06	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U51(X)) -> MARK(X)
744.30/263.06	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.06	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.06	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.06	
744.30/263.06	The TRS R consists of the following rules:
744.30/263.06	
744.30/263.06	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.06	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.06	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.06	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.06	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.06	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.06	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.06	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.06	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.06	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.06	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.06	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.06	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.06	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.06	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.06	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.06	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.06	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.06	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.06	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.06	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.06	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.06	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.06	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.06	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.06	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.06	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.06	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.06	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.06	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.06	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.06	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.06	   active(U72(tt, N)) -> mark(N)
744.30/263.06	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.06	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.06	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.06	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.06	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.06	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.06	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.06	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.06	   mark(s(X)) -> active(s(mark(X)))
744.30/263.06	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.06	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.06	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.06	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.06	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.06	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.06	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.06	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.06	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.06	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.06	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.06	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.06	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.06	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.06	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.06	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.06	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.06	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.06	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.06	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.06	   mark(isNat(X)) -> active(isNat(X))
744.30/263.06	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.06	   mark(tt) -> active(tt)
744.30/263.06	   mark(0) -> active(0)
744.30/263.06	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.06	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.06	   active(U16(tt)) -> mark(tt)
744.30/263.06	   active(U23(tt)) -> mark(tt)
744.30/263.06	   active(U36(tt)) -> mark(tt)
744.30/263.06	   active(U42(tt)) -> mark(tt)
744.30/263.06	   active(U51(tt)) -> mark(tt)
744.30/263.06	   active(U62(tt)) -> mark(tt)
744.30/263.06	   active(U92(tt)) -> mark(0)
744.30/263.06	   active(isNat(0)) -> mark(tt)
744.30/263.06	   active(isNatKind(0)) -> mark(tt)
744.30/263.06	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.06	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.06	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.06	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.06	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.06	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.06	   U16(active(X)) -> U16(X)
744.30/263.06	   U16(mark(X)) -> U16(X)
744.30/263.06	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.06	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.06	   U23(active(X)) -> U23(X)
744.30/263.06	   U23(mark(X)) -> U23(X)
744.30/263.06	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.06	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.06	   U36(active(X)) -> U36(X)
744.30/263.06	   U36(mark(X)) -> U36(X)
744.30/263.06	   U42(active(X)) -> U42(X)
744.30/263.06	   U42(mark(X)) -> U42(X)
744.30/263.06	   U62(active(X)) -> U62(X)
744.30/263.06	   U62(mark(X)) -> U62(X)
744.30/263.06	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.06	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.06	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.06	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.06	   s(active(X)) -> s(X)
744.30/263.06	   s(mark(X)) -> s(X)
744.30/263.06	   U92(active(X)) -> U92(X)
744.30/263.06	   U92(mark(X)) -> U92(X)
744.30/263.06	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.06	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.06	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.06	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.06	   U51(active(X)) -> U51(X)
744.30/263.06	   U51(mark(X)) -> U51(X)
744.30/263.06	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.06	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.06	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.06	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.06	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.06	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.06	   x(active(X1), X2) -> x(X1, X2)
744.30/263.06	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.06	
744.30/263.06	The set Q consists of the following terms:
744.30/263.06	
744.30/263.06	   active(U101(tt, x0, x1))
744.30/263.06	   active(U102(tt, x0, x1))
744.30/263.06	   active(U103(tt, x0, x1))
744.30/263.06	   active(U104(tt, x0, x1))
744.30/263.06	   active(U11(tt, x0, x1))
744.30/263.06	   active(U12(tt, x0, x1))
744.30/263.06	   active(U13(tt, x0, x1))
744.30/263.06	   active(U14(tt, x0, x1))
744.30/263.06	   active(U15(tt, x0))
744.30/263.06	   active(U16(tt))
744.30/263.06	   active(U21(tt, x0))
744.30/263.06	   active(U22(tt, x0))
744.30/263.06	   active(U23(tt))
744.30/263.06	   active(U31(tt, x0, x1))
744.30/263.06	   active(U32(tt, x0, x1))
744.30/263.06	   active(U33(tt, x0, x1))
744.30/263.06	   active(U34(tt, x0, x1))
744.30/263.06	   active(U35(tt, x0))
744.30/263.06	   active(U36(tt))
744.30/263.06	   active(U41(tt, x0))
744.30/263.06	   active(U42(tt))
744.30/263.06	   active(U51(tt))
744.30/263.06	   active(U61(tt, x0))
744.30/263.06	   active(U62(tt))
744.30/263.06	   active(U71(tt, x0))
744.30/263.06	   active(U72(tt, x0))
744.30/263.06	   active(U81(tt, x0, x1))
744.30/263.06	   active(U82(tt, x0, x1))
744.30/263.06	   active(U83(tt, x0, x1))
744.30/263.06	   active(U84(tt, x0, x1))
744.30/263.06	   active(U91(tt, x0))
744.30/263.06	   active(U92(tt))
744.30/263.06	   active(isNat(0))
744.30/263.06	   active(isNat(plus(x0, x1)))
744.30/263.06	   active(isNat(s(x0)))
744.30/263.06	   active(isNat(x(x0, x1)))
744.30/263.06	   active(isNatKind(0))
744.30/263.06	   active(isNatKind(plus(x0, x1)))
744.30/263.06	   active(isNatKind(s(x0)))
744.30/263.06	   active(isNatKind(x(x0, x1)))
744.30/263.06	   active(plus(x0, 0))
744.30/263.06	   active(plus(x0, s(x1)))
744.30/263.06	   active(x(x0, 0))
744.30/263.06	   active(x(x0, s(x1)))
744.30/263.06	   mark(U101(x0, x1, x2))
744.30/263.06	   mark(tt)
744.30/263.06	   mark(U102(x0, x1, x2))
744.30/263.06	   mark(isNatKind(x0))
744.30/263.06	   mark(U103(x0, x1, x2))
744.30/263.06	   mark(isNat(x0))
744.30/263.06	   mark(U104(x0, x1, x2))
744.30/263.06	   mark(plus(x0, x1))
744.30/263.06	   mark(x(x0, x1))
744.30/263.06	   mark(U11(x0, x1, x2))
744.30/263.06	   mark(U12(x0, x1, x2))
744.30/263.06	   mark(U13(x0, x1, x2))
744.30/263.06	   mark(U14(x0, x1, x2))
744.30/263.06	   mark(U15(x0, x1))
744.30/263.06	   mark(U16(x0))
744.30/263.06	   mark(U21(x0, x1))
744.30/263.06	   mark(U22(x0, x1))
744.30/263.06	   mark(U23(x0))
744.30/263.06	   mark(U31(x0, x1, x2))
744.30/263.06	   mark(U32(x0, x1, x2))
744.30/263.06	   mark(U33(x0, x1, x2))
744.30/263.06	   mark(U34(x0, x1, x2))
744.30/263.06	   mark(U35(x0, x1))
744.30/263.06	   mark(U36(x0))
744.30/263.06	   mark(U41(x0, x1))
744.30/263.06	   mark(U42(x0))
744.30/263.06	   mark(U51(x0))
744.30/263.06	   mark(U61(x0, x1))
744.30/263.06	   mark(U62(x0))
744.30/263.06	   mark(U71(x0, x1))
744.30/263.06	   mark(U72(x0, x1))
744.30/263.06	   mark(U81(x0, x1, x2))
744.30/263.06	   mark(U82(x0, x1, x2))
744.30/263.06	   mark(U83(x0, x1, x2))
744.30/263.06	   mark(U84(x0, x1, x2))
744.30/263.06	   mark(s(x0))
744.30/263.06	   mark(U91(x0, x1))
744.30/263.06	   mark(U92(x0))
744.30/263.06	   mark(0)
744.30/263.06	   U101(mark(x0), x1, x2)
744.30/263.06	   U101(x0, mark(x1), x2)
744.30/263.06	   U101(x0, x1, mark(x2))
744.30/263.06	   U101(active(x0), x1, x2)
744.30/263.06	   U101(x0, active(x1), x2)
744.30/263.06	   U101(x0, x1, active(x2))
744.30/263.06	   U102(mark(x0), x1, x2)
744.30/263.06	   U102(x0, mark(x1), x2)
744.30/263.06	   U102(x0, x1, mark(x2))
744.30/263.06	   U102(active(x0), x1, x2)
744.30/263.06	   U102(x0, active(x1), x2)
744.30/263.06	   U102(x0, x1, active(x2))
744.30/263.06	   isNatKind(mark(x0))
744.30/263.06	   isNatKind(active(x0))
744.30/263.06	   U103(mark(x0), x1, x2)
744.30/263.06	   U103(x0, mark(x1), x2)
744.30/263.06	   U103(x0, x1, mark(x2))
744.30/263.06	   U103(active(x0), x1, x2)
744.30/263.06	   U103(x0, active(x1), x2)
744.30/263.06	   U103(x0, x1, active(x2))
744.30/263.06	   isNat(mark(x0))
744.30/263.06	   isNat(active(x0))
744.30/263.06	   U104(mark(x0), x1, x2)
744.30/263.06	   U104(x0, mark(x1), x2)
744.30/263.06	   U104(x0, x1, mark(x2))
744.30/263.06	   U104(active(x0), x1, x2)
744.30/263.06	   U104(x0, active(x1), x2)
744.30/263.06	   U104(x0, x1, active(x2))
744.30/263.06	   plus(mark(x0), x1)
744.30/263.06	   plus(x0, mark(x1))
744.30/263.06	   plus(active(x0), x1)
744.30/263.06	   plus(x0, active(x1))
744.30/263.06	   x(mark(x0), x1)
744.30/263.06	   x(x0, mark(x1))
744.30/263.06	   x(active(x0), x1)
744.30/263.06	   x(x0, active(x1))
744.30/263.06	   U11(mark(x0), x1, x2)
744.30/263.06	   U11(x0, mark(x1), x2)
744.30/263.06	   U11(x0, x1, mark(x2))
744.30/263.06	   U11(active(x0), x1, x2)
744.30/263.06	   U11(x0, active(x1), x2)
744.30/263.06	   U11(x0, x1, active(x2))
744.30/263.06	   U12(mark(x0), x1, x2)
744.30/263.06	   U12(x0, mark(x1), x2)
744.30/263.06	   U12(x0, x1, mark(x2))
744.30/263.06	   U12(active(x0), x1, x2)
744.30/263.06	   U12(x0, active(x1), x2)
744.30/263.06	   U12(x0, x1, active(x2))
744.30/263.06	   U13(mark(x0), x1, x2)
744.30/263.06	   U13(x0, mark(x1), x2)
744.30/263.06	   U13(x0, x1, mark(x2))
744.30/263.06	   U13(active(x0), x1, x2)
744.30/263.06	   U13(x0, active(x1), x2)
744.30/263.06	   U13(x0, x1, active(x2))
744.30/263.06	   U14(mark(x0), x1, x2)
744.30/263.06	   U14(x0, mark(x1), x2)
744.30/263.06	   U14(x0, x1, mark(x2))
744.30/263.06	   U14(active(x0), x1, x2)
744.30/263.06	   U14(x0, active(x1), x2)
744.30/263.06	   U14(x0, x1, active(x2))
744.30/263.06	   U15(mark(x0), x1)
744.30/263.06	   U15(x0, mark(x1))
744.30/263.06	   U15(active(x0), x1)
744.30/263.06	   U15(x0, active(x1))
744.30/263.06	   U16(mark(x0))
744.30/263.06	   U16(active(x0))
744.30/263.06	   U21(mark(x0), x1)
744.30/263.06	   U21(x0, mark(x1))
744.30/263.06	   U21(active(x0), x1)
744.30/263.06	   U21(x0, active(x1))
744.30/263.06	   U22(mark(x0), x1)
744.30/263.06	   U22(x0, mark(x1))
744.30/263.06	   U22(active(x0), x1)
744.30/263.06	   U22(x0, active(x1))
744.30/263.06	   U23(mark(x0))
744.30/263.06	   U23(active(x0))
744.30/263.06	   U31(mark(x0), x1, x2)
744.30/263.06	   U31(x0, mark(x1), x2)
744.30/263.06	   U31(x0, x1, mark(x2))
744.30/263.06	   U31(active(x0), x1, x2)
744.30/263.06	   U31(x0, active(x1), x2)
744.30/263.06	   U31(x0, x1, active(x2))
744.30/263.06	   U32(mark(x0), x1, x2)
744.30/263.06	   U32(x0, mark(x1), x2)
744.30/263.06	   U32(x0, x1, mark(x2))
744.30/263.06	   U32(active(x0), x1, x2)
744.30/263.06	   U32(x0, active(x1), x2)
744.30/263.06	   U32(x0, x1, active(x2))
744.30/263.06	   U33(mark(x0), x1, x2)
744.30/263.06	   U33(x0, mark(x1), x2)
744.30/263.06	   U33(x0, x1, mark(x2))
744.30/263.06	   U33(active(x0), x1, x2)
744.30/263.06	   U33(x0, active(x1), x2)
744.30/263.06	   U33(x0, x1, active(x2))
744.30/263.06	   U34(mark(x0), x1, x2)
744.30/263.06	   U34(x0, mark(x1), x2)
744.30/263.06	   U34(x0, x1, mark(x2))
744.30/263.06	   U34(active(x0), x1, x2)
744.30/263.06	   U34(x0, active(x1), x2)
744.30/263.06	   U34(x0, x1, active(x2))
744.30/263.06	   U35(mark(x0), x1)
744.30/263.06	   U35(x0, mark(x1))
744.30/263.06	   U35(active(x0), x1)
744.30/263.06	   U35(x0, active(x1))
744.30/263.06	   U36(mark(x0))
744.30/263.06	   U36(active(x0))
744.30/263.06	   U41(mark(x0), x1)
744.30/263.06	   U41(x0, mark(x1))
744.30/263.06	   U41(active(x0), x1)
744.30/263.06	   U41(x0, active(x1))
744.30/263.06	   U42(mark(x0))
744.30/263.06	   U42(active(x0))
744.30/263.06	   U51(mark(x0))
744.30/263.06	   U51(active(x0))
744.30/263.06	   U61(mark(x0), x1)
744.30/263.06	   U61(x0, mark(x1))
744.30/263.06	   U61(active(x0), x1)
744.30/263.06	   U61(x0, active(x1))
744.30/263.06	   U62(mark(x0))
744.30/263.06	   U62(active(x0))
744.30/263.06	   U71(mark(x0), x1)
744.30/263.06	   U71(x0, mark(x1))
744.30/263.06	   U71(active(x0), x1)
744.30/263.06	   U71(x0, active(x1))
744.30/263.06	   U72(mark(x0), x1)
744.30/263.06	   U72(x0, mark(x1))
744.30/263.06	   U72(active(x0), x1)
744.30/263.06	   U72(x0, active(x1))
744.30/263.06	   U81(mark(x0), x1, x2)
744.30/263.06	   U81(x0, mark(x1), x2)
744.30/263.06	   U81(x0, x1, mark(x2))
744.30/263.06	   U81(active(x0), x1, x2)
744.30/263.06	   U81(x0, active(x1), x2)
744.30/263.06	   U81(x0, x1, active(x2))
744.30/263.06	   U82(mark(x0), x1, x2)
744.30/263.06	   U82(x0, mark(x1), x2)
744.30/263.06	   U82(x0, x1, mark(x2))
744.30/263.06	   U82(active(x0), x1, x2)
744.30/263.06	   U82(x0, active(x1), x2)
744.30/263.06	   U82(x0, x1, active(x2))
744.30/263.06	   U83(mark(x0), x1, x2)
744.30/263.06	   U83(x0, mark(x1), x2)
744.30/263.06	   U83(x0, x1, mark(x2))
744.30/263.06	   U83(active(x0), x1, x2)
744.30/263.06	   U83(x0, active(x1), x2)
744.30/263.06	   U83(x0, x1, active(x2))
744.30/263.06	   U84(mark(x0), x1, x2)
744.30/263.06	   U84(x0, mark(x1), x2)
744.30/263.06	   U84(x0, x1, mark(x2))
744.30/263.06	   U84(active(x0), x1, x2)
744.30/263.06	   U84(x0, active(x1), x2)
744.30/263.06	   U84(x0, x1, active(x2))
744.30/263.06	   s(mark(x0))
744.30/263.06	   s(active(x0))
744.30/263.06	   U91(mark(x0), x1)
744.30/263.06	   U91(x0, mark(x1))
744.30/263.06	   U91(active(x0), x1)
744.30/263.06	   U91(x0, active(x1))
744.30/263.06	   U92(mark(x0))
744.30/263.06	   U92(active(x0))
744.30/263.06	
744.30/263.06	We have to consider all minimal (P,Q,R)-chains.
744.30/263.06	----------------------------------------
744.30/263.06	
744.30/263.06	(315) QDPOrderProof (EQUIVALENT)
744.30/263.06	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.06	
744.30/263.06	
744.30/263.06	The following pairs can be oriented strictly and are deleted.
744.30/263.06	
744.30/263.06	   MARK(U12(X1, X2, X3)) -> MARK(X1)
744.30/263.06	The remaining pairs can at least be oriented weakly.
744.30/263.06	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U12(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U11(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(tt) =  	[[0A]]
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(plus(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U21(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U31(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U101(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	   <<<
744.30/263.06	 POL(0) =  	[[0A]]
744.30/263.06	>>>
744.30/263.06	
744.30/263.06	
744.30/263.06	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.06	
744.30/263.06	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.06	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.06	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.06	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.06	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.06	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.06	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.06	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.06	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.06	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.06	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.06	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.06	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.06	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.06	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.06	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.06	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.06	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.06	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.06	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.06	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.06	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.06	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.06	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.06	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.06	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.06	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.06	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.06	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.06	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.06	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.06	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.06	   active(U72(tt, N)) -> mark(N)
744.30/263.06	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.06	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.06	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.06	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.06	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.06	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.06	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.06	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.06	   mark(s(X)) -> active(s(mark(X)))
744.30/263.06	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.06	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.06	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.06	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.06	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.06	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.06	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.06	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.06	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.06	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.06	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.06	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.06	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.06	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.06	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.06	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.06	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.06	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.06	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.06	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.06	   mark(isNat(X)) -> active(isNat(X))
744.30/263.06	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.06	   mark(tt) -> active(tt)
744.30/263.06	   mark(0) -> active(0)
744.30/263.06	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.06	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.06	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.06	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.06	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.06	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.06	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.06	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.06	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.06	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.06	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.06	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.06	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.06	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.06	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.06	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.06	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.06	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.06	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.06	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.06	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.06	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.06	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.06	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.06	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.06	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.06	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.06	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.06	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.06	   active(U16(tt)) -> mark(tt)
744.30/263.06	   active(U23(tt)) -> mark(tt)
744.30/263.06	   active(U36(tt)) -> mark(tt)
744.30/263.06	   active(U42(tt)) -> mark(tt)
744.30/263.06	   active(U51(tt)) -> mark(tt)
744.30/263.06	   active(U62(tt)) -> mark(tt)
744.30/263.06	   active(U92(tt)) -> mark(0)
744.30/263.06	   active(isNat(0)) -> mark(tt)
744.30/263.06	   active(isNatKind(0)) -> mark(tt)
744.30/263.06	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.06	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.06	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.06	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.06	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.06	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.06	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.06	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.06	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.06	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.06	   U16(active(X)) -> U16(X)
744.30/263.06	   U16(mark(X)) -> U16(X)
744.30/263.06	   U23(active(X)) -> U23(X)
744.30/263.06	   U23(mark(X)) -> U23(X)
744.30/263.06	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.06	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.06	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.06	   U36(active(X)) -> U36(X)
744.30/263.06	   U36(mark(X)) -> U36(X)
744.30/263.06	   U42(active(X)) -> U42(X)
744.30/263.06	   U42(mark(X)) -> U42(X)
744.30/263.06	   U62(active(X)) -> U62(X)
744.30/263.06	   U62(mark(X)) -> U62(X)
744.30/263.06	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.06	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.06	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.06	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.06	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.06	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.06	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.06	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.06	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.06	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.06	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.06	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.06	   s(active(X)) -> s(X)
744.30/263.06	   s(mark(X)) -> s(X)
744.30/263.06	   U92(active(X)) -> U92(X)
744.30/263.06	   U92(mark(X)) -> U92(X)
744.30/263.06	   U51(active(X)) -> U51(X)
744.30/263.06	   U51(mark(X)) -> U51(X)
744.30/263.06	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.06	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.06	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.06	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.06	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.06	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.06	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.06	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.06	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.06	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.06	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.06	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.06	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.06	   x(active(X1), X2) -> x(X1, X2)
744.30/263.06	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.06	
744.30/263.06	
744.30/263.06	----------------------------------------
744.30/263.06	
744.30/263.06	(316)
744.30/263.06	Obligation:
744.30/263.06	Q DP problem:
744.30/263.06	The TRS P consists of the following rules:
744.30/263.06	
744.30/263.06	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.06	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.06	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.06	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.06	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.06	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.06	   MARK(U16(X)) -> MARK(X)
744.30/263.06	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.06	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.06	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.06	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.06	   MARK(U23(X)) -> MARK(X)
744.30/263.06	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.06	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.06	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.06	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.06	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.06	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.06	   MARK(U42(X)) -> MARK(X)
744.30/263.06	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.06	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.06	   MARK(U51(X)) -> MARK(X)
744.30/263.06	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.06	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.06	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.06	
744.30/263.06	The TRS R consists of the following rules:
744.30/263.06	
744.30/263.06	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.06	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.06	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.06	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.06	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.06	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.06	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.06	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.06	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.06	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.06	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.06	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.06	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.06	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.06	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.06	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.06	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.06	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.06	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.06	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.06	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.06	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.06	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.06	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.06	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.06	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.06	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.06	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.06	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.06	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.06	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.06	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.06	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.06	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.06	   active(U72(tt, N)) -> mark(N)
744.30/263.06	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.06	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.06	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.06	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.07	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.07	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.07	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.07	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.07	   mark(s(X)) -> active(s(mark(X)))
744.30/263.07	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.07	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.07	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.07	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.07	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.07	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.07	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.07	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.07	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.07	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.07	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.07	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.07	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.07	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.07	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.07	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.07	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.07	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.07	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.07	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.07	   mark(isNat(X)) -> active(isNat(X))
744.30/263.07	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.07	   mark(tt) -> active(tt)
744.30/263.07	   mark(0) -> active(0)
744.30/263.07	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.07	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.07	   active(U16(tt)) -> mark(tt)
744.30/263.07	   active(U23(tt)) -> mark(tt)
744.30/263.07	   active(U36(tt)) -> mark(tt)
744.30/263.07	   active(U42(tt)) -> mark(tt)
744.30/263.07	   active(U51(tt)) -> mark(tt)
744.30/263.07	   active(U62(tt)) -> mark(tt)
744.30/263.07	   active(U92(tt)) -> mark(0)
744.30/263.07	   active(isNat(0)) -> mark(tt)
744.30/263.07	   active(isNatKind(0)) -> mark(tt)
744.30/263.07	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.07	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.07	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.07	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.07	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.07	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.07	   U16(active(X)) -> U16(X)
744.30/263.07	   U16(mark(X)) -> U16(X)
744.30/263.07	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.07	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.07	   U23(active(X)) -> U23(X)
744.30/263.07	   U23(mark(X)) -> U23(X)
744.30/263.07	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.07	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.07	   U36(active(X)) -> U36(X)
744.30/263.07	   U36(mark(X)) -> U36(X)
744.30/263.07	   U42(active(X)) -> U42(X)
744.30/263.07	   U42(mark(X)) -> U42(X)
744.30/263.07	   U62(active(X)) -> U62(X)
744.30/263.07	   U62(mark(X)) -> U62(X)
744.30/263.07	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.07	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.07	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.07	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.07	   s(active(X)) -> s(X)
744.30/263.07	   s(mark(X)) -> s(X)
744.30/263.07	   U92(active(X)) -> U92(X)
744.30/263.07	   U92(mark(X)) -> U92(X)
744.30/263.07	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.07	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.07	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.07	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.07	   U51(active(X)) -> U51(X)
744.30/263.07	   U51(mark(X)) -> U51(X)
744.30/263.07	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.07	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.07	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.07	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.07	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.07	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.07	   x(active(X1), X2) -> x(X1, X2)
744.30/263.07	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.07	
744.30/263.07	The set Q consists of the following terms:
744.30/263.07	
744.30/263.07	   active(U101(tt, x0, x1))
744.30/263.07	   active(U102(tt, x0, x1))
744.30/263.07	   active(U103(tt, x0, x1))
744.30/263.07	   active(U104(tt, x0, x1))
744.30/263.07	   active(U11(tt, x0, x1))
744.30/263.07	   active(U12(tt, x0, x1))
744.30/263.07	   active(U13(tt, x0, x1))
744.30/263.07	   active(U14(tt, x0, x1))
744.30/263.07	   active(U15(tt, x0))
744.30/263.07	   active(U16(tt))
744.30/263.07	   active(U21(tt, x0))
744.30/263.07	   active(U22(tt, x0))
744.30/263.07	   active(U23(tt))
744.30/263.07	   active(U31(tt, x0, x1))
744.30/263.07	   active(U32(tt, x0, x1))
744.30/263.07	   active(U33(tt, x0, x1))
744.30/263.07	   active(U34(tt, x0, x1))
744.30/263.07	   active(U35(tt, x0))
744.30/263.07	   active(U36(tt))
744.30/263.07	   active(U41(tt, x0))
744.30/263.07	   active(U42(tt))
744.30/263.07	   active(U51(tt))
744.30/263.07	   active(U61(tt, x0))
744.30/263.07	   active(U62(tt))
744.30/263.07	   active(U71(tt, x0))
744.30/263.07	   active(U72(tt, x0))
744.30/263.07	   active(U81(tt, x0, x1))
744.30/263.07	   active(U82(tt, x0, x1))
744.30/263.07	   active(U83(tt, x0, x1))
744.30/263.07	   active(U84(tt, x0, x1))
744.30/263.07	   active(U91(tt, x0))
744.30/263.07	   active(U92(tt))
744.30/263.07	   active(isNat(0))
744.30/263.07	   active(isNat(plus(x0, x1)))
744.30/263.07	   active(isNat(s(x0)))
744.30/263.07	   active(isNat(x(x0, x1)))
744.30/263.07	   active(isNatKind(0))
744.30/263.07	   active(isNatKind(plus(x0, x1)))
744.30/263.07	   active(isNatKind(s(x0)))
744.30/263.07	   active(isNatKind(x(x0, x1)))
744.30/263.07	   active(plus(x0, 0))
744.30/263.07	   active(plus(x0, s(x1)))
744.30/263.07	   active(x(x0, 0))
744.30/263.07	   active(x(x0, s(x1)))
744.30/263.07	   mark(U101(x0, x1, x2))
744.30/263.07	   mark(tt)
744.30/263.07	   mark(U102(x0, x1, x2))
744.30/263.07	   mark(isNatKind(x0))
744.30/263.07	   mark(U103(x0, x1, x2))
744.30/263.07	   mark(isNat(x0))
744.30/263.07	   mark(U104(x0, x1, x2))
744.30/263.07	   mark(plus(x0, x1))
744.30/263.07	   mark(x(x0, x1))
744.30/263.07	   mark(U11(x0, x1, x2))
744.30/263.07	   mark(U12(x0, x1, x2))
744.30/263.07	   mark(U13(x0, x1, x2))
744.30/263.07	   mark(U14(x0, x1, x2))
744.30/263.07	   mark(U15(x0, x1))
744.30/263.07	   mark(U16(x0))
744.30/263.07	   mark(U21(x0, x1))
744.30/263.07	   mark(U22(x0, x1))
744.30/263.07	   mark(U23(x0))
744.30/263.07	   mark(U31(x0, x1, x2))
744.30/263.07	   mark(U32(x0, x1, x2))
744.30/263.07	   mark(U33(x0, x1, x2))
744.30/263.07	   mark(U34(x0, x1, x2))
744.30/263.07	   mark(U35(x0, x1))
744.30/263.07	   mark(U36(x0))
744.30/263.07	   mark(U41(x0, x1))
744.30/263.07	   mark(U42(x0))
744.30/263.07	   mark(U51(x0))
744.30/263.07	   mark(U61(x0, x1))
744.30/263.07	   mark(U62(x0))
744.30/263.07	   mark(U71(x0, x1))
744.30/263.07	   mark(U72(x0, x1))
744.30/263.07	   mark(U81(x0, x1, x2))
744.30/263.07	   mark(U82(x0, x1, x2))
744.30/263.07	   mark(U83(x0, x1, x2))
744.30/263.07	   mark(U84(x0, x1, x2))
744.30/263.07	   mark(s(x0))
744.30/263.07	   mark(U91(x0, x1))
744.30/263.07	   mark(U92(x0))
744.30/263.07	   mark(0)
744.30/263.07	   U101(mark(x0), x1, x2)
744.30/263.07	   U101(x0, mark(x1), x2)
744.30/263.07	   U101(x0, x1, mark(x2))
744.30/263.07	   U101(active(x0), x1, x2)
744.30/263.07	   U101(x0, active(x1), x2)
744.30/263.07	   U101(x0, x1, active(x2))
744.30/263.07	   U102(mark(x0), x1, x2)
744.30/263.07	   U102(x0, mark(x1), x2)
744.30/263.07	   U102(x0, x1, mark(x2))
744.30/263.07	   U102(active(x0), x1, x2)
744.30/263.07	   U102(x0, active(x1), x2)
744.30/263.07	   U102(x0, x1, active(x2))
744.30/263.07	   isNatKind(mark(x0))
744.30/263.07	   isNatKind(active(x0))
744.30/263.07	   U103(mark(x0), x1, x2)
744.30/263.07	   U103(x0, mark(x1), x2)
744.30/263.07	   U103(x0, x1, mark(x2))
744.30/263.07	   U103(active(x0), x1, x2)
744.30/263.07	   U103(x0, active(x1), x2)
744.30/263.07	   U103(x0, x1, active(x2))
744.30/263.07	   isNat(mark(x0))
744.30/263.07	   isNat(active(x0))
744.30/263.07	   U104(mark(x0), x1, x2)
744.30/263.07	   U104(x0, mark(x1), x2)
744.30/263.07	   U104(x0, x1, mark(x2))
744.30/263.07	   U104(active(x0), x1, x2)
744.30/263.07	   U104(x0, active(x1), x2)
744.30/263.07	   U104(x0, x1, active(x2))
744.30/263.07	   plus(mark(x0), x1)
744.30/263.07	   plus(x0, mark(x1))
744.30/263.07	   plus(active(x0), x1)
744.30/263.07	   plus(x0, active(x1))
744.30/263.07	   x(mark(x0), x1)
744.30/263.07	   x(x0, mark(x1))
744.30/263.07	   x(active(x0), x1)
744.30/263.07	   x(x0, active(x1))
744.30/263.07	   U11(mark(x0), x1, x2)
744.30/263.07	   U11(x0, mark(x1), x2)
744.30/263.07	   U11(x0, x1, mark(x2))
744.30/263.07	   U11(active(x0), x1, x2)
744.30/263.07	   U11(x0, active(x1), x2)
744.30/263.07	   U11(x0, x1, active(x2))
744.30/263.07	   U12(mark(x0), x1, x2)
744.30/263.07	   U12(x0, mark(x1), x2)
744.30/263.07	   U12(x0, x1, mark(x2))
744.30/263.07	   U12(active(x0), x1, x2)
744.30/263.07	   U12(x0, active(x1), x2)
744.30/263.07	   U12(x0, x1, active(x2))
744.30/263.07	   U13(mark(x0), x1, x2)
744.30/263.07	   U13(x0, mark(x1), x2)
744.30/263.07	   U13(x0, x1, mark(x2))
744.30/263.07	   U13(active(x0), x1, x2)
744.30/263.07	   U13(x0, active(x1), x2)
744.30/263.07	   U13(x0, x1, active(x2))
744.30/263.07	   U14(mark(x0), x1, x2)
744.30/263.07	   U14(x0, mark(x1), x2)
744.30/263.07	   U14(x0, x1, mark(x2))
744.30/263.07	   U14(active(x0), x1, x2)
744.30/263.07	   U14(x0, active(x1), x2)
744.30/263.07	   U14(x0, x1, active(x2))
744.30/263.07	   U15(mark(x0), x1)
744.30/263.07	   U15(x0, mark(x1))
744.30/263.07	   U15(active(x0), x1)
744.30/263.07	   U15(x0, active(x1))
744.30/263.07	   U16(mark(x0))
744.30/263.07	   U16(active(x0))
744.30/263.07	   U21(mark(x0), x1)
744.30/263.07	   U21(x0, mark(x1))
744.30/263.07	   U21(active(x0), x1)
744.30/263.07	   U21(x0, active(x1))
744.30/263.07	   U22(mark(x0), x1)
744.30/263.07	   U22(x0, mark(x1))
744.30/263.07	   U22(active(x0), x1)
744.30/263.07	   U22(x0, active(x1))
744.30/263.07	   U23(mark(x0))
744.30/263.07	   U23(active(x0))
744.30/263.07	   U31(mark(x0), x1, x2)
744.30/263.07	   U31(x0, mark(x1), x2)
744.30/263.07	   U31(x0, x1, mark(x2))
744.30/263.07	   U31(active(x0), x1, x2)
744.30/263.07	   U31(x0, active(x1), x2)
744.30/263.07	   U31(x0, x1, active(x2))
744.30/263.07	   U32(mark(x0), x1, x2)
744.30/263.07	   U32(x0, mark(x1), x2)
744.30/263.07	   U32(x0, x1, mark(x2))
744.30/263.07	   U32(active(x0), x1, x2)
744.30/263.07	   U32(x0, active(x1), x2)
744.30/263.07	   U32(x0, x1, active(x2))
744.30/263.07	   U33(mark(x0), x1, x2)
744.30/263.07	   U33(x0, mark(x1), x2)
744.30/263.07	   U33(x0, x1, mark(x2))
744.30/263.07	   U33(active(x0), x1, x2)
744.30/263.07	   U33(x0, active(x1), x2)
744.30/263.07	   U33(x0, x1, active(x2))
744.30/263.07	   U34(mark(x0), x1, x2)
744.30/263.07	   U34(x0, mark(x1), x2)
744.30/263.07	   U34(x0, x1, mark(x2))
744.30/263.07	   U34(active(x0), x1, x2)
744.30/263.07	   U34(x0, active(x1), x2)
744.30/263.07	   U34(x0, x1, active(x2))
744.30/263.07	   U35(mark(x0), x1)
744.30/263.07	   U35(x0, mark(x1))
744.30/263.07	   U35(active(x0), x1)
744.30/263.07	   U35(x0, active(x1))
744.30/263.07	   U36(mark(x0))
744.30/263.07	   U36(active(x0))
744.30/263.07	   U41(mark(x0), x1)
744.30/263.07	   U41(x0, mark(x1))
744.30/263.07	   U41(active(x0), x1)
744.30/263.07	   U41(x0, active(x1))
744.30/263.07	   U42(mark(x0))
744.30/263.07	   U42(active(x0))
744.30/263.07	   U51(mark(x0))
744.30/263.07	   U51(active(x0))
744.30/263.07	   U61(mark(x0), x1)
744.30/263.07	   U61(x0, mark(x1))
744.30/263.07	   U61(active(x0), x1)
744.30/263.07	   U61(x0, active(x1))
744.30/263.07	   U62(mark(x0))
744.30/263.07	   U62(active(x0))
744.30/263.07	   U71(mark(x0), x1)
744.30/263.07	   U71(x0, mark(x1))
744.30/263.07	   U71(active(x0), x1)
744.30/263.07	   U71(x0, active(x1))
744.30/263.07	   U72(mark(x0), x1)
744.30/263.07	   U72(x0, mark(x1))
744.30/263.07	   U72(active(x0), x1)
744.30/263.07	   U72(x0, active(x1))
744.30/263.07	   U81(mark(x0), x1, x2)
744.30/263.07	   U81(x0, mark(x1), x2)
744.30/263.07	   U81(x0, x1, mark(x2))
744.30/263.07	   U81(active(x0), x1, x2)
744.30/263.07	   U81(x0, active(x1), x2)
744.30/263.07	   U81(x0, x1, active(x2))
744.30/263.07	   U82(mark(x0), x1, x2)
744.30/263.07	   U82(x0, mark(x1), x2)
744.30/263.07	   U82(x0, x1, mark(x2))
744.30/263.07	   U82(active(x0), x1, x2)
744.30/263.07	   U82(x0, active(x1), x2)
744.30/263.07	   U82(x0, x1, active(x2))
744.30/263.07	   U83(mark(x0), x1, x2)
744.30/263.07	   U83(x0, mark(x1), x2)
744.30/263.07	   U83(x0, x1, mark(x2))
744.30/263.07	   U83(active(x0), x1, x2)
744.30/263.07	   U83(x0, active(x1), x2)
744.30/263.07	   U83(x0, x1, active(x2))
744.30/263.07	   U84(mark(x0), x1, x2)
744.30/263.07	   U84(x0, mark(x1), x2)
744.30/263.07	   U84(x0, x1, mark(x2))
744.30/263.07	   U84(active(x0), x1, x2)
744.30/263.07	   U84(x0, active(x1), x2)
744.30/263.07	   U84(x0, x1, active(x2))
744.30/263.07	   s(mark(x0))
744.30/263.07	   s(active(x0))
744.30/263.07	   U91(mark(x0), x1)
744.30/263.07	   U91(x0, mark(x1))
744.30/263.07	   U91(active(x0), x1)
744.30/263.07	   U91(x0, active(x1))
744.30/263.07	   U92(mark(x0))
744.30/263.07	   U92(active(x0))
744.30/263.07	
744.30/263.07	We have to consider all minimal (P,Q,R)-chains.
744.30/263.07	----------------------------------------
744.30/263.07	
744.30/263.07	(317) QDPOrderProof (EQUIVALENT)
744.30/263.07	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.07	
744.30/263.07	
744.30/263.07	The following pairs can be oriented strictly and are deleted.
744.30/263.07	
744.30/263.07	   MARK(U34(X1, X2, X3)) -> MARK(X1)
744.30/263.07	The remaining pairs can at least be oriented weakly.
744.30/263.07	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(ACTIVE(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(tt) =  	[[0A]]
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(plus(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U41(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U23(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U31(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U33(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U34(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(s(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(x(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U103(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U91(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(0) =  	[[0A]]
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	
744.30/263.07	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.07	
744.30/263.07	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.07	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.07	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.07	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.07	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.07	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.07	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.07	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.07	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.07	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.07	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.07	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.07	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.07	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.07	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.07	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.07	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.07	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.07	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.07	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.07	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.07	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.07	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.07	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.07	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.07	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.07	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.07	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.07	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.07	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.07	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.07	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.07	   active(U72(tt, N)) -> mark(N)
744.30/263.07	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.07	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.07	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.07	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.07	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.07	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.07	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.07	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.07	   mark(s(X)) -> active(s(mark(X)))
744.30/263.07	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.07	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.07	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.07	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.07	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.07	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.07	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.07	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.07	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.07	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.07	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.07	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.07	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.07	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.07	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.07	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.07	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.07	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.07	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.07	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.07	   mark(isNat(X)) -> active(isNat(X))
744.30/263.07	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.07	   mark(tt) -> active(tt)
744.30/263.07	   mark(0) -> active(0)
744.30/263.07	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.07	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.07	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.07	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.07	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.07	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.07	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.07	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.07	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.07	   active(U16(tt)) -> mark(tt)
744.30/263.07	   active(U23(tt)) -> mark(tt)
744.30/263.07	   active(U36(tt)) -> mark(tt)
744.30/263.07	   active(U42(tt)) -> mark(tt)
744.30/263.07	   active(U51(tt)) -> mark(tt)
744.30/263.07	   active(U62(tt)) -> mark(tt)
744.30/263.07	   active(U92(tt)) -> mark(0)
744.30/263.07	   active(isNat(0)) -> mark(tt)
744.30/263.07	   active(isNatKind(0)) -> mark(tt)
744.30/263.07	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.07	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.07	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.07	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.07	   U16(active(X)) -> U16(X)
744.30/263.07	   U16(mark(X)) -> U16(X)
744.30/263.07	   U23(active(X)) -> U23(X)
744.30/263.07	   U23(mark(X)) -> U23(X)
744.30/263.07	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.07	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.07	   U36(active(X)) -> U36(X)
744.30/263.07	   U36(mark(X)) -> U36(X)
744.30/263.07	   U42(active(X)) -> U42(X)
744.30/263.07	   U42(mark(X)) -> U42(X)
744.30/263.07	   U62(active(X)) -> U62(X)
744.30/263.07	   U62(mark(X)) -> U62(X)
744.30/263.07	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.07	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.07	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.07	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.07	   s(active(X)) -> s(X)
744.30/263.07	   s(mark(X)) -> s(X)
744.30/263.07	   U92(active(X)) -> U92(X)
744.30/263.07	   U92(mark(X)) -> U92(X)
744.30/263.07	   U51(active(X)) -> U51(X)
744.30/263.07	   U51(mark(X)) -> U51(X)
744.30/263.07	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.07	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.07	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.07	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.07	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.07	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.07	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.07	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.07	   x(active(X1), X2) -> x(X1, X2)
744.30/263.07	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.07	
744.30/263.07	
744.30/263.07	----------------------------------------
744.30/263.07	
744.30/263.07	(318)
744.30/263.07	Obligation:
744.30/263.07	Q DP problem:
744.30/263.07	The TRS P consists of the following rules:
744.30/263.07	
744.30/263.07	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.07	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.07	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.07	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.07	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.07	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.07	   MARK(U16(X)) -> MARK(X)
744.30/263.07	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.07	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.07	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.07	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.07	   MARK(U23(X)) -> MARK(X)
744.30/263.07	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.07	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.07	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.07	   MARK(U42(X)) -> MARK(X)
744.30/263.07	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U51(X)) -> MARK(X)
744.30/263.07	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.07	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.07	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.07	
744.30/263.07	The TRS R consists of the following rules:
744.30/263.07	
744.30/263.07	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.07	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.07	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.07	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.07	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.07	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.07	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.07	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.07	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.07	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.07	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.07	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.07	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.07	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.07	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.07	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.07	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.07	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.07	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.07	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.07	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.07	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.07	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.07	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.07	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.07	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.07	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.07	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.07	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.07	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.07	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.07	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.07	   active(U72(tt, N)) -> mark(N)
744.30/263.07	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.07	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.07	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.07	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.07	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.07	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.07	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.07	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.07	   mark(s(X)) -> active(s(mark(X)))
744.30/263.07	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.07	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.07	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.07	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.07	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.07	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.07	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.07	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.07	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.07	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.07	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.07	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.07	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.07	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.07	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.07	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.07	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.07	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.07	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.07	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.07	   mark(isNat(X)) -> active(isNat(X))
744.30/263.07	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.07	   mark(tt) -> active(tt)
744.30/263.07	   mark(0) -> active(0)
744.30/263.07	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.07	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.07	   active(U16(tt)) -> mark(tt)
744.30/263.07	   active(U23(tt)) -> mark(tt)
744.30/263.07	   active(U36(tt)) -> mark(tt)
744.30/263.07	   active(U42(tt)) -> mark(tt)
744.30/263.07	   active(U51(tt)) -> mark(tt)
744.30/263.07	   active(U62(tt)) -> mark(tt)
744.30/263.07	   active(U92(tt)) -> mark(0)
744.30/263.07	   active(isNat(0)) -> mark(tt)
744.30/263.07	   active(isNatKind(0)) -> mark(tt)
744.30/263.07	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.07	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.07	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.07	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.07	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.07	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.07	   U16(active(X)) -> U16(X)
744.30/263.07	   U16(mark(X)) -> U16(X)
744.30/263.07	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.07	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.07	   U23(active(X)) -> U23(X)
744.30/263.07	   U23(mark(X)) -> U23(X)
744.30/263.07	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.07	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.07	   U36(active(X)) -> U36(X)
744.30/263.07	   U36(mark(X)) -> U36(X)
744.30/263.07	   U42(active(X)) -> U42(X)
744.30/263.07	   U42(mark(X)) -> U42(X)
744.30/263.07	   U62(active(X)) -> U62(X)
744.30/263.07	   U62(mark(X)) -> U62(X)
744.30/263.07	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.07	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.07	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.07	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.07	   s(active(X)) -> s(X)
744.30/263.07	   s(mark(X)) -> s(X)
744.30/263.07	   U92(active(X)) -> U92(X)
744.30/263.07	   U92(mark(X)) -> U92(X)
744.30/263.07	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.07	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.07	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.07	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.07	   U51(active(X)) -> U51(X)
744.30/263.07	   U51(mark(X)) -> U51(X)
744.30/263.07	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.07	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.07	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.07	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.07	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.07	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.07	   x(active(X1), X2) -> x(X1, X2)
744.30/263.07	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.07	
744.30/263.07	The set Q consists of the following terms:
744.30/263.07	
744.30/263.07	   active(U101(tt, x0, x1))
744.30/263.07	   active(U102(tt, x0, x1))
744.30/263.07	   active(U103(tt, x0, x1))
744.30/263.07	   active(U104(tt, x0, x1))
744.30/263.07	   active(U11(tt, x0, x1))
744.30/263.07	   active(U12(tt, x0, x1))
744.30/263.07	   active(U13(tt, x0, x1))
744.30/263.07	   active(U14(tt, x0, x1))
744.30/263.07	   active(U15(tt, x0))
744.30/263.07	   active(U16(tt))
744.30/263.07	   active(U21(tt, x0))
744.30/263.07	   active(U22(tt, x0))
744.30/263.07	   active(U23(tt))
744.30/263.07	   active(U31(tt, x0, x1))
744.30/263.07	   active(U32(tt, x0, x1))
744.30/263.07	   active(U33(tt, x0, x1))
744.30/263.07	   active(U34(tt, x0, x1))
744.30/263.07	   active(U35(tt, x0))
744.30/263.07	   active(U36(tt))
744.30/263.07	   active(U41(tt, x0))
744.30/263.07	   active(U42(tt))
744.30/263.07	   active(U51(tt))
744.30/263.07	   active(U61(tt, x0))
744.30/263.07	   active(U62(tt))
744.30/263.07	   active(U71(tt, x0))
744.30/263.07	   active(U72(tt, x0))
744.30/263.07	   active(U81(tt, x0, x1))
744.30/263.07	   active(U82(tt, x0, x1))
744.30/263.07	   active(U83(tt, x0, x1))
744.30/263.07	   active(U84(tt, x0, x1))
744.30/263.07	   active(U91(tt, x0))
744.30/263.07	   active(U92(tt))
744.30/263.07	   active(isNat(0))
744.30/263.07	   active(isNat(plus(x0, x1)))
744.30/263.07	   active(isNat(s(x0)))
744.30/263.07	   active(isNat(x(x0, x1)))
744.30/263.07	   active(isNatKind(0))
744.30/263.07	   active(isNatKind(plus(x0, x1)))
744.30/263.07	   active(isNatKind(s(x0)))
744.30/263.07	   active(isNatKind(x(x0, x1)))
744.30/263.07	   active(plus(x0, 0))
744.30/263.07	   active(plus(x0, s(x1)))
744.30/263.07	   active(x(x0, 0))
744.30/263.07	   active(x(x0, s(x1)))
744.30/263.07	   mark(U101(x0, x1, x2))
744.30/263.07	   mark(tt)
744.30/263.07	   mark(U102(x0, x1, x2))
744.30/263.07	   mark(isNatKind(x0))
744.30/263.07	   mark(U103(x0, x1, x2))
744.30/263.07	   mark(isNat(x0))
744.30/263.07	   mark(U104(x0, x1, x2))
744.30/263.07	   mark(plus(x0, x1))
744.30/263.07	   mark(x(x0, x1))
744.30/263.07	   mark(U11(x0, x1, x2))
744.30/263.07	   mark(U12(x0, x1, x2))
744.30/263.07	   mark(U13(x0, x1, x2))
744.30/263.07	   mark(U14(x0, x1, x2))
744.30/263.07	   mark(U15(x0, x1))
744.30/263.07	   mark(U16(x0))
744.30/263.07	   mark(U21(x0, x1))
744.30/263.07	   mark(U22(x0, x1))
744.30/263.07	   mark(U23(x0))
744.30/263.07	   mark(U31(x0, x1, x2))
744.30/263.07	   mark(U32(x0, x1, x2))
744.30/263.07	   mark(U33(x0, x1, x2))
744.30/263.07	   mark(U34(x0, x1, x2))
744.30/263.07	   mark(U35(x0, x1))
744.30/263.07	   mark(U36(x0))
744.30/263.07	   mark(U41(x0, x1))
744.30/263.07	   mark(U42(x0))
744.30/263.07	   mark(U51(x0))
744.30/263.07	   mark(U61(x0, x1))
744.30/263.07	   mark(U62(x0))
744.30/263.07	   mark(U71(x0, x1))
744.30/263.07	   mark(U72(x0, x1))
744.30/263.07	   mark(U81(x0, x1, x2))
744.30/263.07	   mark(U82(x0, x1, x2))
744.30/263.07	   mark(U83(x0, x1, x2))
744.30/263.07	   mark(U84(x0, x1, x2))
744.30/263.07	   mark(s(x0))
744.30/263.07	   mark(U91(x0, x1))
744.30/263.07	   mark(U92(x0))
744.30/263.07	   mark(0)
744.30/263.07	   U101(mark(x0), x1, x2)
744.30/263.07	   U101(x0, mark(x1), x2)
744.30/263.07	   U101(x0, x1, mark(x2))
744.30/263.07	   U101(active(x0), x1, x2)
744.30/263.07	   U101(x0, active(x1), x2)
744.30/263.07	   U101(x0, x1, active(x2))
744.30/263.07	   U102(mark(x0), x1, x2)
744.30/263.07	   U102(x0, mark(x1), x2)
744.30/263.07	   U102(x0, x1, mark(x2))
744.30/263.07	   U102(active(x0), x1, x2)
744.30/263.07	   U102(x0, active(x1), x2)
744.30/263.07	   U102(x0, x1, active(x2))
744.30/263.07	   isNatKind(mark(x0))
744.30/263.07	   isNatKind(active(x0))
744.30/263.07	   U103(mark(x0), x1, x2)
744.30/263.07	   U103(x0, mark(x1), x2)
744.30/263.07	   U103(x0, x1, mark(x2))
744.30/263.07	   U103(active(x0), x1, x2)
744.30/263.07	   U103(x0, active(x1), x2)
744.30/263.07	   U103(x0, x1, active(x2))
744.30/263.07	   isNat(mark(x0))
744.30/263.07	   isNat(active(x0))
744.30/263.07	   U104(mark(x0), x1, x2)
744.30/263.07	   U104(x0, mark(x1), x2)
744.30/263.07	   U104(x0, x1, mark(x2))
744.30/263.07	   U104(active(x0), x1, x2)
744.30/263.07	   U104(x0, active(x1), x2)
744.30/263.07	   U104(x0, x1, active(x2))
744.30/263.07	   plus(mark(x0), x1)
744.30/263.07	   plus(x0, mark(x1))
744.30/263.07	   plus(active(x0), x1)
744.30/263.07	   plus(x0, active(x1))
744.30/263.07	   x(mark(x0), x1)
744.30/263.07	   x(x0, mark(x1))
744.30/263.07	   x(active(x0), x1)
744.30/263.07	   x(x0, active(x1))
744.30/263.07	   U11(mark(x0), x1, x2)
744.30/263.07	   U11(x0, mark(x1), x2)
744.30/263.07	   U11(x0, x1, mark(x2))
744.30/263.07	   U11(active(x0), x1, x2)
744.30/263.07	   U11(x0, active(x1), x2)
744.30/263.07	   U11(x0, x1, active(x2))
744.30/263.07	   U12(mark(x0), x1, x2)
744.30/263.07	   U12(x0, mark(x1), x2)
744.30/263.07	   U12(x0, x1, mark(x2))
744.30/263.07	   U12(active(x0), x1, x2)
744.30/263.07	   U12(x0, active(x1), x2)
744.30/263.07	   U12(x0, x1, active(x2))
744.30/263.07	   U13(mark(x0), x1, x2)
744.30/263.07	   U13(x0, mark(x1), x2)
744.30/263.07	   U13(x0, x1, mark(x2))
744.30/263.07	   U13(active(x0), x1, x2)
744.30/263.07	   U13(x0, active(x1), x2)
744.30/263.07	   U13(x0, x1, active(x2))
744.30/263.07	   U14(mark(x0), x1, x2)
744.30/263.07	   U14(x0, mark(x1), x2)
744.30/263.07	   U14(x0, x1, mark(x2))
744.30/263.07	   U14(active(x0), x1, x2)
744.30/263.07	   U14(x0, active(x1), x2)
744.30/263.07	   U14(x0, x1, active(x2))
744.30/263.07	   U15(mark(x0), x1)
744.30/263.07	   U15(x0, mark(x1))
744.30/263.07	   U15(active(x0), x1)
744.30/263.07	   U15(x0, active(x1))
744.30/263.07	   U16(mark(x0))
744.30/263.07	   U16(active(x0))
744.30/263.07	   U21(mark(x0), x1)
744.30/263.07	   U21(x0, mark(x1))
744.30/263.07	   U21(active(x0), x1)
744.30/263.07	   U21(x0, active(x1))
744.30/263.07	   U22(mark(x0), x1)
744.30/263.07	   U22(x0, mark(x1))
744.30/263.07	   U22(active(x0), x1)
744.30/263.07	   U22(x0, active(x1))
744.30/263.07	   U23(mark(x0))
744.30/263.07	   U23(active(x0))
744.30/263.07	   U31(mark(x0), x1, x2)
744.30/263.07	   U31(x0, mark(x1), x2)
744.30/263.07	   U31(x0, x1, mark(x2))
744.30/263.07	   U31(active(x0), x1, x2)
744.30/263.07	   U31(x0, active(x1), x2)
744.30/263.07	   U31(x0, x1, active(x2))
744.30/263.07	   U32(mark(x0), x1, x2)
744.30/263.07	   U32(x0, mark(x1), x2)
744.30/263.07	   U32(x0, x1, mark(x2))
744.30/263.07	   U32(active(x0), x1, x2)
744.30/263.07	   U32(x0, active(x1), x2)
744.30/263.07	   U32(x0, x1, active(x2))
744.30/263.07	   U33(mark(x0), x1, x2)
744.30/263.07	   U33(x0, mark(x1), x2)
744.30/263.07	   U33(x0, x1, mark(x2))
744.30/263.07	   U33(active(x0), x1, x2)
744.30/263.07	   U33(x0, active(x1), x2)
744.30/263.07	   U33(x0, x1, active(x2))
744.30/263.07	   U34(mark(x0), x1, x2)
744.30/263.07	   U34(x0, mark(x1), x2)
744.30/263.07	   U34(x0, x1, mark(x2))
744.30/263.07	   U34(active(x0), x1, x2)
744.30/263.07	   U34(x0, active(x1), x2)
744.30/263.07	   U34(x0, x1, active(x2))
744.30/263.07	   U35(mark(x0), x1)
744.30/263.07	   U35(x0, mark(x1))
744.30/263.07	   U35(active(x0), x1)
744.30/263.07	   U35(x0, active(x1))
744.30/263.07	   U36(mark(x0))
744.30/263.07	   U36(active(x0))
744.30/263.07	   U41(mark(x0), x1)
744.30/263.07	   U41(x0, mark(x1))
744.30/263.07	   U41(active(x0), x1)
744.30/263.07	   U41(x0, active(x1))
744.30/263.07	   U42(mark(x0))
744.30/263.07	   U42(active(x0))
744.30/263.07	   U51(mark(x0))
744.30/263.07	   U51(active(x0))
744.30/263.07	   U61(mark(x0), x1)
744.30/263.07	   U61(x0, mark(x1))
744.30/263.07	   U61(active(x0), x1)
744.30/263.07	   U61(x0, active(x1))
744.30/263.07	   U62(mark(x0))
744.30/263.07	   U62(active(x0))
744.30/263.07	   U71(mark(x0), x1)
744.30/263.07	   U71(x0, mark(x1))
744.30/263.07	   U71(active(x0), x1)
744.30/263.07	   U71(x0, active(x1))
744.30/263.07	   U72(mark(x0), x1)
744.30/263.07	   U72(x0, mark(x1))
744.30/263.07	   U72(active(x0), x1)
744.30/263.07	   U72(x0, active(x1))
744.30/263.07	   U81(mark(x0), x1, x2)
744.30/263.07	   U81(x0, mark(x1), x2)
744.30/263.07	   U81(x0, x1, mark(x2))
744.30/263.07	   U81(active(x0), x1, x2)
744.30/263.07	   U81(x0, active(x1), x2)
744.30/263.07	   U81(x0, x1, active(x2))
744.30/263.07	   U82(mark(x0), x1, x2)
744.30/263.07	   U82(x0, mark(x1), x2)
744.30/263.07	   U82(x0, x1, mark(x2))
744.30/263.07	   U82(active(x0), x1, x2)
744.30/263.07	   U82(x0, active(x1), x2)
744.30/263.07	   U82(x0, x1, active(x2))
744.30/263.07	   U83(mark(x0), x1, x2)
744.30/263.07	   U83(x0, mark(x1), x2)
744.30/263.07	   U83(x0, x1, mark(x2))
744.30/263.07	   U83(active(x0), x1, x2)
744.30/263.07	   U83(x0, active(x1), x2)
744.30/263.07	   U83(x0, x1, active(x2))
744.30/263.07	   U84(mark(x0), x1, x2)
744.30/263.07	   U84(x0, mark(x1), x2)
744.30/263.07	   U84(x0, x1, mark(x2))
744.30/263.07	   U84(active(x0), x1, x2)
744.30/263.07	   U84(x0, active(x1), x2)
744.30/263.07	   U84(x0, x1, active(x2))
744.30/263.07	   s(mark(x0))
744.30/263.07	   s(active(x0))
744.30/263.07	   U91(mark(x0), x1)
744.30/263.07	   U91(x0, mark(x1))
744.30/263.07	   U91(active(x0), x1)
744.30/263.07	   U91(x0, active(x1))
744.30/263.07	   U92(mark(x0))
744.30/263.07	   U92(active(x0))
744.30/263.07	
744.30/263.07	We have to consider all minimal (P,Q,R)-chains.
744.30/263.07	----------------------------------------
744.30/263.07	
744.30/263.07	(319) QDPOrderProof (EQUIVALENT)
744.30/263.07	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.07	
744.30/263.07	
744.30/263.07	The following pairs can be oriented strictly and are deleted.
744.30/263.07	
744.30/263.07	   MARK(U21(X1, X2)) -> MARK(X1)
744.30/263.07	The remaining pairs can at least be oriented weakly.
744.30/263.07	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U12(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(mark(x_1)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U11(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(tt) =  	[[0A]]
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(isNatKind(x_1)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U41(x_1, x_2)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U13(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U14(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U15(x_1, x_2)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(isNat(x_1)) =  	[[2A]] 	 +  	[[1A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U21(x_1, x_2)) =  	[[3A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U22(x_1, x_2)) =  	[[3A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U23(x_1)) =  	[[3A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U31(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U32(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U33(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U34(x_1, x_2, x_3)) =  	[[2A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(s(x_1)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(active(x_1)) =  	[[2A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U81(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	   <<<
744.30/263.07	 POL(0) =  	[[2A]]
744.30/263.07	>>>
744.30/263.07	
744.30/263.07	
744.30/263.07	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.07	
744.30/263.07	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.07	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.07	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.07	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.07	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.07	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.07	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.07	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.07	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.07	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.07	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.07	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.07	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.07	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.07	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.07	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.07	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.07	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.07	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.07	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.07	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.07	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.07	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.07	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.07	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.07	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.07	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.07	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.07	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.07	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.07	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.07	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.07	   active(U72(tt, N)) -> mark(N)
744.30/263.07	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.07	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.07	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.07	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.07	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.07	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.07	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.07	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.07	   mark(s(X)) -> active(s(mark(X)))
744.30/263.07	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.07	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.07	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.07	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.07	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.07	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.07	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.07	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.07	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.07	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.07	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.07	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.07	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.07	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.07	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.07	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.07	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.07	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.07	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.07	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.07	   mark(isNat(X)) -> active(isNat(X))
744.30/263.07	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.07	   mark(tt) -> active(tt)
744.30/263.07	   mark(0) -> active(0)
744.30/263.07	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.07	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.07	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.07	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.07	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.07	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.07	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.07	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.07	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.07	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.07	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.07	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.07	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.07	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.07	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.07	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.07	   active(U16(tt)) -> mark(tt)
744.30/263.07	   active(U23(tt)) -> mark(tt)
744.30/263.07	   active(U36(tt)) -> mark(tt)
744.30/263.07	   active(U42(tt)) -> mark(tt)
744.30/263.07	   active(U51(tt)) -> mark(tt)
744.30/263.07	   active(U62(tt)) -> mark(tt)
744.30/263.07	   active(U92(tt)) -> mark(0)
744.30/263.07	   active(isNat(0)) -> mark(tt)
744.30/263.07	   active(isNatKind(0)) -> mark(tt)
744.30/263.07	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.07	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.07	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.07	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.07	   U16(active(X)) -> U16(X)
744.30/263.07	   U16(mark(X)) -> U16(X)
744.30/263.07	   U23(active(X)) -> U23(X)
744.30/263.07	   U23(mark(X)) -> U23(X)
744.30/263.07	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.07	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.07	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.07	   U36(active(X)) -> U36(X)
744.30/263.07	   U36(mark(X)) -> U36(X)
744.30/263.07	   U42(active(X)) -> U42(X)
744.30/263.07	   U42(mark(X)) -> U42(X)
744.30/263.07	   U62(active(X)) -> U62(X)
744.30/263.07	   U62(mark(X)) -> U62(X)
744.30/263.07	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.07	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.07	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.07	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.07	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.07	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.07	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.07	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.07	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.07	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.07	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.07	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.07	   s(active(X)) -> s(X)
744.30/263.07	   s(mark(X)) -> s(X)
744.30/263.07	   U92(active(X)) -> U92(X)
744.30/263.07	   U92(mark(X)) -> U92(X)
744.30/263.07	   U51(active(X)) -> U51(X)
744.30/263.07	   U51(mark(X)) -> U51(X)
744.30/263.07	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.07	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.07	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.07	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.07	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.07	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.07	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.07	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.07	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.07	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.07	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.07	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.07	   x(active(X1), X2) -> x(X1, X2)
744.30/263.07	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.07	
744.30/263.07	
744.30/263.07	----------------------------------------
744.30/263.07	
744.30/263.07	(320)
744.30/263.07	Obligation:
744.30/263.07	Q DP problem:
744.30/263.07	The TRS P consists of the following rules:
744.30/263.07	
744.30/263.07	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.07	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.07	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.07	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.07	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.07	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.07	   MARK(U16(X)) -> MARK(X)
744.30/263.07	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.07	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.07	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.07	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.07	   MARK(U23(X)) -> MARK(X)
744.30/263.07	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.07	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.07	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.07	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.07	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.07	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.07	   MARK(U42(X)) -> MARK(X)
744.30/263.07	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.07	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.07	   MARK(U51(X)) -> MARK(X)
744.30/263.07	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.07	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.07	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.07	
744.30/263.07	The TRS R consists of the following rules:
744.30/263.07	
744.30/263.07	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.07	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.07	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.07	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.07	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.07	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.07	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.07	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.07	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.07	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.07	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.07	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.07	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.07	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.07	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.07	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.07	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.07	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.07	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.07	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.07	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.07	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.07	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.07	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.07	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.07	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.07	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.07	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.07	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.07	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.07	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.07	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.07	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.07	   active(U72(tt, N)) -> mark(N)
744.30/263.07	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.07	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.07	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.07	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.07	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.07	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.07	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.07	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.07	   mark(s(X)) -> active(s(mark(X)))
744.30/263.07	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.07	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.07	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.07	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.07	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.07	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.07	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.07	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.07	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.07	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.07	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.07	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.07	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.07	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.07	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.07	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.07	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.07	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.07	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.07	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.07	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.07	   mark(isNat(X)) -> active(isNat(X))
744.30/263.07	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.07	   mark(tt) -> active(tt)
744.30/263.07	   mark(0) -> active(0)
744.30/263.07	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.07	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.07	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.07	   active(U16(tt)) -> mark(tt)
744.30/263.07	   active(U23(tt)) -> mark(tt)
744.30/263.07	   active(U36(tt)) -> mark(tt)
744.30/263.07	   active(U42(tt)) -> mark(tt)
744.30/263.07	   active(U51(tt)) -> mark(tt)
744.30/263.07	   active(U62(tt)) -> mark(tt)
744.30/263.07	   active(U92(tt)) -> mark(0)
744.30/263.07	   active(isNat(0)) -> mark(tt)
744.30/263.07	   active(isNatKind(0)) -> mark(tt)
744.30/263.07	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.07	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.07	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.07	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.07	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.07	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.07	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.07	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.07	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.07	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.07	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.07	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.07	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.07	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.07	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.07	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.07	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.07	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.07	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.07	   U16(active(X)) -> U16(X)
744.30/263.07	   U16(mark(X)) -> U16(X)
744.30/263.07	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.07	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.07	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.07	   U23(active(X)) -> U23(X)
744.30/263.07	   U23(mark(X)) -> U23(X)
744.30/263.07	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.07	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.07	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.07	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.07	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.07	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.08	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.08	   U36(active(X)) -> U36(X)
744.30/263.08	   U36(mark(X)) -> U36(X)
744.30/263.08	   U42(active(X)) -> U42(X)
744.30/263.08	   U42(mark(X)) -> U42(X)
744.30/263.08	   U62(active(X)) -> U62(X)
744.30/263.08	   U62(mark(X)) -> U62(X)
744.30/263.08	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.08	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.08	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.08	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.08	   s(active(X)) -> s(X)
744.30/263.08	   s(mark(X)) -> s(X)
744.30/263.08	   U92(active(X)) -> U92(X)
744.30/263.08	   U92(mark(X)) -> U92(X)
744.30/263.08	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.08	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.08	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.08	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.08	   U51(active(X)) -> U51(X)
744.30/263.08	   U51(mark(X)) -> U51(X)
744.30/263.08	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.08	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.08	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.08	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.08	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.08	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.08	   x(active(X1), X2) -> x(X1, X2)
744.30/263.08	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.08	
744.30/263.08	The set Q consists of the following terms:
744.30/263.08	
744.30/263.08	   active(U101(tt, x0, x1))
744.30/263.08	   active(U102(tt, x0, x1))
744.30/263.08	   active(U103(tt, x0, x1))
744.30/263.08	   active(U104(tt, x0, x1))
744.30/263.08	   active(U11(tt, x0, x1))
744.30/263.08	   active(U12(tt, x0, x1))
744.30/263.08	   active(U13(tt, x0, x1))
744.30/263.08	   active(U14(tt, x0, x1))
744.30/263.08	   active(U15(tt, x0))
744.30/263.08	   active(U16(tt))
744.30/263.08	   active(U21(tt, x0))
744.30/263.08	   active(U22(tt, x0))
744.30/263.08	   active(U23(tt))
744.30/263.08	   active(U31(tt, x0, x1))
744.30/263.08	   active(U32(tt, x0, x1))
744.30/263.08	   active(U33(tt, x0, x1))
744.30/263.08	   active(U34(tt, x0, x1))
744.30/263.08	   active(U35(tt, x0))
744.30/263.08	   active(U36(tt))
744.30/263.08	   active(U41(tt, x0))
744.30/263.08	   active(U42(tt))
744.30/263.08	   active(U51(tt))
744.30/263.08	   active(U61(tt, x0))
744.30/263.08	   active(U62(tt))
744.30/263.08	   active(U71(tt, x0))
744.30/263.08	   active(U72(tt, x0))
744.30/263.08	   active(U81(tt, x0, x1))
744.30/263.08	   active(U82(tt, x0, x1))
744.30/263.08	   active(U83(tt, x0, x1))
744.30/263.08	   active(U84(tt, x0, x1))
744.30/263.08	   active(U91(tt, x0))
744.30/263.08	   active(U92(tt))
744.30/263.08	   active(isNat(0))
744.30/263.08	   active(isNat(plus(x0, x1)))
744.30/263.08	   active(isNat(s(x0)))
744.30/263.08	   active(isNat(x(x0, x1)))
744.30/263.08	   active(isNatKind(0))
744.30/263.08	   active(isNatKind(plus(x0, x1)))
744.30/263.08	   active(isNatKind(s(x0)))
744.30/263.08	   active(isNatKind(x(x0, x1)))
744.30/263.08	   active(plus(x0, 0))
744.30/263.08	   active(plus(x0, s(x1)))
744.30/263.08	   active(x(x0, 0))
744.30/263.08	   active(x(x0, s(x1)))
744.30/263.08	   mark(U101(x0, x1, x2))
744.30/263.08	   mark(tt)
744.30/263.08	   mark(U102(x0, x1, x2))
744.30/263.08	   mark(isNatKind(x0))
744.30/263.08	   mark(U103(x0, x1, x2))
744.30/263.08	   mark(isNat(x0))
744.30/263.08	   mark(U104(x0, x1, x2))
744.30/263.08	   mark(plus(x0, x1))
744.30/263.08	   mark(x(x0, x1))
744.30/263.08	   mark(U11(x0, x1, x2))
744.30/263.08	   mark(U12(x0, x1, x2))
744.30/263.08	   mark(U13(x0, x1, x2))
744.30/263.08	   mark(U14(x0, x1, x2))
744.30/263.08	   mark(U15(x0, x1))
744.30/263.08	   mark(U16(x0))
744.30/263.08	   mark(U21(x0, x1))
744.30/263.08	   mark(U22(x0, x1))
744.30/263.08	   mark(U23(x0))
744.30/263.08	   mark(U31(x0, x1, x2))
744.30/263.08	   mark(U32(x0, x1, x2))
744.30/263.08	   mark(U33(x0, x1, x2))
744.30/263.08	   mark(U34(x0, x1, x2))
744.30/263.08	   mark(U35(x0, x1))
744.30/263.08	   mark(U36(x0))
744.30/263.08	   mark(U41(x0, x1))
744.30/263.08	   mark(U42(x0))
744.30/263.08	   mark(U51(x0))
744.30/263.08	   mark(U61(x0, x1))
744.30/263.08	   mark(U62(x0))
744.30/263.08	   mark(U71(x0, x1))
744.30/263.08	   mark(U72(x0, x1))
744.30/263.08	   mark(U81(x0, x1, x2))
744.30/263.08	   mark(U82(x0, x1, x2))
744.30/263.08	   mark(U83(x0, x1, x2))
744.30/263.08	   mark(U84(x0, x1, x2))
744.30/263.08	   mark(s(x0))
744.30/263.08	   mark(U91(x0, x1))
744.30/263.08	   mark(U92(x0))
744.30/263.08	   mark(0)
744.30/263.08	   U101(mark(x0), x1, x2)
744.30/263.08	   U101(x0, mark(x1), x2)
744.30/263.08	   U101(x0, x1, mark(x2))
744.30/263.08	   U101(active(x0), x1, x2)
744.30/263.08	   U101(x0, active(x1), x2)
744.30/263.08	   U101(x0, x1, active(x2))
744.30/263.08	   U102(mark(x0), x1, x2)
744.30/263.08	   U102(x0, mark(x1), x2)
744.30/263.08	   U102(x0, x1, mark(x2))
744.30/263.08	   U102(active(x0), x1, x2)
744.30/263.08	   U102(x0, active(x1), x2)
744.30/263.08	   U102(x0, x1, active(x2))
744.30/263.08	   isNatKind(mark(x0))
744.30/263.08	   isNatKind(active(x0))
744.30/263.08	   U103(mark(x0), x1, x2)
744.30/263.08	   U103(x0, mark(x1), x2)
744.30/263.08	   U103(x0, x1, mark(x2))
744.30/263.08	   U103(active(x0), x1, x2)
744.30/263.08	   U103(x0, active(x1), x2)
744.30/263.08	   U103(x0, x1, active(x2))
744.30/263.08	   isNat(mark(x0))
744.30/263.08	   isNat(active(x0))
744.30/263.08	   U104(mark(x0), x1, x2)
744.30/263.08	   U104(x0, mark(x1), x2)
744.30/263.08	   U104(x0, x1, mark(x2))
744.30/263.08	   U104(active(x0), x1, x2)
744.30/263.08	   U104(x0, active(x1), x2)
744.30/263.08	   U104(x0, x1, active(x2))
744.30/263.08	   plus(mark(x0), x1)
744.30/263.08	   plus(x0, mark(x1))
744.30/263.08	   plus(active(x0), x1)
744.30/263.08	   plus(x0, active(x1))
744.30/263.08	   x(mark(x0), x1)
744.30/263.08	   x(x0, mark(x1))
744.30/263.08	   x(active(x0), x1)
744.30/263.08	   x(x0, active(x1))
744.30/263.08	   U11(mark(x0), x1, x2)
744.30/263.08	   U11(x0, mark(x1), x2)
744.30/263.08	   U11(x0, x1, mark(x2))
744.30/263.08	   U11(active(x0), x1, x2)
744.30/263.08	   U11(x0, active(x1), x2)
744.30/263.08	   U11(x0, x1, active(x2))
744.30/263.08	   U12(mark(x0), x1, x2)
744.30/263.08	   U12(x0, mark(x1), x2)
744.30/263.08	   U12(x0, x1, mark(x2))
744.30/263.08	   U12(active(x0), x1, x2)
744.30/263.08	   U12(x0, active(x1), x2)
744.30/263.08	   U12(x0, x1, active(x2))
744.30/263.08	   U13(mark(x0), x1, x2)
744.30/263.08	   U13(x0, mark(x1), x2)
744.30/263.08	   U13(x0, x1, mark(x2))
744.30/263.08	   U13(active(x0), x1, x2)
744.30/263.08	   U13(x0, active(x1), x2)
744.30/263.08	   U13(x0, x1, active(x2))
744.30/263.08	   U14(mark(x0), x1, x2)
744.30/263.08	   U14(x0, mark(x1), x2)
744.30/263.08	   U14(x0, x1, mark(x2))
744.30/263.08	   U14(active(x0), x1, x2)
744.30/263.08	   U14(x0, active(x1), x2)
744.30/263.08	   U14(x0, x1, active(x2))
744.30/263.08	   U15(mark(x0), x1)
744.30/263.08	   U15(x0, mark(x1))
744.30/263.08	   U15(active(x0), x1)
744.30/263.08	   U15(x0, active(x1))
744.30/263.08	   U16(mark(x0))
744.30/263.08	   U16(active(x0))
744.30/263.08	   U21(mark(x0), x1)
744.30/263.08	   U21(x0, mark(x1))
744.30/263.08	   U21(active(x0), x1)
744.30/263.08	   U21(x0, active(x1))
744.30/263.08	   U22(mark(x0), x1)
744.30/263.08	   U22(x0, mark(x1))
744.30/263.08	   U22(active(x0), x1)
744.30/263.08	   U22(x0, active(x1))
744.30/263.08	   U23(mark(x0))
744.30/263.08	   U23(active(x0))
744.30/263.08	   U31(mark(x0), x1, x2)
744.30/263.08	   U31(x0, mark(x1), x2)
744.30/263.08	   U31(x0, x1, mark(x2))
744.30/263.08	   U31(active(x0), x1, x2)
744.30/263.08	   U31(x0, active(x1), x2)
744.30/263.08	   U31(x0, x1, active(x2))
744.30/263.08	   U32(mark(x0), x1, x2)
744.30/263.08	   U32(x0, mark(x1), x2)
744.30/263.08	   U32(x0, x1, mark(x2))
744.30/263.08	   U32(active(x0), x1, x2)
744.30/263.08	   U32(x0, active(x1), x2)
744.30/263.08	   U32(x0, x1, active(x2))
744.30/263.08	   U33(mark(x0), x1, x2)
744.30/263.08	   U33(x0, mark(x1), x2)
744.30/263.08	   U33(x0, x1, mark(x2))
744.30/263.08	   U33(active(x0), x1, x2)
744.30/263.08	   U33(x0, active(x1), x2)
744.30/263.08	   U33(x0, x1, active(x2))
744.30/263.08	   U34(mark(x0), x1, x2)
744.30/263.08	   U34(x0, mark(x1), x2)
744.30/263.08	   U34(x0, x1, mark(x2))
744.30/263.08	   U34(active(x0), x1, x2)
744.30/263.08	   U34(x0, active(x1), x2)
744.30/263.08	   U34(x0, x1, active(x2))
744.30/263.08	   U35(mark(x0), x1)
744.30/263.08	   U35(x0, mark(x1))
744.30/263.08	   U35(active(x0), x1)
744.30/263.08	   U35(x0, active(x1))
744.30/263.08	   U36(mark(x0))
744.30/263.08	   U36(active(x0))
744.30/263.08	   U41(mark(x0), x1)
744.30/263.08	   U41(x0, mark(x1))
744.30/263.08	   U41(active(x0), x1)
744.30/263.08	   U41(x0, active(x1))
744.30/263.08	   U42(mark(x0))
744.30/263.08	   U42(active(x0))
744.30/263.08	   U51(mark(x0))
744.30/263.08	   U51(active(x0))
744.30/263.08	   U61(mark(x0), x1)
744.30/263.08	   U61(x0, mark(x1))
744.30/263.08	   U61(active(x0), x1)
744.30/263.08	   U61(x0, active(x1))
744.30/263.08	   U62(mark(x0))
744.30/263.08	   U62(active(x0))
744.30/263.08	   U71(mark(x0), x1)
744.30/263.08	   U71(x0, mark(x1))
744.30/263.08	   U71(active(x0), x1)
744.30/263.08	   U71(x0, active(x1))
744.30/263.08	   U72(mark(x0), x1)
744.30/263.08	   U72(x0, mark(x1))
744.30/263.08	   U72(active(x0), x1)
744.30/263.08	   U72(x0, active(x1))
744.30/263.08	   U81(mark(x0), x1, x2)
744.30/263.08	   U81(x0, mark(x1), x2)
744.30/263.08	   U81(x0, x1, mark(x2))
744.30/263.08	   U81(active(x0), x1, x2)
744.30/263.08	   U81(x0, active(x1), x2)
744.30/263.08	   U81(x0, x1, active(x2))
744.30/263.08	   U82(mark(x0), x1, x2)
744.30/263.08	   U82(x0, mark(x1), x2)
744.30/263.08	   U82(x0, x1, mark(x2))
744.30/263.08	   U82(active(x0), x1, x2)
744.30/263.08	   U82(x0, active(x1), x2)
744.30/263.08	   U82(x0, x1, active(x2))
744.30/263.08	   U83(mark(x0), x1, x2)
744.30/263.08	   U83(x0, mark(x1), x2)
744.30/263.08	   U83(x0, x1, mark(x2))
744.30/263.08	   U83(active(x0), x1, x2)
744.30/263.08	   U83(x0, active(x1), x2)
744.30/263.08	   U83(x0, x1, active(x2))
744.30/263.08	   U84(mark(x0), x1, x2)
744.30/263.08	   U84(x0, mark(x1), x2)
744.30/263.08	   U84(x0, x1, mark(x2))
744.30/263.08	   U84(active(x0), x1, x2)
744.30/263.08	   U84(x0, active(x1), x2)
744.30/263.08	   U84(x0, x1, active(x2))
744.30/263.08	   s(mark(x0))
744.30/263.08	   s(active(x0))
744.30/263.08	   U91(mark(x0), x1)
744.30/263.08	   U91(x0, mark(x1))
744.30/263.08	   U91(active(x0), x1)
744.30/263.08	   U91(x0, active(x1))
744.30/263.08	   U92(mark(x0))
744.30/263.08	   U92(active(x0))
744.30/263.08	
744.30/263.08	We have to consider all minimal (P,Q,R)-chains.
744.30/263.08	----------------------------------------
744.30/263.08	
744.30/263.08	(321) QDPOrderProof (EQUIVALENT)
744.30/263.08	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.08	
744.30/263.08	
744.30/263.08	The following pairs can be oriented strictly and are deleted.
744.30/263.08	
744.30/263.08	   MARK(U11(X1, X2, X3)) -> MARK(X1)
744.30/263.08	The remaining pairs can at least be oriented weakly.
744.30/263.08	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U12(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U11(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(tt) =  	[[0A]]
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(plus(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U41(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U13(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U14(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U15(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(isNat(x_1)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U21(x_1, x_2)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U22(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U23(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U31(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U33(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U34(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U42(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U51(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(s(x_1)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(x(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U102(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U101(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U103(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U104(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U81(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U82(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U83(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U84(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U91(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(0) =  	[[0A]]
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	
744.30/263.08	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.08	
744.30/263.08	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.08	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.08	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.08	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.08	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.08	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.08	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.08	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.08	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.08	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.08	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.08	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.08	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.08	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.08	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.08	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.08	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.08	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.08	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.08	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.08	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.08	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.08	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.08	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.08	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.08	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.08	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.08	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.08	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.08	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.08	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.08	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.08	   active(U72(tt, N)) -> mark(N)
744.30/263.08	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.08	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.08	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.08	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.08	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.08	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.08	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.08	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.08	   mark(s(X)) -> active(s(mark(X)))
744.30/263.08	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.08	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.08	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.08	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.08	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.08	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.08	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.08	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.08	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.08	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.08	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.08	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.08	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.08	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.08	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.08	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.08	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.08	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.08	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.08	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.08	   mark(isNat(X)) -> active(isNat(X))
744.30/263.08	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.08	   mark(tt) -> active(tt)
744.30/263.08	   mark(0) -> active(0)
744.30/263.08	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.08	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.08	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.08	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.08	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.08	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.08	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.08	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.08	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.08	   active(U16(tt)) -> mark(tt)
744.30/263.08	   active(U23(tt)) -> mark(tt)
744.30/263.08	   active(U36(tt)) -> mark(tt)
744.30/263.08	   active(U42(tt)) -> mark(tt)
744.30/263.08	   active(U51(tt)) -> mark(tt)
744.30/263.08	   active(U62(tt)) -> mark(tt)
744.30/263.08	   active(U92(tt)) -> mark(0)
744.30/263.08	   active(isNat(0)) -> mark(tt)
744.30/263.08	   active(isNatKind(0)) -> mark(tt)
744.30/263.08	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.08	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.08	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.08	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.08	   U16(active(X)) -> U16(X)
744.30/263.08	   U16(mark(X)) -> U16(X)
744.30/263.08	   U23(active(X)) -> U23(X)
744.30/263.08	   U23(mark(X)) -> U23(X)
744.30/263.08	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.08	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.08	   U36(active(X)) -> U36(X)
744.30/263.08	   U36(mark(X)) -> U36(X)
744.30/263.08	   U42(active(X)) -> U42(X)
744.30/263.08	   U42(mark(X)) -> U42(X)
744.30/263.08	   U62(active(X)) -> U62(X)
744.30/263.08	   U62(mark(X)) -> U62(X)
744.30/263.08	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.08	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.08	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.08	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.08	   s(active(X)) -> s(X)
744.30/263.08	   s(mark(X)) -> s(X)
744.30/263.08	   U92(active(X)) -> U92(X)
744.30/263.08	   U92(mark(X)) -> U92(X)
744.30/263.08	   U51(active(X)) -> U51(X)
744.30/263.08	   U51(mark(X)) -> U51(X)
744.30/263.08	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.08	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.08	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.08	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.08	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.08	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.08	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.08	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.08	   x(active(X1), X2) -> x(X1, X2)
744.30/263.08	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.08	
744.30/263.08	
744.30/263.08	----------------------------------------
744.30/263.08	
744.30/263.08	(322)
744.30/263.08	Obligation:
744.30/263.08	Q DP problem:
744.30/263.08	The TRS P consists of the following rules:
744.30/263.08	
744.30/263.08	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.08	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.08	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.08	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.08	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.08	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.08	   MARK(U16(X)) -> MARK(X)
744.30/263.08	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.08	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.08	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.08	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.08	   MARK(U23(X)) -> MARK(X)
744.30/263.08	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.08	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.08	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.08	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.08	   MARK(U42(X)) -> MARK(X)
744.30/263.08	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.08	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U51(X)) -> MARK(X)
744.30/263.08	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.08	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.08	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.08	
744.30/263.08	The TRS R consists of the following rules:
744.30/263.08	
744.30/263.08	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.08	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.08	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.08	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.08	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.08	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.08	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.08	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.08	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.08	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.08	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.08	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.08	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.08	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.08	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.08	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.08	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.08	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.08	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.08	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.08	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.08	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.08	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.08	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.08	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.08	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.08	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.08	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.08	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.08	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.08	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.08	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.08	   active(U72(tt, N)) -> mark(N)
744.30/263.08	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.08	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.08	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.08	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.08	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.08	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.08	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.08	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.08	   mark(s(X)) -> active(s(mark(X)))
744.30/263.08	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.08	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.08	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.08	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.08	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.08	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.08	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.08	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.08	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.08	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.08	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.08	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.08	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.08	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.08	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.08	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.08	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.08	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.08	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.08	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.08	   mark(isNat(X)) -> active(isNat(X))
744.30/263.08	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.08	   mark(tt) -> active(tt)
744.30/263.08	   mark(0) -> active(0)
744.30/263.08	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.08	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.08	   active(U16(tt)) -> mark(tt)
744.30/263.08	   active(U23(tt)) -> mark(tt)
744.30/263.08	   active(U36(tt)) -> mark(tt)
744.30/263.08	   active(U42(tt)) -> mark(tt)
744.30/263.08	   active(U51(tt)) -> mark(tt)
744.30/263.08	   active(U62(tt)) -> mark(tt)
744.30/263.08	   active(U92(tt)) -> mark(0)
744.30/263.08	   active(isNat(0)) -> mark(tt)
744.30/263.08	   active(isNatKind(0)) -> mark(tt)
744.30/263.08	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.08	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.08	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.08	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.08	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.08	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.08	   U16(active(X)) -> U16(X)
744.30/263.08	   U16(mark(X)) -> U16(X)
744.30/263.08	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.08	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.08	   U23(active(X)) -> U23(X)
744.30/263.08	   U23(mark(X)) -> U23(X)
744.30/263.08	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.08	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.08	   U36(active(X)) -> U36(X)
744.30/263.08	   U36(mark(X)) -> U36(X)
744.30/263.08	   U42(active(X)) -> U42(X)
744.30/263.08	   U42(mark(X)) -> U42(X)
744.30/263.08	   U62(active(X)) -> U62(X)
744.30/263.08	   U62(mark(X)) -> U62(X)
744.30/263.08	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.08	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.08	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.08	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.08	   s(active(X)) -> s(X)
744.30/263.08	   s(mark(X)) -> s(X)
744.30/263.08	   U92(active(X)) -> U92(X)
744.30/263.08	   U92(mark(X)) -> U92(X)
744.30/263.08	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.08	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.08	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.08	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.08	   U51(active(X)) -> U51(X)
744.30/263.08	   U51(mark(X)) -> U51(X)
744.30/263.08	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.08	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.08	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.08	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.08	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.08	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.08	   x(active(X1), X2) -> x(X1, X2)
744.30/263.08	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.08	
744.30/263.08	The set Q consists of the following terms:
744.30/263.08	
744.30/263.08	   active(U101(tt, x0, x1))
744.30/263.08	   active(U102(tt, x0, x1))
744.30/263.08	   active(U103(tt, x0, x1))
744.30/263.08	   active(U104(tt, x0, x1))
744.30/263.08	   active(U11(tt, x0, x1))
744.30/263.08	   active(U12(tt, x0, x1))
744.30/263.08	   active(U13(tt, x0, x1))
744.30/263.08	   active(U14(tt, x0, x1))
744.30/263.08	   active(U15(tt, x0))
744.30/263.08	   active(U16(tt))
744.30/263.08	   active(U21(tt, x0))
744.30/263.08	   active(U22(tt, x0))
744.30/263.08	   active(U23(tt))
744.30/263.08	   active(U31(tt, x0, x1))
744.30/263.08	   active(U32(tt, x0, x1))
744.30/263.08	   active(U33(tt, x0, x1))
744.30/263.08	   active(U34(tt, x0, x1))
744.30/263.08	   active(U35(tt, x0))
744.30/263.08	   active(U36(tt))
744.30/263.08	   active(U41(tt, x0))
744.30/263.08	   active(U42(tt))
744.30/263.08	   active(U51(tt))
744.30/263.08	   active(U61(tt, x0))
744.30/263.08	   active(U62(tt))
744.30/263.08	   active(U71(tt, x0))
744.30/263.08	   active(U72(tt, x0))
744.30/263.08	   active(U81(tt, x0, x1))
744.30/263.08	   active(U82(tt, x0, x1))
744.30/263.08	   active(U83(tt, x0, x1))
744.30/263.08	   active(U84(tt, x0, x1))
744.30/263.08	   active(U91(tt, x0))
744.30/263.08	   active(U92(tt))
744.30/263.08	   active(isNat(0))
744.30/263.08	   active(isNat(plus(x0, x1)))
744.30/263.08	   active(isNat(s(x0)))
744.30/263.08	   active(isNat(x(x0, x1)))
744.30/263.08	   active(isNatKind(0))
744.30/263.08	   active(isNatKind(plus(x0, x1)))
744.30/263.08	   active(isNatKind(s(x0)))
744.30/263.08	   active(isNatKind(x(x0, x1)))
744.30/263.08	   active(plus(x0, 0))
744.30/263.08	   active(plus(x0, s(x1)))
744.30/263.08	   active(x(x0, 0))
744.30/263.08	   active(x(x0, s(x1)))
744.30/263.08	   mark(U101(x0, x1, x2))
744.30/263.08	   mark(tt)
744.30/263.08	   mark(U102(x0, x1, x2))
744.30/263.08	   mark(isNatKind(x0))
744.30/263.08	   mark(U103(x0, x1, x2))
744.30/263.08	   mark(isNat(x0))
744.30/263.08	   mark(U104(x0, x1, x2))
744.30/263.08	   mark(plus(x0, x1))
744.30/263.08	   mark(x(x0, x1))
744.30/263.08	   mark(U11(x0, x1, x2))
744.30/263.08	   mark(U12(x0, x1, x2))
744.30/263.08	   mark(U13(x0, x1, x2))
744.30/263.08	   mark(U14(x0, x1, x2))
744.30/263.08	   mark(U15(x0, x1))
744.30/263.08	   mark(U16(x0))
744.30/263.08	   mark(U21(x0, x1))
744.30/263.08	   mark(U22(x0, x1))
744.30/263.08	   mark(U23(x0))
744.30/263.08	   mark(U31(x0, x1, x2))
744.30/263.08	   mark(U32(x0, x1, x2))
744.30/263.08	   mark(U33(x0, x1, x2))
744.30/263.08	   mark(U34(x0, x1, x2))
744.30/263.08	   mark(U35(x0, x1))
744.30/263.08	   mark(U36(x0))
744.30/263.08	   mark(U41(x0, x1))
744.30/263.08	   mark(U42(x0))
744.30/263.08	   mark(U51(x0))
744.30/263.08	   mark(U61(x0, x1))
744.30/263.08	   mark(U62(x0))
744.30/263.08	   mark(U71(x0, x1))
744.30/263.08	   mark(U72(x0, x1))
744.30/263.08	   mark(U81(x0, x1, x2))
744.30/263.08	   mark(U82(x0, x1, x2))
744.30/263.08	   mark(U83(x0, x1, x2))
744.30/263.08	   mark(U84(x0, x1, x2))
744.30/263.08	   mark(s(x0))
744.30/263.08	   mark(U91(x0, x1))
744.30/263.08	   mark(U92(x0))
744.30/263.08	   mark(0)
744.30/263.08	   U101(mark(x0), x1, x2)
744.30/263.08	   U101(x0, mark(x1), x2)
744.30/263.08	   U101(x0, x1, mark(x2))
744.30/263.08	   U101(active(x0), x1, x2)
744.30/263.08	   U101(x0, active(x1), x2)
744.30/263.08	   U101(x0, x1, active(x2))
744.30/263.08	   U102(mark(x0), x1, x2)
744.30/263.08	   U102(x0, mark(x1), x2)
744.30/263.08	   U102(x0, x1, mark(x2))
744.30/263.08	   U102(active(x0), x1, x2)
744.30/263.08	   U102(x0, active(x1), x2)
744.30/263.08	   U102(x0, x1, active(x2))
744.30/263.08	   isNatKind(mark(x0))
744.30/263.08	   isNatKind(active(x0))
744.30/263.08	   U103(mark(x0), x1, x2)
744.30/263.08	   U103(x0, mark(x1), x2)
744.30/263.08	   U103(x0, x1, mark(x2))
744.30/263.08	   U103(active(x0), x1, x2)
744.30/263.08	   U103(x0, active(x1), x2)
744.30/263.08	   U103(x0, x1, active(x2))
744.30/263.08	   isNat(mark(x0))
744.30/263.08	   isNat(active(x0))
744.30/263.08	   U104(mark(x0), x1, x2)
744.30/263.08	   U104(x0, mark(x1), x2)
744.30/263.08	   U104(x0, x1, mark(x2))
744.30/263.08	   U104(active(x0), x1, x2)
744.30/263.08	   U104(x0, active(x1), x2)
744.30/263.08	   U104(x0, x1, active(x2))
744.30/263.08	   plus(mark(x0), x1)
744.30/263.08	   plus(x0, mark(x1))
744.30/263.08	   plus(active(x0), x1)
744.30/263.08	   plus(x0, active(x1))
744.30/263.08	   x(mark(x0), x1)
744.30/263.08	   x(x0, mark(x1))
744.30/263.08	   x(active(x0), x1)
744.30/263.08	   x(x0, active(x1))
744.30/263.08	   U11(mark(x0), x1, x2)
744.30/263.08	   U11(x0, mark(x1), x2)
744.30/263.08	   U11(x0, x1, mark(x2))
744.30/263.08	   U11(active(x0), x1, x2)
744.30/263.08	   U11(x0, active(x1), x2)
744.30/263.08	   U11(x0, x1, active(x2))
744.30/263.08	   U12(mark(x0), x1, x2)
744.30/263.08	   U12(x0, mark(x1), x2)
744.30/263.08	   U12(x0, x1, mark(x2))
744.30/263.08	   U12(active(x0), x1, x2)
744.30/263.08	   U12(x0, active(x1), x2)
744.30/263.08	   U12(x0, x1, active(x2))
744.30/263.08	   U13(mark(x0), x1, x2)
744.30/263.08	   U13(x0, mark(x1), x2)
744.30/263.08	   U13(x0, x1, mark(x2))
744.30/263.08	   U13(active(x0), x1, x2)
744.30/263.08	   U13(x0, active(x1), x2)
744.30/263.08	   U13(x0, x1, active(x2))
744.30/263.08	   U14(mark(x0), x1, x2)
744.30/263.08	   U14(x0, mark(x1), x2)
744.30/263.08	   U14(x0, x1, mark(x2))
744.30/263.08	   U14(active(x0), x1, x2)
744.30/263.08	   U14(x0, active(x1), x2)
744.30/263.08	   U14(x0, x1, active(x2))
744.30/263.08	   U15(mark(x0), x1)
744.30/263.08	   U15(x0, mark(x1))
744.30/263.08	   U15(active(x0), x1)
744.30/263.08	   U15(x0, active(x1))
744.30/263.08	   U16(mark(x0))
744.30/263.08	   U16(active(x0))
744.30/263.08	   U21(mark(x0), x1)
744.30/263.08	   U21(x0, mark(x1))
744.30/263.08	   U21(active(x0), x1)
744.30/263.08	   U21(x0, active(x1))
744.30/263.08	   U22(mark(x0), x1)
744.30/263.08	   U22(x0, mark(x1))
744.30/263.08	   U22(active(x0), x1)
744.30/263.08	   U22(x0, active(x1))
744.30/263.08	   U23(mark(x0))
744.30/263.08	   U23(active(x0))
744.30/263.08	   U31(mark(x0), x1, x2)
744.30/263.08	   U31(x0, mark(x1), x2)
744.30/263.08	   U31(x0, x1, mark(x2))
744.30/263.08	   U31(active(x0), x1, x2)
744.30/263.08	   U31(x0, active(x1), x2)
744.30/263.08	   U31(x0, x1, active(x2))
744.30/263.08	   U32(mark(x0), x1, x2)
744.30/263.08	   U32(x0, mark(x1), x2)
744.30/263.08	   U32(x0, x1, mark(x2))
744.30/263.08	   U32(active(x0), x1, x2)
744.30/263.08	   U32(x0, active(x1), x2)
744.30/263.08	   U32(x0, x1, active(x2))
744.30/263.08	   U33(mark(x0), x1, x2)
744.30/263.08	   U33(x0, mark(x1), x2)
744.30/263.08	   U33(x0, x1, mark(x2))
744.30/263.08	   U33(active(x0), x1, x2)
744.30/263.08	   U33(x0, active(x1), x2)
744.30/263.08	   U33(x0, x1, active(x2))
744.30/263.08	   U34(mark(x0), x1, x2)
744.30/263.08	   U34(x0, mark(x1), x2)
744.30/263.08	   U34(x0, x1, mark(x2))
744.30/263.08	   U34(active(x0), x1, x2)
744.30/263.08	   U34(x0, active(x1), x2)
744.30/263.08	   U34(x0, x1, active(x2))
744.30/263.08	   U35(mark(x0), x1)
744.30/263.08	   U35(x0, mark(x1))
744.30/263.08	   U35(active(x0), x1)
744.30/263.08	   U35(x0, active(x1))
744.30/263.08	   U36(mark(x0))
744.30/263.08	   U36(active(x0))
744.30/263.08	   U41(mark(x0), x1)
744.30/263.08	   U41(x0, mark(x1))
744.30/263.08	   U41(active(x0), x1)
744.30/263.08	   U41(x0, active(x1))
744.30/263.08	   U42(mark(x0))
744.30/263.08	   U42(active(x0))
744.30/263.08	   U51(mark(x0))
744.30/263.08	   U51(active(x0))
744.30/263.08	   U61(mark(x0), x1)
744.30/263.08	   U61(x0, mark(x1))
744.30/263.08	   U61(active(x0), x1)
744.30/263.08	   U61(x0, active(x1))
744.30/263.08	   U62(mark(x0))
744.30/263.08	   U62(active(x0))
744.30/263.08	   U71(mark(x0), x1)
744.30/263.08	   U71(x0, mark(x1))
744.30/263.08	   U71(active(x0), x1)
744.30/263.08	   U71(x0, active(x1))
744.30/263.08	   U72(mark(x0), x1)
744.30/263.08	   U72(x0, mark(x1))
744.30/263.08	   U72(active(x0), x1)
744.30/263.08	   U72(x0, active(x1))
744.30/263.08	   U81(mark(x0), x1, x2)
744.30/263.08	   U81(x0, mark(x1), x2)
744.30/263.08	   U81(x0, x1, mark(x2))
744.30/263.08	   U81(active(x0), x1, x2)
744.30/263.08	   U81(x0, active(x1), x2)
744.30/263.08	   U81(x0, x1, active(x2))
744.30/263.08	   U82(mark(x0), x1, x2)
744.30/263.08	   U82(x0, mark(x1), x2)
744.30/263.08	   U82(x0, x1, mark(x2))
744.30/263.08	   U82(active(x0), x1, x2)
744.30/263.08	   U82(x0, active(x1), x2)
744.30/263.08	   U82(x0, x1, active(x2))
744.30/263.08	   U83(mark(x0), x1, x2)
744.30/263.08	   U83(x0, mark(x1), x2)
744.30/263.08	   U83(x0, x1, mark(x2))
744.30/263.08	   U83(active(x0), x1, x2)
744.30/263.08	   U83(x0, active(x1), x2)
744.30/263.08	   U83(x0, x1, active(x2))
744.30/263.08	   U84(mark(x0), x1, x2)
744.30/263.08	   U84(x0, mark(x1), x2)
744.30/263.08	   U84(x0, x1, mark(x2))
744.30/263.08	   U84(active(x0), x1, x2)
744.30/263.08	   U84(x0, active(x1), x2)
744.30/263.08	   U84(x0, x1, active(x2))
744.30/263.08	   s(mark(x0))
744.30/263.08	   s(active(x0))
744.30/263.08	   U91(mark(x0), x1)
744.30/263.08	   U91(x0, mark(x1))
744.30/263.08	   U91(active(x0), x1)
744.30/263.08	   U91(x0, active(x1))
744.30/263.08	   U92(mark(x0))
744.30/263.08	   U92(active(x0))
744.30/263.08	
744.30/263.08	We have to consider all minimal (P,Q,R)-chains.
744.30/263.08	----------------------------------------
744.30/263.08	
744.30/263.08	(323) QDPOrderProof (EQUIVALENT)
744.30/263.08	We use the reduction pair processor [LPAR04,JAR06].
744.30/263.08	
744.30/263.08	
744.30/263.08	The following pairs can be oriented strictly and are deleted.
744.30/263.08	
744.30/263.08	   MARK(U35(X1, X2)) -> MARK(X1)
744.30/263.08	The remaining pairs can at least be oriented weakly.
744.30/263.08	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(MARK(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(ACTIVE(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(tt) =  	[[0A]]
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U15(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U22(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U31(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U33(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U34(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U101(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U62(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(U92(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	   <<<
744.30/263.08	 POL(0) =  	[[0A]]
744.30/263.08	>>>
744.30/263.08	
744.30/263.08	
744.30/263.08	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.30/263.08	
744.30/263.08	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.08	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.08	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.08	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.08	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.08	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.08	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.08	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.08	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.08	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.08	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.08	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.08	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.08	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.08	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.08	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.08	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.08	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.08	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.08	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.08	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.08	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.08	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.08	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.08	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.08	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.08	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.08	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.08	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.08	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.08	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.08	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.08	   active(U72(tt, N)) -> mark(N)
744.30/263.08	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.08	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.08	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.08	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.08	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.08	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.08	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.08	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.08	   mark(s(X)) -> active(s(mark(X)))
744.30/263.08	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.08	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.08	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.08	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.08	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.08	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.08	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.08	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.08	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.08	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.08	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.08	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.08	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.08	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.08	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.08	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.08	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.08	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.08	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.08	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.08	   mark(isNat(X)) -> active(isNat(X))
744.30/263.08	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.08	   mark(tt) -> active(tt)
744.30/263.08	   mark(0) -> active(0)
744.30/263.08	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.08	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.08	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.08	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.08	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.08	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.08	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.08	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.08	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.08	   active(U16(tt)) -> mark(tt)
744.30/263.08	   active(U23(tt)) -> mark(tt)
744.30/263.08	   active(U36(tt)) -> mark(tt)
744.30/263.08	   active(U42(tt)) -> mark(tt)
744.30/263.08	   active(U51(tt)) -> mark(tt)
744.30/263.08	   active(U62(tt)) -> mark(tt)
744.30/263.08	   active(U92(tt)) -> mark(0)
744.30/263.08	   active(isNat(0)) -> mark(tt)
744.30/263.08	   active(isNatKind(0)) -> mark(tt)
744.30/263.08	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.08	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.08	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.08	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.08	   U16(active(X)) -> U16(X)
744.30/263.08	   U16(mark(X)) -> U16(X)
744.30/263.08	   U23(active(X)) -> U23(X)
744.30/263.08	   U23(mark(X)) -> U23(X)
744.30/263.08	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.08	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.08	   U36(active(X)) -> U36(X)
744.30/263.08	   U36(mark(X)) -> U36(X)
744.30/263.08	   U42(active(X)) -> U42(X)
744.30/263.08	   U42(mark(X)) -> U42(X)
744.30/263.08	   U62(active(X)) -> U62(X)
744.30/263.08	   U62(mark(X)) -> U62(X)
744.30/263.08	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.08	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.08	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.08	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.08	   s(active(X)) -> s(X)
744.30/263.08	   s(mark(X)) -> s(X)
744.30/263.08	   U92(active(X)) -> U92(X)
744.30/263.08	   U92(mark(X)) -> U92(X)
744.30/263.08	   U51(active(X)) -> U51(X)
744.30/263.08	   U51(mark(X)) -> U51(X)
744.30/263.08	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.08	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.08	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.08	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.08	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.08	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.08	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.08	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.08	   x(active(X1), X2) -> x(X1, X2)
744.30/263.08	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.08	
744.30/263.08	
744.30/263.08	----------------------------------------
744.30/263.08	
744.30/263.08	(324)
744.30/263.08	Obligation:
744.30/263.08	Q DP problem:
744.30/263.08	The TRS P consists of the following rules:
744.30/263.08	
744.30/263.08	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.08	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.08	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.08	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.08	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.08	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.08	   MARK(U16(X)) -> MARK(X)
744.30/263.08	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.08	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.08	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.08	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.08	   MARK(U23(X)) -> MARK(X)
744.30/263.08	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.08	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.08	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.08	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.08	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U34(tt, V1, V2)) -> MARK(U35(isNat(V1), V2))
744.30/263.08	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.08	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.08	   MARK(U42(X)) -> MARK(X)
744.30/263.08	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.08	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.08	   MARK(U51(X)) -> MARK(X)
744.30/263.08	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.08	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.08	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.08	
744.30/263.08	The TRS R consists of the following rules:
744.30/263.08	
744.30/263.08	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.08	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.08	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.08	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.08	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.08	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.08	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.08	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.08	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.08	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.08	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.08	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.08	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.08	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.08	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.08	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.08	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.08	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.08	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.08	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.08	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.08	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.08	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.08	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.08	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.08	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.08	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.08	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.08	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.08	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.08	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.08	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.08	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.08	   active(U72(tt, N)) -> mark(N)
744.30/263.08	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.08	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.08	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.08	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.08	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.08	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.08	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.08	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.08	   mark(s(X)) -> active(s(mark(X)))
744.30/263.08	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.08	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.08	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.08	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.08	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.08	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.08	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.08	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.08	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.08	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.08	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.08	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.08	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.08	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.08	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.08	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.08	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.08	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.08	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.08	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.08	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.08	   mark(isNat(X)) -> active(isNat(X))
744.30/263.08	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.08	   mark(tt) -> active(tt)
744.30/263.08	   mark(0) -> active(0)
744.30/263.08	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.08	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.08	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.08	   active(U16(tt)) -> mark(tt)
744.30/263.08	   active(U23(tt)) -> mark(tt)
744.30/263.08	   active(U36(tt)) -> mark(tt)
744.30/263.08	   active(U42(tt)) -> mark(tt)
744.30/263.08	   active(U51(tt)) -> mark(tt)
744.30/263.08	   active(U62(tt)) -> mark(tt)
744.30/263.08	   active(U92(tt)) -> mark(0)
744.30/263.08	   active(isNat(0)) -> mark(tt)
744.30/263.08	   active(isNatKind(0)) -> mark(tt)
744.30/263.08	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.08	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.08	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.08	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.08	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.08	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.08	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.08	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.08	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.08	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.08	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.08	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.08	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.08	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.08	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.08	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.08	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.08	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.08	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.08	   U16(active(X)) -> U16(X)
744.30/263.08	   U16(mark(X)) -> U16(X)
744.30/263.08	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.08	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.08	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.08	   U23(active(X)) -> U23(X)
744.30/263.08	   U23(mark(X)) -> U23(X)
744.30/263.08	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.08	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.08	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.08	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.08	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.08	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.08	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.08	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.08	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.08	   U36(active(X)) -> U36(X)
744.30/263.08	   U36(mark(X)) -> U36(X)
744.30/263.08	   U42(active(X)) -> U42(X)
744.30/263.08	   U42(mark(X)) -> U42(X)
744.30/263.08	   U62(active(X)) -> U62(X)
744.30/263.08	   U62(mark(X)) -> U62(X)
744.30/263.08	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.08	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.08	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.08	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.08	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.08	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.08	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.08	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.08	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.08	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.08	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.08	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.08	   s(active(X)) -> s(X)
744.30/263.08	   s(mark(X)) -> s(X)
744.30/263.08	   U92(active(X)) -> U92(X)
744.30/263.08	   U92(mark(X)) -> U92(X)
744.30/263.08	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.08	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.08	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.08	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.08	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.08	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.08	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.08	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.08	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.08	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.08	   U51(active(X)) -> U51(X)
744.30/263.08	   U51(mark(X)) -> U51(X)
744.30/263.08	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.08	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.08	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.08	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.08	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.08	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.08	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.08	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.08	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.08	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.08	   x(active(X1), X2) -> x(X1, X2)
744.30/263.08	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.08	
744.30/263.08	The set Q consists of the following terms:
744.30/263.08	
744.30/263.08	   active(U101(tt, x0, x1))
744.30/263.08	   active(U102(tt, x0, x1))
744.30/263.08	   active(U103(tt, x0, x1))
744.30/263.08	   active(U104(tt, x0, x1))
744.30/263.08	   active(U11(tt, x0, x1))
744.30/263.08	   active(U12(tt, x0, x1))
744.30/263.08	   active(U13(tt, x0, x1))
744.30/263.08	   active(U14(tt, x0, x1))
744.30/263.08	   active(U15(tt, x0))
744.30/263.08	   active(U16(tt))
744.30/263.08	   active(U21(tt, x0))
744.30/263.08	   active(U22(tt, x0))
744.30/263.08	   active(U23(tt))
744.30/263.08	   active(U31(tt, x0, x1))
744.30/263.08	   active(U32(tt, x0, x1))
744.30/263.08	   active(U33(tt, x0, x1))
744.30/263.08	   active(U34(tt, x0, x1))
744.30/263.08	   active(U35(tt, x0))
744.30/263.08	   active(U36(tt))
744.30/263.09	   active(U41(tt, x0))
744.30/263.09	   active(U42(tt))
744.30/263.09	   active(U51(tt))
744.30/263.09	   active(U61(tt, x0))
744.30/263.09	   active(U62(tt))
744.30/263.09	   active(U71(tt, x0))
744.30/263.09	   active(U72(tt, x0))
744.30/263.09	   active(U81(tt, x0, x1))
744.30/263.09	   active(U82(tt, x0, x1))
744.30/263.09	   active(U83(tt, x0, x1))
744.30/263.09	   active(U84(tt, x0, x1))
744.30/263.09	   active(U91(tt, x0))
744.30/263.09	   active(U92(tt))
744.30/263.09	   active(isNat(0))
744.30/263.09	   active(isNat(plus(x0, x1)))
744.30/263.09	   active(isNat(s(x0)))
744.30/263.09	   active(isNat(x(x0, x1)))
744.30/263.09	   active(isNatKind(0))
744.30/263.09	   active(isNatKind(plus(x0, x1)))
744.30/263.09	   active(isNatKind(s(x0)))
744.30/263.09	   active(isNatKind(x(x0, x1)))
744.30/263.09	   active(plus(x0, 0))
744.30/263.09	   active(plus(x0, s(x1)))
744.30/263.09	   active(x(x0, 0))
744.30/263.09	   active(x(x0, s(x1)))
744.30/263.09	   mark(U101(x0, x1, x2))
744.30/263.09	   mark(tt)
744.30/263.09	   mark(U102(x0, x1, x2))
744.30/263.09	   mark(isNatKind(x0))
744.30/263.09	   mark(U103(x0, x1, x2))
744.30/263.09	   mark(isNat(x0))
744.30/263.09	   mark(U104(x0, x1, x2))
744.30/263.09	   mark(plus(x0, x1))
744.30/263.09	   mark(x(x0, x1))
744.30/263.09	   mark(U11(x0, x1, x2))
744.30/263.09	   mark(U12(x0, x1, x2))
744.30/263.09	   mark(U13(x0, x1, x2))
744.30/263.09	   mark(U14(x0, x1, x2))
744.30/263.09	   mark(U15(x0, x1))
744.30/263.09	   mark(U16(x0))
744.30/263.09	   mark(U21(x0, x1))
744.30/263.09	   mark(U22(x0, x1))
744.30/263.09	   mark(U23(x0))
744.30/263.09	   mark(U31(x0, x1, x2))
744.30/263.09	   mark(U32(x0, x1, x2))
744.30/263.09	   mark(U33(x0, x1, x2))
744.30/263.09	   mark(U34(x0, x1, x2))
744.30/263.09	   mark(U35(x0, x1))
744.30/263.09	   mark(U36(x0))
744.30/263.09	   mark(U41(x0, x1))
744.30/263.09	   mark(U42(x0))
744.30/263.09	   mark(U51(x0))
744.30/263.09	   mark(U61(x0, x1))
744.30/263.09	   mark(U62(x0))
744.30/263.09	   mark(U71(x0, x1))
744.30/263.09	   mark(U72(x0, x1))
744.30/263.09	   mark(U81(x0, x1, x2))
744.30/263.09	   mark(U82(x0, x1, x2))
744.30/263.09	   mark(U83(x0, x1, x2))
744.30/263.09	   mark(U84(x0, x1, x2))
744.30/263.09	   mark(s(x0))
744.30/263.09	   mark(U91(x0, x1))
744.30/263.09	   mark(U92(x0))
744.30/263.09	   mark(0)
744.30/263.09	   U101(mark(x0), x1, x2)
744.30/263.09	   U101(x0, mark(x1), x2)
744.30/263.09	   U101(x0, x1, mark(x2))
744.30/263.09	   U101(active(x0), x1, x2)
744.30/263.09	   U101(x0, active(x1), x2)
744.30/263.09	   U101(x0, x1, active(x2))
744.30/263.09	   U102(mark(x0), x1, x2)
744.30/263.09	   U102(x0, mark(x1), x2)
744.30/263.09	   U102(x0, x1, mark(x2))
744.30/263.09	   U102(active(x0), x1, x2)
744.30/263.09	   U102(x0, active(x1), x2)
744.30/263.09	   U102(x0, x1, active(x2))
744.30/263.09	   isNatKind(mark(x0))
744.30/263.09	   isNatKind(active(x0))
744.30/263.09	   U103(mark(x0), x1, x2)
744.30/263.09	   U103(x0, mark(x1), x2)
744.30/263.09	   U103(x0, x1, mark(x2))
744.30/263.09	   U103(active(x0), x1, x2)
744.30/263.09	   U103(x0, active(x1), x2)
744.30/263.09	   U103(x0, x1, active(x2))
744.30/263.09	   isNat(mark(x0))
744.30/263.09	   isNat(active(x0))
744.30/263.09	   U104(mark(x0), x1, x2)
744.30/263.09	   U104(x0, mark(x1), x2)
744.30/263.09	   U104(x0, x1, mark(x2))
744.30/263.09	   U104(active(x0), x1, x2)
744.30/263.09	   U104(x0, active(x1), x2)
744.30/263.09	   U104(x0, x1, active(x2))
744.30/263.09	   plus(mark(x0), x1)
744.30/263.09	   plus(x0, mark(x1))
744.30/263.09	   plus(active(x0), x1)
744.30/263.09	   plus(x0, active(x1))
744.30/263.09	   x(mark(x0), x1)
744.30/263.09	   x(x0, mark(x1))
744.30/263.09	   x(active(x0), x1)
744.30/263.09	   x(x0, active(x1))
744.30/263.09	   U11(mark(x0), x1, x2)
744.30/263.09	   U11(x0, mark(x1), x2)
744.30/263.09	   U11(x0, x1, mark(x2))
744.30/263.09	   U11(active(x0), x1, x2)
744.30/263.09	   U11(x0, active(x1), x2)
744.30/263.09	   U11(x0, x1, active(x2))
744.30/263.09	   U12(mark(x0), x1, x2)
744.30/263.09	   U12(x0, mark(x1), x2)
744.30/263.09	   U12(x0, x1, mark(x2))
744.30/263.09	   U12(active(x0), x1, x2)
744.30/263.09	   U12(x0, active(x1), x2)
744.30/263.09	   U12(x0, x1, active(x2))
744.30/263.09	   U13(mark(x0), x1, x2)
744.30/263.09	   U13(x0, mark(x1), x2)
744.30/263.09	   U13(x0, x1, mark(x2))
744.30/263.09	   U13(active(x0), x1, x2)
744.30/263.09	   U13(x0, active(x1), x2)
744.30/263.09	   U13(x0, x1, active(x2))
744.30/263.09	   U14(mark(x0), x1, x2)
744.30/263.09	   U14(x0, mark(x1), x2)
744.30/263.09	   U14(x0, x1, mark(x2))
744.30/263.09	   U14(active(x0), x1, x2)
744.30/263.09	   U14(x0, active(x1), x2)
744.30/263.09	   U14(x0, x1, active(x2))
744.30/263.09	   U15(mark(x0), x1)
744.30/263.09	   U15(x0, mark(x1))
744.30/263.09	   U15(active(x0), x1)
744.30/263.09	   U15(x0, active(x1))
744.30/263.09	   U16(mark(x0))
744.30/263.09	   U16(active(x0))
744.30/263.09	   U21(mark(x0), x1)
744.30/263.09	   U21(x0, mark(x1))
744.30/263.09	   U21(active(x0), x1)
744.30/263.09	   U21(x0, active(x1))
744.30/263.09	   U22(mark(x0), x1)
744.30/263.09	   U22(x0, mark(x1))
744.30/263.09	   U22(active(x0), x1)
744.30/263.09	   U22(x0, active(x1))
744.30/263.09	   U23(mark(x0))
744.30/263.09	   U23(active(x0))
744.30/263.09	   U31(mark(x0), x1, x2)
744.30/263.09	   U31(x0, mark(x1), x2)
744.30/263.09	   U31(x0, x1, mark(x2))
744.30/263.09	   U31(active(x0), x1, x2)
744.30/263.09	   U31(x0, active(x1), x2)
744.30/263.09	   U31(x0, x1, active(x2))
744.30/263.09	   U32(mark(x0), x1, x2)
744.30/263.09	   U32(x0, mark(x1), x2)
744.30/263.09	   U32(x0, x1, mark(x2))
744.30/263.09	   U32(active(x0), x1, x2)
744.30/263.09	   U32(x0, active(x1), x2)
744.30/263.09	   U32(x0, x1, active(x2))
744.30/263.09	   U33(mark(x0), x1, x2)
744.30/263.09	   U33(x0, mark(x1), x2)
744.30/263.09	   U33(x0, x1, mark(x2))
744.30/263.09	   U33(active(x0), x1, x2)
744.30/263.09	   U33(x0, active(x1), x2)
744.30/263.09	   U33(x0, x1, active(x2))
744.30/263.09	   U34(mark(x0), x1, x2)
744.30/263.09	   U34(x0, mark(x1), x2)
744.30/263.09	   U34(x0, x1, mark(x2))
744.30/263.09	   U34(active(x0), x1, x2)
744.30/263.09	   U34(x0, active(x1), x2)
744.30/263.09	   U34(x0, x1, active(x2))
744.30/263.09	   U35(mark(x0), x1)
744.30/263.09	   U35(x0, mark(x1))
744.30/263.09	   U35(active(x0), x1)
744.30/263.09	   U35(x0, active(x1))
744.30/263.09	   U36(mark(x0))
744.30/263.09	   U36(active(x0))
744.30/263.09	   U41(mark(x0), x1)
744.30/263.09	   U41(x0, mark(x1))
744.30/263.09	   U41(active(x0), x1)
744.30/263.09	   U41(x0, active(x1))
744.30/263.09	   U42(mark(x0))
744.30/263.09	   U42(active(x0))
744.30/263.09	   U51(mark(x0))
744.30/263.09	   U51(active(x0))
744.30/263.09	   U61(mark(x0), x1)
744.30/263.09	   U61(x0, mark(x1))
744.30/263.09	   U61(active(x0), x1)
744.30/263.09	   U61(x0, active(x1))
744.30/263.09	   U62(mark(x0))
744.30/263.09	   U62(active(x0))
744.30/263.09	   U71(mark(x0), x1)
744.30/263.09	   U71(x0, mark(x1))
744.30/263.09	   U71(active(x0), x1)
744.30/263.09	   U71(x0, active(x1))
744.30/263.09	   U72(mark(x0), x1)
744.30/263.09	   U72(x0, mark(x1))
744.30/263.09	   U72(active(x0), x1)
744.30/263.09	   U72(x0, active(x1))
744.30/263.09	   U81(mark(x0), x1, x2)
744.30/263.09	   U81(x0, mark(x1), x2)
744.30/263.09	   U81(x0, x1, mark(x2))
744.30/263.09	   U81(active(x0), x1, x2)
744.30/263.09	   U81(x0, active(x1), x2)
744.30/263.09	   U81(x0, x1, active(x2))
744.30/263.09	   U82(mark(x0), x1, x2)
744.30/263.09	   U82(x0, mark(x1), x2)
744.30/263.09	   U82(x0, x1, mark(x2))
744.30/263.09	   U82(active(x0), x1, x2)
744.30/263.09	   U82(x0, active(x1), x2)
744.30/263.09	   U82(x0, x1, active(x2))
744.30/263.09	   U83(mark(x0), x1, x2)
744.30/263.09	   U83(x0, mark(x1), x2)
744.30/263.09	   U83(x0, x1, mark(x2))
744.30/263.09	   U83(active(x0), x1, x2)
744.30/263.09	   U83(x0, active(x1), x2)
744.30/263.09	   U83(x0, x1, active(x2))
744.30/263.09	   U84(mark(x0), x1, x2)
744.30/263.09	   U84(x0, mark(x1), x2)
744.30/263.09	   U84(x0, x1, mark(x2))
744.30/263.09	   U84(active(x0), x1, x2)
744.30/263.09	   U84(x0, active(x1), x2)
744.30/263.09	   U84(x0, x1, active(x2))
744.30/263.09	   s(mark(x0))
744.30/263.09	   s(active(x0))
744.30/263.09	   U91(mark(x0), x1)
744.30/263.09	   U91(x0, mark(x1))
744.30/263.09	   U91(active(x0), x1)
744.30/263.09	   U91(x0, active(x1))
744.30/263.09	   U92(mark(x0))
744.30/263.09	   U92(active(x0))
744.30/263.09	
744.30/263.09	We have to consider all minimal (P,Q,R)-chains.
744.30/263.09	----------------------------------------
744.30/263.09	
744.30/263.09	(325) DependencyGraphProof (EQUIVALENT)
744.30/263.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.30/263.09	----------------------------------------
744.30/263.09	
744.30/263.09	(326)
744.30/263.09	Obligation:
744.30/263.09	Q DP problem:
744.30/263.09	The TRS P consists of the following rules:
744.30/263.09	
744.30/263.09	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.30/263.09	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.30/263.09	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.30/263.09	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.30/263.09	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.30/263.09	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.30/263.09	   MARK(U16(X)) -> MARK(X)
744.30/263.09	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.30/263.09	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.30/263.09	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.30/263.09	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.30/263.09	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.30/263.09	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.30/263.09	   MARK(U23(X)) -> MARK(X)
744.30/263.09	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.30/263.09	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.30/263.09	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.30/263.09	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.30/263.09	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.30/263.09	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.30/263.09	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.30/263.09	   MARK(U42(X)) -> MARK(X)
744.30/263.09	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.30/263.09	   MARK(U15(X1, X2)) -> MARK(X1)
744.30/263.09	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.30/263.09	   MARK(U22(X1, X2)) -> MARK(X1)
744.30/263.09	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.30/263.09	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.30/263.09	   MARK(U41(X1, X2)) -> MARK(X1)
744.30/263.09	   MARK(U51(X)) -> MARK(X)
744.30/263.09	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.30/263.09	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.30/263.09	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.30/263.09	
744.30/263.09	The TRS R consists of the following rules:
744.30/263.09	
744.30/263.09	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.30/263.09	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.30/263.09	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.30/263.09	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.30/263.09	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.30/263.09	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.30/263.09	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.30/263.09	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.30/263.09	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.30/263.09	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.30/263.09	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.30/263.09	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.30/263.09	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.30/263.09	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.30/263.09	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.30/263.09	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.30/263.09	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.30/263.09	   mark(U16(X)) -> active(U16(mark(X)))
744.30/263.09	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.30/263.09	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.30/263.09	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.30/263.09	   mark(U23(X)) -> active(U23(mark(X)))
744.30/263.09	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.30/263.09	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.30/263.09	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.30/263.09	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.30/263.09	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.30/263.09	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.30/263.09	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.30/263.09	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.30/263.09	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.30/263.09	   mark(U36(X)) -> active(U36(mark(X)))
744.30/263.09	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.30/263.09	   mark(U42(X)) -> active(U42(mark(X)))
744.30/263.09	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.30/263.09	   mark(U62(X)) -> active(U62(mark(X)))
744.30/263.09	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.30/263.09	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.30/263.09	   active(U72(tt, N)) -> mark(N)
744.30/263.09	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.30/263.09	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.30/263.09	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.30/263.09	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.30/263.09	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.30/263.09	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.30/263.09	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.30/263.09	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.30/263.09	   mark(s(X)) -> active(s(mark(X)))
744.30/263.09	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.30/263.09	   mark(U92(X)) -> active(U92(mark(X)))
744.30/263.09	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.30/263.09	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.30/263.09	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.30/263.09	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.30/263.09	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.30/263.09	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.30/263.09	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.30/263.09	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.30/263.09	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.30/263.09	   mark(U51(X)) -> active(U51(mark(X)))
744.30/263.09	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.30/263.09	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.30/263.09	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.30/263.09	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.30/263.09	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.30/263.09	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.30/263.09	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.30/263.09	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.30/263.09	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.30/263.09	   mark(isNatKind(X)) -> active(isNatKind(X))
744.30/263.09	   mark(isNat(X)) -> active(isNat(X))
744.30/263.09	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.30/263.09	   mark(tt) -> active(tt)
744.30/263.09	   mark(0) -> active(0)
744.30/263.09	   U61(X1, mark(X2)) -> U61(X1, X2)
744.30/263.09	   U61(mark(X1), X2) -> U61(X1, X2)
744.30/263.09	   U61(active(X1), X2) -> U61(X1, X2)
744.30/263.09	   U61(X1, active(X2)) -> U61(X1, X2)
744.30/263.09	   active(U16(tt)) -> mark(tt)
744.30/263.09	   active(U23(tt)) -> mark(tt)
744.30/263.09	   active(U36(tt)) -> mark(tt)
744.30/263.09	   active(U42(tt)) -> mark(tt)
744.30/263.09	   active(U51(tt)) -> mark(tt)
744.30/263.09	   active(U62(tt)) -> mark(tt)
744.30/263.09	   active(U92(tt)) -> mark(0)
744.30/263.09	   active(isNat(0)) -> mark(tt)
744.30/263.09	   active(isNatKind(0)) -> mark(tt)
744.30/263.09	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.30/263.09	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.09	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.30/263.09	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.30/263.09	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.30/263.09	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.30/263.09	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.30/263.09	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.09	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.30/263.09	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.30/263.09	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.30/263.09	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.30/263.09	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.30/263.09	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.09	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.30/263.09	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.30/263.09	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.30/263.09	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.30/263.09	   plus(X1, mark(X2)) -> plus(X1, X2)
744.30/263.09	   plus(mark(X1), X2) -> plus(X1, X2)
744.30/263.09	   plus(active(X1), X2) -> plus(X1, X2)
744.30/263.09	   plus(X1, active(X2)) -> plus(X1, X2)
744.30/263.09	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.30/263.09	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.09	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.30/263.09	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.30/263.09	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.30/263.09	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.30/263.09	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.30/263.09	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.09	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.30/263.09	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.30/263.09	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.30/263.09	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.30/263.09	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.30/263.09	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.09	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.30/263.09	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.30/263.09	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.30/263.09	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.30/263.09	   U15(X1, mark(X2)) -> U15(X1, X2)
744.30/263.09	   U15(mark(X1), X2) -> U15(X1, X2)
744.30/263.09	   U15(active(X1), X2) -> U15(X1, X2)
744.30/263.09	   U15(X1, active(X2)) -> U15(X1, X2)
744.30/263.09	   U16(active(X)) -> U16(X)
744.30/263.09	   U16(mark(X)) -> U16(X)
744.30/263.09	   U22(X1, mark(X2)) -> U22(X1, X2)
744.30/263.09	   U22(mark(X1), X2) -> U22(X1, X2)
744.30/263.09	   U22(active(X1), X2) -> U22(X1, X2)
744.30/263.09	   U22(X1, active(X2)) -> U22(X1, X2)
744.30/263.09	   U23(active(X)) -> U23(X)
744.30/263.09	   U23(mark(X)) -> U23(X)
744.30/263.09	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.30/263.09	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.09	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.30/263.09	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.30/263.09	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.30/263.09	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.30/263.09	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.30/263.09	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.09	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.30/263.09	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.30/263.09	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.30/263.09	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.30/263.09	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.30/263.09	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.09	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.30/263.09	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.30/263.09	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.30/263.09	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.30/263.09	   U35(X1, mark(X2)) -> U35(X1, X2)
744.30/263.09	   U35(mark(X1), X2) -> U35(X1, X2)
744.30/263.09	   U35(active(X1), X2) -> U35(X1, X2)
744.30/263.09	   U35(X1, active(X2)) -> U35(X1, X2)
744.30/263.09	   U36(active(X)) -> U36(X)
744.30/263.09	   U36(mark(X)) -> U36(X)
744.30/263.09	   U42(active(X)) -> U42(X)
744.30/263.09	   U42(mark(X)) -> U42(X)
744.30/263.09	   U62(active(X)) -> U62(X)
744.30/263.09	   U62(mark(X)) -> U62(X)
744.30/263.09	   U72(X1, mark(X2)) -> U72(X1, X2)
744.30/263.09	   U72(mark(X1), X2) -> U72(X1, X2)
744.30/263.09	   U72(active(X1), X2) -> U72(X1, X2)
744.30/263.09	   U72(X1, active(X2)) -> U72(X1, X2)
744.30/263.09	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.30/263.09	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.09	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.30/263.09	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.30/263.09	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.30/263.09	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.30/263.09	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.30/263.09	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.09	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.30/263.09	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.30/263.09	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.30/263.09	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.30/263.09	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.30/263.09	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.09	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.30/263.09	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.30/263.09	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.30/263.09	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.30/263.09	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.30/263.09	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.09	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.30/263.09	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.30/263.09	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.30/263.09	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.30/263.09	   s(active(X)) -> s(X)
744.30/263.09	   s(mark(X)) -> s(X)
744.30/263.09	   U92(active(X)) -> U92(X)
744.30/263.09	   U92(mark(X)) -> U92(X)
744.30/263.09	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.30/263.09	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.09	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.30/263.09	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.30/263.09	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.30/263.09	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.30/263.09	   U21(X1, mark(X2)) -> U21(X1, X2)
744.30/263.09	   U21(mark(X1), X2) -> U21(X1, X2)
744.30/263.09	   U21(active(X1), X2) -> U21(X1, X2)
744.30/263.09	   U21(X1, active(X2)) -> U21(X1, X2)
744.30/263.09	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.30/263.09	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.09	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.30/263.09	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.30/263.09	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.30/263.09	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.30/263.09	   U41(X1, mark(X2)) -> U41(X1, X2)
744.30/263.09	   U41(mark(X1), X2) -> U41(X1, X2)
744.30/263.09	   U41(active(X1), X2) -> U41(X1, X2)
744.30/263.09	   U41(X1, active(X2)) -> U41(X1, X2)
744.30/263.09	   U51(active(X)) -> U51(X)
744.30/263.09	   U51(mark(X)) -> U51(X)
744.30/263.09	   U71(X1, mark(X2)) -> U71(X1, X2)
744.30/263.09	   U71(mark(X1), X2) -> U71(X1, X2)
744.30/263.09	   U71(active(X1), X2) -> U71(X1, X2)
744.30/263.09	   U71(X1, active(X2)) -> U71(X1, X2)
744.30/263.09	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.30/263.09	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.09	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.30/263.09	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.30/263.09	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.30/263.09	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.30/263.09	   U91(X1, mark(X2)) -> U91(X1, X2)
744.30/263.09	   U91(mark(X1), X2) -> U91(X1, X2)
744.30/263.09	   U91(active(X1), X2) -> U91(X1, X2)
744.30/263.09	   U91(X1, active(X2)) -> U91(X1, X2)
744.30/263.09	   x(X1, mark(X2)) -> x(X1, X2)
744.30/263.09	   x(mark(X1), X2) -> x(X1, X2)
744.30/263.09	   x(active(X1), X2) -> x(X1, X2)
744.30/263.09	   x(X1, active(X2)) -> x(X1, X2)
744.30/263.09	
744.30/263.09	The set Q consists of the following terms:
744.30/263.09	
744.30/263.09	   active(U101(tt, x0, x1))
744.30/263.09	   active(U102(tt, x0, x1))
744.30/263.09	   active(U103(tt, x0, x1))
744.30/263.09	   active(U104(tt, x0, x1))
744.30/263.09	   active(U11(tt, x0, x1))
744.30/263.09	   active(U12(tt, x0, x1))
744.30/263.09	   active(U13(tt, x0, x1))
744.30/263.09	   active(U14(tt, x0, x1))
744.30/263.09	   active(U15(tt, x0))
744.30/263.09	   active(U16(tt))
744.30/263.09	   active(U21(tt, x0))
744.30/263.09	   active(U22(tt, x0))
744.30/263.09	   active(U23(tt))
744.30/263.09	   active(U31(tt, x0, x1))
744.30/263.09	   active(U32(tt, x0, x1))
744.30/263.09	   active(U33(tt, x0, x1))
744.30/263.09	   active(U34(tt, x0, x1))
744.30/263.09	   active(U35(tt, x0))
744.30/263.09	   active(U36(tt))
744.30/263.09	   active(U41(tt, x0))
744.30/263.09	   active(U42(tt))
744.30/263.09	   active(U51(tt))
744.30/263.09	   active(U61(tt, x0))
744.30/263.09	   active(U62(tt))
744.30/263.09	   active(U71(tt, x0))
744.30/263.09	   active(U72(tt, x0))
744.30/263.09	   active(U81(tt, x0, x1))
744.30/263.09	   active(U82(tt, x0, x1))
744.30/263.09	   active(U83(tt, x0, x1))
744.30/263.09	   active(U84(tt, x0, x1))
744.30/263.09	   active(U91(tt, x0))
744.30/263.09	   active(U92(tt))
744.30/263.09	   active(isNat(0))
744.30/263.09	   active(isNat(plus(x0, x1)))
744.30/263.09	   active(isNat(s(x0)))
744.30/263.09	   active(isNat(x(x0, x1)))
744.30/263.09	   active(isNatKind(0))
744.30/263.09	   active(isNatKind(plus(x0, x1)))
744.30/263.09	   active(isNatKind(s(x0)))
744.30/263.09	   active(isNatKind(x(x0, x1)))
744.30/263.09	   active(plus(x0, 0))
744.30/263.09	   active(plus(x0, s(x1)))
744.30/263.09	   active(x(x0, 0))
744.30/263.09	   active(x(x0, s(x1)))
744.30/263.09	   mark(U101(x0, x1, x2))
744.30/263.09	   mark(tt)
744.30/263.09	   mark(U102(x0, x1, x2))
744.30/263.09	   mark(isNatKind(x0))
744.30/263.09	   mark(U103(x0, x1, x2))
744.30/263.09	   mark(isNat(x0))
744.30/263.09	   mark(U104(x0, x1, x2))
744.30/263.09	   mark(plus(x0, x1))
744.30/263.09	   mark(x(x0, x1))
744.30/263.09	   mark(U11(x0, x1, x2))
744.30/263.09	   mark(U12(x0, x1, x2))
744.30/263.09	   mark(U13(x0, x1, x2))
744.30/263.09	   mark(U14(x0, x1, x2))
744.30/263.09	   mark(U15(x0, x1))
744.30/263.09	   mark(U16(x0))
744.30/263.09	   mark(U21(x0, x1))
744.30/263.09	   mark(U22(x0, x1))
744.30/263.09	   mark(U23(x0))
744.30/263.09	   mark(U31(x0, x1, x2))
744.30/263.09	   mark(U32(x0, x1, x2))
744.30/263.09	   mark(U33(x0, x1, x2))
744.30/263.09	   mark(U34(x0, x1, x2))
744.30/263.09	   mark(U35(x0, x1))
744.30/263.09	   mark(U36(x0))
744.30/263.09	   mark(U41(x0, x1))
744.30/263.09	   mark(U42(x0))
744.30/263.09	   mark(U51(x0))
744.30/263.09	   mark(U61(x0, x1))
744.30/263.09	   mark(U62(x0))
744.30/263.09	   mark(U71(x0, x1))
744.30/263.09	   mark(U72(x0, x1))
744.30/263.09	   mark(U81(x0, x1, x2))
744.30/263.09	   mark(U82(x0, x1, x2))
744.30/263.09	   mark(U83(x0, x1, x2))
744.30/263.09	   mark(U84(x0, x1, x2))
744.30/263.09	   mark(s(x0))
744.30/263.09	   mark(U91(x0, x1))
744.30/263.09	   mark(U92(x0))
744.30/263.09	   mark(0)
744.30/263.09	   U101(mark(x0), x1, x2)
744.30/263.09	   U101(x0, mark(x1), x2)
744.30/263.09	   U101(x0, x1, mark(x2))
744.30/263.09	   U101(active(x0), x1, x2)
744.30/263.09	   U101(x0, active(x1), x2)
744.30/263.09	   U101(x0, x1, active(x2))
744.30/263.09	   U102(mark(x0), x1, x2)
744.30/263.09	   U102(x0, mark(x1), x2)
744.30/263.09	   U102(x0, x1, mark(x2))
744.30/263.09	   U102(active(x0), x1, x2)
744.35/263.09	   U102(x0, active(x1), x2)
744.35/263.09	   U102(x0, x1, active(x2))
744.35/263.09	   isNatKind(mark(x0))
744.35/263.09	   isNatKind(active(x0))
744.35/263.09	   U103(mark(x0), x1, x2)
744.35/263.09	   U103(x0, mark(x1), x2)
744.35/263.09	   U103(x0, x1, mark(x2))
744.35/263.09	   U103(active(x0), x1, x2)
744.35/263.09	   U103(x0, active(x1), x2)
744.35/263.09	   U103(x0, x1, active(x2))
744.35/263.09	   isNat(mark(x0))
744.35/263.09	   isNat(active(x0))
744.35/263.09	   U104(mark(x0), x1, x2)
744.35/263.09	   U104(x0, mark(x1), x2)
744.35/263.09	   U104(x0, x1, mark(x2))
744.35/263.09	   U104(active(x0), x1, x2)
744.35/263.09	   U104(x0, active(x1), x2)
744.35/263.09	   U104(x0, x1, active(x2))
744.35/263.09	   plus(mark(x0), x1)
744.35/263.09	   plus(x0, mark(x1))
744.35/263.09	   plus(active(x0), x1)
744.35/263.09	   plus(x0, active(x1))
744.35/263.09	   x(mark(x0), x1)
744.35/263.09	   x(x0, mark(x1))
744.35/263.09	   x(active(x0), x1)
744.35/263.09	   x(x0, active(x1))
744.35/263.09	   U11(mark(x0), x1, x2)
744.35/263.09	   U11(x0, mark(x1), x2)
744.35/263.09	   U11(x0, x1, mark(x2))
744.35/263.09	   U11(active(x0), x1, x2)
744.35/263.09	   U11(x0, active(x1), x2)
744.35/263.09	   U11(x0, x1, active(x2))
744.35/263.09	   U12(mark(x0), x1, x2)
744.35/263.09	   U12(x0, mark(x1), x2)
744.35/263.09	   U12(x0, x1, mark(x2))
744.35/263.09	   U12(active(x0), x1, x2)
744.35/263.09	   U12(x0, active(x1), x2)
744.35/263.09	   U12(x0, x1, active(x2))
744.35/263.09	   U13(mark(x0), x1, x2)
744.35/263.09	   U13(x0, mark(x1), x2)
744.35/263.09	   U13(x0, x1, mark(x2))
744.35/263.09	   U13(active(x0), x1, x2)
744.35/263.09	   U13(x0, active(x1), x2)
744.35/263.09	   U13(x0, x1, active(x2))
744.35/263.09	   U14(mark(x0), x1, x2)
744.35/263.09	   U14(x0, mark(x1), x2)
744.35/263.09	   U14(x0, x1, mark(x2))
744.35/263.09	   U14(active(x0), x1, x2)
744.35/263.09	   U14(x0, active(x1), x2)
744.35/263.09	   U14(x0, x1, active(x2))
744.35/263.09	   U15(mark(x0), x1)
744.35/263.09	   U15(x0, mark(x1))
744.35/263.09	   U15(active(x0), x1)
744.35/263.09	   U15(x0, active(x1))
744.35/263.09	   U16(mark(x0))
744.35/263.09	   U16(active(x0))
744.35/263.09	   U21(mark(x0), x1)
744.35/263.09	   U21(x0, mark(x1))
744.35/263.09	   U21(active(x0), x1)
744.35/263.09	   U21(x0, active(x1))
744.35/263.09	   U22(mark(x0), x1)
744.35/263.09	   U22(x0, mark(x1))
744.35/263.09	   U22(active(x0), x1)
744.35/263.09	   U22(x0, active(x1))
744.35/263.09	   U23(mark(x0))
744.35/263.09	   U23(active(x0))
744.35/263.09	   U31(mark(x0), x1, x2)
744.35/263.09	   U31(x0, mark(x1), x2)
744.35/263.09	   U31(x0, x1, mark(x2))
744.35/263.09	   U31(active(x0), x1, x2)
744.35/263.09	   U31(x0, active(x1), x2)
744.35/263.09	   U31(x0, x1, active(x2))
744.35/263.09	   U32(mark(x0), x1, x2)
744.35/263.09	   U32(x0, mark(x1), x2)
744.35/263.09	   U32(x0, x1, mark(x2))
744.35/263.09	   U32(active(x0), x1, x2)
744.35/263.09	   U32(x0, active(x1), x2)
744.35/263.09	   U32(x0, x1, active(x2))
744.35/263.09	   U33(mark(x0), x1, x2)
744.35/263.09	   U33(x0, mark(x1), x2)
744.35/263.09	   U33(x0, x1, mark(x2))
744.35/263.09	   U33(active(x0), x1, x2)
744.35/263.09	   U33(x0, active(x1), x2)
744.35/263.09	   U33(x0, x1, active(x2))
744.35/263.09	   U34(mark(x0), x1, x2)
744.35/263.09	   U34(x0, mark(x1), x2)
744.35/263.09	   U34(x0, x1, mark(x2))
744.35/263.09	   U34(active(x0), x1, x2)
744.35/263.09	   U34(x0, active(x1), x2)
744.35/263.09	   U34(x0, x1, active(x2))
744.35/263.09	   U35(mark(x0), x1)
744.35/263.09	   U35(x0, mark(x1))
744.35/263.09	   U35(active(x0), x1)
744.35/263.09	   U35(x0, active(x1))
744.35/263.09	   U36(mark(x0))
744.35/263.09	   U36(active(x0))
744.35/263.09	   U41(mark(x0), x1)
744.35/263.09	   U41(x0, mark(x1))
744.35/263.09	   U41(active(x0), x1)
744.35/263.09	   U41(x0, active(x1))
744.35/263.09	   U42(mark(x0))
744.35/263.09	   U42(active(x0))
744.35/263.09	   U51(mark(x0))
744.35/263.09	   U51(active(x0))
744.35/263.09	   U61(mark(x0), x1)
744.35/263.09	   U61(x0, mark(x1))
744.35/263.09	   U61(active(x0), x1)
744.35/263.09	   U61(x0, active(x1))
744.35/263.09	   U62(mark(x0))
744.35/263.09	   U62(active(x0))
744.35/263.09	   U71(mark(x0), x1)
744.35/263.09	   U71(x0, mark(x1))
744.35/263.09	   U71(active(x0), x1)
744.35/263.09	   U71(x0, active(x1))
744.35/263.09	   U72(mark(x0), x1)
744.35/263.09	   U72(x0, mark(x1))
744.35/263.09	   U72(active(x0), x1)
744.35/263.09	   U72(x0, active(x1))
744.35/263.09	   U81(mark(x0), x1, x2)
744.35/263.09	   U81(x0, mark(x1), x2)
744.35/263.09	   U81(x0, x1, mark(x2))
744.35/263.09	   U81(active(x0), x1, x2)
744.35/263.09	   U81(x0, active(x1), x2)
744.35/263.09	   U81(x0, x1, active(x2))
744.35/263.09	   U82(mark(x0), x1, x2)
744.35/263.09	   U82(x0, mark(x1), x2)
744.35/263.09	   U82(x0, x1, mark(x2))
744.35/263.09	   U82(active(x0), x1, x2)
744.35/263.09	   U82(x0, active(x1), x2)
744.35/263.09	   U82(x0, x1, active(x2))
744.35/263.09	   U83(mark(x0), x1, x2)
744.35/263.09	   U83(x0, mark(x1), x2)
744.35/263.09	   U83(x0, x1, mark(x2))
744.35/263.09	   U83(active(x0), x1, x2)
744.35/263.09	   U83(x0, active(x1), x2)
744.35/263.09	   U83(x0, x1, active(x2))
744.35/263.09	   U84(mark(x0), x1, x2)
744.35/263.09	   U84(x0, mark(x1), x2)
744.35/263.09	   U84(x0, x1, mark(x2))
744.35/263.09	   U84(active(x0), x1, x2)
744.35/263.09	   U84(x0, active(x1), x2)
744.35/263.09	   U84(x0, x1, active(x2))
744.35/263.09	   s(mark(x0))
744.35/263.09	   s(active(x0))
744.35/263.09	   U91(mark(x0), x1)
744.35/263.09	   U91(x0, mark(x1))
744.35/263.09	   U91(active(x0), x1)
744.35/263.09	   U91(x0, active(x1))
744.35/263.09	   U92(mark(x0))
744.35/263.09	   U92(active(x0))
744.35/263.09	
744.35/263.09	We have to consider all minimal (P,Q,R)-chains.
744.35/263.09	----------------------------------------
744.35/263.09	
744.35/263.09	(327) QDPOrderProof (EQUIVALENT)
744.35/263.09	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.09	
744.35/263.09	
744.35/263.09	The following pairs can be oriented strictly and are deleted.
744.35/263.09	
744.35/263.09	   MARK(U34(X1, X2, X3)) -> ACTIVE(U34(mark(X1), X2, X3))
744.35/263.09	The remaining pairs can at least be oriented weakly.
744.35/263.09	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.09	
744.35/263.09	POL( ACTIVE_1(x_1) ) = max{0, 2x_1 - 1}
744.35/263.09	POL( U11_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U12_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U13_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U14_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U15_2(x_1, x_2) ) = 1
744.35/263.09	POL( U21_2(x_1, x_2) ) = 1
744.35/263.09	POL( U22_2(x_1, x_2) ) = 1
744.35/263.09	POL( U31_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U32_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U33_3(x_1, ..., x_3) ) = 1
744.35/263.09	POL( U34_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.09	POL( U41_2(x_1, x_2) ) = 1
744.35/263.09	POL( mark_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U102_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.09	POL( active_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U101_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 - 2}
744.35/263.09	POL( tt ) = 0
744.35/263.09	POL( isNatKind_1(x_1) ) = 1
744.35/263.09	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( isNat_1(x_1) ) = 1
744.35/263.09	POL( U104_3(x_1, ..., x_3) ) = max{0, x_2 + x_3 - 2}
744.35/263.09	POL( plus_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.09	POL( x_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.09	POL( U16_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U23_1(x_1) ) = max{0, x_1 - 2}
744.35/263.09	POL( U35_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.09	POL( U36_1(x_1) ) = 1
744.35/263.09	POL( U42_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U61_2(x_1, x_2) ) = 2x_1 + 2
744.35/263.09	POL( U62_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U71_2(x_1, x_2) ) = max{0, x_1 + x_2 - 1}
744.35/263.09	POL( U72_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( U81_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + 2x_3 - 2}
744.35/263.09	POL( U82_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U83_3(x_1, ..., x_3) ) = 2x_1 + x_2 + x_3 + 2
744.35/263.09	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.35/263.09	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.35/263.09	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( U92_1(x_1) ) = 2
744.35/263.09	POL( U51_1(x_1) ) = max{0, x_1 - 2}
744.35/263.09	POL( 0 ) = 0
744.35/263.09	POL( MARK_1(x_1) ) = 1
744.35/263.09	
744.35/263.09	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.09	
744.35/263.09	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.09	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.09	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.09	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.09	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.09	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.09	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.09	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.09	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.09	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.09	
744.35/263.09	
744.35/263.09	----------------------------------------
744.35/263.09	
744.35/263.09	(328)
744.35/263.09	Obligation:
744.35/263.09	Q DP problem:
744.35/263.09	The TRS P consists of the following rules:
744.35/263.09	
744.35/263.09	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.09	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.09	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.09	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.09	   MARK(U16(X)) -> MARK(X)
744.35/263.09	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.09	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.09	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.09	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.09	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.09	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.09	   MARK(U23(X)) -> MARK(X)
744.35/263.09	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.09	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.09	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.09	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U33(tt, V1, V2)) -> MARK(U34(isNatKind(V2), V1, V2))
744.35/263.09	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.09	   MARK(U42(X)) -> MARK(X)
744.35/263.09	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.09	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.09	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.09	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.35/263.09	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U51(X)) -> MARK(X)
744.35/263.09	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.09	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.09	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.09	
744.35/263.09	The TRS R consists of the following rules:
744.35/263.09	
744.35/263.09	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.09	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.09	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.09	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.09	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.09	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.09	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.09	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.09	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.09	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.09	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.09	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.09	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.09	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.09	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.09	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.09	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.09	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.09	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.09	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.09	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.09	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.09	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.09	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.09	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.09	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.09	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.09	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.09	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.09	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.09	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.09	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.09	   active(U72(tt, N)) -> mark(N)
744.35/263.09	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.09	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.09	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.09	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.09	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.09	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.09	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.09	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.09	   mark(s(X)) -> active(s(mark(X)))
744.35/263.09	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.09	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.09	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.09	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.09	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.09	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.09	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.09	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.09	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.09	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.09	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.09	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.09	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.09	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.09	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.09	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.09	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.09	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.09	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.09	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.09	   mark(isNat(X)) -> active(isNat(X))
744.35/263.09	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.09	   mark(tt) -> active(tt)
744.35/263.09	   mark(0) -> active(0)
744.35/263.09	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.09	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.09	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.09	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.09	   active(U16(tt)) -> mark(tt)
744.35/263.09	   active(U23(tt)) -> mark(tt)
744.35/263.09	   active(U36(tt)) -> mark(tt)
744.35/263.09	   active(U42(tt)) -> mark(tt)
744.35/263.09	   active(U51(tt)) -> mark(tt)
744.35/263.09	   active(U62(tt)) -> mark(tt)
744.35/263.09	   active(U92(tt)) -> mark(0)
744.35/263.09	   active(isNat(0)) -> mark(tt)
744.35/263.09	   active(isNatKind(0)) -> mark(tt)
744.35/263.09	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.09	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.09	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.09	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.09	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.09	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.09	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.09	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.09	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.09	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.09	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.09	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.09	   U16(active(X)) -> U16(X)
744.35/263.09	   U16(mark(X)) -> U16(X)
744.35/263.09	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.09	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.09	   U23(active(X)) -> U23(X)
744.35/263.09	   U23(mark(X)) -> U23(X)
744.35/263.09	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.09	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.09	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.09	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.09	   U36(active(X)) -> U36(X)
744.35/263.09	   U36(mark(X)) -> U36(X)
744.35/263.09	   U42(active(X)) -> U42(X)
744.35/263.09	   U42(mark(X)) -> U42(X)
744.35/263.09	   U62(active(X)) -> U62(X)
744.35/263.09	   U62(mark(X)) -> U62(X)
744.35/263.09	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.09	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.09	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.09	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.09	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.09	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.09	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.09	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.09	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.09	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.09	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.09	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.09	   s(active(X)) -> s(X)
744.35/263.09	   s(mark(X)) -> s(X)
744.35/263.09	   U92(active(X)) -> U92(X)
744.35/263.09	   U92(mark(X)) -> U92(X)
744.35/263.09	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.09	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.09	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.09	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.09	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.09	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.09	   U51(active(X)) -> U51(X)
744.35/263.09	   U51(mark(X)) -> U51(X)
744.35/263.09	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.09	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.09	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.09	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.09	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.09	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.09	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.09	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.09	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.09	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.09	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.09	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.09	   x(active(X1), X2) -> x(X1, X2)
744.35/263.09	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.09	
744.35/263.09	The set Q consists of the following terms:
744.35/263.09	
744.35/263.09	   active(U101(tt, x0, x1))
744.35/263.09	   active(U102(tt, x0, x1))
744.35/263.09	   active(U103(tt, x0, x1))
744.35/263.09	   active(U104(tt, x0, x1))
744.35/263.09	   active(U11(tt, x0, x1))
744.35/263.09	   active(U12(tt, x0, x1))
744.35/263.09	   active(U13(tt, x0, x1))
744.35/263.09	   active(U14(tt, x0, x1))
744.35/263.09	   active(U15(tt, x0))
744.35/263.09	   active(U16(tt))
744.35/263.09	   active(U21(tt, x0))
744.35/263.09	   active(U22(tt, x0))
744.35/263.09	   active(U23(tt))
744.35/263.09	   active(U31(tt, x0, x1))
744.35/263.09	   active(U32(tt, x0, x1))
744.35/263.09	   active(U33(tt, x0, x1))
744.35/263.09	   active(U34(tt, x0, x1))
744.35/263.09	   active(U35(tt, x0))
744.35/263.09	   active(U36(tt))
744.35/263.09	   active(U41(tt, x0))
744.35/263.09	   active(U42(tt))
744.35/263.09	   active(U51(tt))
744.35/263.09	   active(U61(tt, x0))
744.35/263.09	   active(U62(tt))
744.35/263.09	   active(U71(tt, x0))
744.35/263.09	   active(U72(tt, x0))
744.35/263.09	   active(U81(tt, x0, x1))
744.35/263.09	   active(U82(tt, x0, x1))
744.35/263.09	   active(U83(tt, x0, x1))
744.35/263.09	   active(U84(tt, x0, x1))
744.35/263.09	   active(U91(tt, x0))
744.35/263.09	   active(U92(tt))
744.35/263.09	   active(isNat(0))
744.35/263.09	   active(isNat(plus(x0, x1)))
744.35/263.09	   active(isNat(s(x0)))
744.35/263.09	   active(isNat(x(x0, x1)))
744.35/263.09	   active(isNatKind(0))
744.35/263.09	   active(isNatKind(plus(x0, x1)))
744.35/263.09	   active(isNatKind(s(x0)))
744.35/263.09	   active(isNatKind(x(x0, x1)))
744.35/263.09	   active(plus(x0, 0))
744.35/263.09	   active(plus(x0, s(x1)))
744.35/263.09	   active(x(x0, 0))
744.35/263.09	   active(x(x0, s(x1)))
744.35/263.09	   mark(U101(x0, x1, x2))
744.35/263.09	   mark(tt)
744.35/263.09	   mark(U102(x0, x1, x2))
744.35/263.09	   mark(isNatKind(x0))
744.35/263.09	   mark(U103(x0, x1, x2))
744.35/263.09	   mark(isNat(x0))
744.35/263.09	   mark(U104(x0, x1, x2))
744.35/263.09	   mark(plus(x0, x1))
744.35/263.09	   mark(x(x0, x1))
744.35/263.09	   mark(U11(x0, x1, x2))
744.35/263.09	   mark(U12(x0, x1, x2))
744.35/263.09	   mark(U13(x0, x1, x2))
744.35/263.09	   mark(U14(x0, x1, x2))
744.35/263.09	   mark(U15(x0, x1))
744.35/263.09	   mark(U16(x0))
744.35/263.09	   mark(U21(x0, x1))
744.35/263.09	   mark(U22(x0, x1))
744.35/263.09	   mark(U23(x0))
744.35/263.09	   mark(U31(x0, x1, x2))
744.35/263.09	   mark(U32(x0, x1, x2))
744.35/263.09	   mark(U33(x0, x1, x2))
744.35/263.09	   mark(U34(x0, x1, x2))
744.35/263.09	   mark(U35(x0, x1))
744.35/263.09	   mark(U36(x0))
744.35/263.09	   mark(U41(x0, x1))
744.35/263.09	   mark(U42(x0))
744.35/263.09	   mark(U51(x0))
744.35/263.09	   mark(U61(x0, x1))
744.35/263.09	   mark(U62(x0))
744.35/263.09	   mark(U71(x0, x1))
744.35/263.09	   mark(U72(x0, x1))
744.35/263.09	   mark(U81(x0, x1, x2))
744.35/263.09	   mark(U82(x0, x1, x2))
744.35/263.09	   mark(U83(x0, x1, x2))
744.35/263.09	   mark(U84(x0, x1, x2))
744.35/263.09	   mark(s(x0))
744.35/263.09	   mark(U91(x0, x1))
744.35/263.09	   mark(U92(x0))
744.35/263.09	   mark(0)
744.35/263.09	   U101(mark(x0), x1, x2)
744.35/263.09	   U101(x0, mark(x1), x2)
744.35/263.09	   U101(x0, x1, mark(x2))
744.35/263.09	   U101(active(x0), x1, x2)
744.35/263.09	   U101(x0, active(x1), x2)
744.35/263.09	   U101(x0, x1, active(x2))
744.35/263.09	   U102(mark(x0), x1, x2)
744.35/263.09	   U102(x0, mark(x1), x2)
744.35/263.09	   U102(x0, x1, mark(x2))
744.35/263.09	   U102(active(x0), x1, x2)
744.35/263.09	   U102(x0, active(x1), x2)
744.35/263.09	   U102(x0, x1, active(x2))
744.35/263.09	   isNatKind(mark(x0))
744.35/263.09	   isNatKind(active(x0))
744.35/263.09	   U103(mark(x0), x1, x2)
744.35/263.09	   U103(x0, mark(x1), x2)
744.35/263.09	   U103(x0, x1, mark(x2))
744.35/263.09	   U103(active(x0), x1, x2)
744.35/263.09	   U103(x0, active(x1), x2)
744.35/263.09	   U103(x0, x1, active(x2))
744.35/263.09	   isNat(mark(x0))
744.35/263.09	   isNat(active(x0))
744.35/263.09	   U104(mark(x0), x1, x2)
744.35/263.09	   U104(x0, mark(x1), x2)
744.35/263.09	   U104(x0, x1, mark(x2))
744.35/263.09	   U104(active(x0), x1, x2)
744.35/263.09	   U104(x0, active(x1), x2)
744.35/263.09	   U104(x0, x1, active(x2))
744.35/263.09	   plus(mark(x0), x1)
744.35/263.09	   plus(x0, mark(x1))
744.35/263.09	   plus(active(x0), x1)
744.35/263.09	   plus(x0, active(x1))
744.35/263.09	   x(mark(x0), x1)
744.35/263.09	   x(x0, mark(x1))
744.35/263.09	   x(active(x0), x1)
744.35/263.09	   x(x0, active(x1))
744.35/263.09	   U11(mark(x0), x1, x2)
744.35/263.09	   U11(x0, mark(x1), x2)
744.35/263.09	   U11(x0, x1, mark(x2))
744.35/263.09	   U11(active(x0), x1, x2)
744.35/263.09	   U11(x0, active(x1), x2)
744.35/263.09	   U11(x0, x1, active(x2))
744.35/263.09	   U12(mark(x0), x1, x2)
744.35/263.09	   U12(x0, mark(x1), x2)
744.35/263.09	   U12(x0, x1, mark(x2))
744.35/263.09	   U12(active(x0), x1, x2)
744.35/263.09	   U12(x0, active(x1), x2)
744.35/263.09	   U12(x0, x1, active(x2))
744.35/263.09	   U13(mark(x0), x1, x2)
744.35/263.09	   U13(x0, mark(x1), x2)
744.35/263.09	   U13(x0, x1, mark(x2))
744.35/263.09	   U13(active(x0), x1, x2)
744.35/263.09	   U13(x0, active(x1), x2)
744.35/263.09	   U13(x0, x1, active(x2))
744.35/263.09	   U14(mark(x0), x1, x2)
744.35/263.09	   U14(x0, mark(x1), x2)
744.35/263.09	   U14(x0, x1, mark(x2))
744.35/263.09	   U14(active(x0), x1, x2)
744.35/263.09	   U14(x0, active(x1), x2)
744.35/263.09	   U14(x0, x1, active(x2))
744.35/263.09	   U15(mark(x0), x1)
744.35/263.09	   U15(x0, mark(x1))
744.35/263.09	   U15(active(x0), x1)
744.35/263.09	   U15(x0, active(x1))
744.35/263.09	   U16(mark(x0))
744.35/263.09	   U16(active(x0))
744.35/263.09	   U21(mark(x0), x1)
744.35/263.09	   U21(x0, mark(x1))
744.35/263.09	   U21(active(x0), x1)
744.35/263.09	   U21(x0, active(x1))
744.35/263.09	   U22(mark(x0), x1)
744.35/263.09	   U22(x0, mark(x1))
744.35/263.09	   U22(active(x0), x1)
744.35/263.09	   U22(x0, active(x1))
744.35/263.09	   U23(mark(x0))
744.35/263.09	   U23(active(x0))
744.35/263.09	   U31(mark(x0), x1, x2)
744.35/263.09	   U31(x0, mark(x1), x2)
744.35/263.09	   U31(x0, x1, mark(x2))
744.35/263.09	   U31(active(x0), x1, x2)
744.35/263.09	   U31(x0, active(x1), x2)
744.35/263.09	   U31(x0, x1, active(x2))
744.35/263.09	   U32(mark(x0), x1, x2)
744.35/263.09	   U32(x0, mark(x1), x2)
744.35/263.09	   U32(x0, x1, mark(x2))
744.35/263.09	   U32(active(x0), x1, x2)
744.35/263.09	   U32(x0, active(x1), x2)
744.35/263.09	   U32(x0, x1, active(x2))
744.35/263.09	   U33(mark(x0), x1, x2)
744.35/263.09	   U33(x0, mark(x1), x2)
744.35/263.09	   U33(x0, x1, mark(x2))
744.35/263.09	   U33(active(x0), x1, x2)
744.35/263.09	   U33(x0, active(x1), x2)
744.35/263.09	   U33(x0, x1, active(x2))
744.35/263.09	   U34(mark(x0), x1, x2)
744.35/263.09	   U34(x0, mark(x1), x2)
744.35/263.09	   U34(x0, x1, mark(x2))
744.35/263.09	   U34(active(x0), x1, x2)
744.35/263.09	   U34(x0, active(x1), x2)
744.35/263.09	   U34(x0, x1, active(x2))
744.35/263.09	   U35(mark(x0), x1)
744.35/263.09	   U35(x0, mark(x1))
744.35/263.09	   U35(active(x0), x1)
744.35/263.09	   U35(x0, active(x1))
744.35/263.09	   U36(mark(x0))
744.35/263.09	   U36(active(x0))
744.35/263.09	   U41(mark(x0), x1)
744.35/263.09	   U41(x0, mark(x1))
744.35/263.09	   U41(active(x0), x1)
744.35/263.09	   U41(x0, active(x1))
744.35/263.09	   U42(mark(x0))
744.35/263.09	   U42(active(x0))
744.35/263.09	   U51(mark(x0))
744.35/263.09	   U51(active(x0))
744.35/263.09	   U61(mark(x0), x1)
744.35/263.09	   U61(x0, mark(x1))
744.35/263.09	   U61(active(x0), x1)
744.35/263.09	   U61(x0, active(x1))
744.35/263.09	   U62(mark(x0))
744.35/263.09	   U62(active(x0))
744.35/263.09	   U71(mark(x0), x1)
744.35/263.09	   U71(x0, mark(x1))
744.35/263.09	   U71(active(x0), x1)
744.35/263.09	   U71(x0, active(x1))
744.35/263.09	   U72(mark(x0), x1)
744.35/263.09	   U72(x0, mark(x1))
744.35/263.09	   U72(active(x0), x1)
744.35/263.09	   U72(x0, active(x1))
744.35/263.09	   U81(mark(x0), x1, x2)
744.35/263.09	   U81(x0, mark(x1), x2)
744.35/263.09	   U81(x0, x1, mark(x2))
744.35/263.09	   U81(active(x0), x1, x2)
744.35/263.09	   U81(x0, active(x1), x2)
744.35/263.09	   U81(x0, x1, active(x2))
744.35/263.09	   U82(mark(x0), x1, x2)
744.35/263.09	   U82(x0, mark(x1), x2)
744.35/263.09	   U82(x0, x1, mark(x2))
744.35/263.09	   U82(active(x0), x1, x2)
744.35/263.09	   U82(x0, active(x1), x2)
744.35/263.09	   U82(x0, x1, active(x2))
744.35/263.09	   U83(mark(x0), x1, x2)
744.35/263.09	   U83(x0, mark(x1), x2)
744.35/263.09	   U83(x0, x1, mark(x2))
744.35/263.09	   U83(active(x0), x1, x2)
744.35/263.09	   U83(x0, active(x1), x2)
744.35/263.09	   U83(x0, x1, active(x2))
744.35/263.09	   U84(mark(x0), x1, x2)
744.35/263.09	   U84(x0, mark(x1), x2)
744.35/263.09	   U84(x0, x1, mark(x2))
744.35/263.09	   U84(active(x0), x1, x2)
744.35/263.09	   U84(x0, active(x1), x2)
744.35/263.09	   U84(x0, x1, active(x2))
744.35/263.09	   s(mark(x0))
744.35/263.09	   s(active(x0))
744.35/263.09	   U91(mark(x0), x1)
744.35/263.09	   U91(x0, mark(x1))
744.35/263.09	   U91(active(x0), x1)
744.35/263.09	   U91(x0, active(x1))
744.35/263.09	   U92(mark(x0))
744.35/263.09	   U92(active(x0))
744.35/263.09	
744.35/263.09	We have to consider all minimal (P,Q,R)-chains.
744.35/263.09	----------------------------------------
744.35/263.09	
744.35/263.09	(329) DependencyGraphProof (EQUIVALENT)
744.35/263.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.35/263.09	----------------------------------------
744.35/263.09	
744.35/263.09	(330)
744.35/263.09	Obligation:
744.35/263.09	Q DP problem:
744.35/263.09	The TRS P consists of the following rules:
744.35/263.09	
744.35/263.09	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.09	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.09	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.09	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.09	   MARK(U16(X)) -> MARK(X)
744.35/263.09	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.09	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.09	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.09	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.09	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.09	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.09	   MARK(U23(X)) -> MARK(X)
744.35/263.09	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.09	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.09	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.09	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.35/263.09	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.35/263.09	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.09	   MARK(U42(X)) -> MARK(X)
744.35/263.09	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.09	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.09	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.09	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.35/263.09	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.09	   MARK(U51(X)) -> MARK(X)
744.35/263.09	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.09	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.09	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.09	
744.35/263.09	The TRS R consists of the following rules:
744.35/263.09	
744.35/263.09	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.09	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.09	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.09	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.09	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.09	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.09	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.09	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.09	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.09	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.09	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.09	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.09	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.09	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.09	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.09	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.09	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.09	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.09	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.09	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.09	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.09	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.09	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.09	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.09	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.09	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.09	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.09	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.09	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.09	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.09	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.09	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.09	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.09	   active(U72(tt, N)) -> mark(N)
744.35/263.09	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.09	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.09	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.09	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.09	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.09	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.09	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.09	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.09	   mark(s(X)) -> active(s(mark(X)))
744.35/263.09	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.09	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.09	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.09	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.09	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.09	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.09	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.09	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.09	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.09	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.09	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.09	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.09	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.09	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.09	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.09	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.09	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.09	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.09	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.09	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.09	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.09	   mark(isNat(X)) -> active(isNat(X))
744.35/263.09	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.09	   mark(tt) -> active(tt)
744.35/263.09	   mark(0) -> active(0)
744.35/263.09	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.09	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.09	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.09	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.09	   active(U16(tt)) -> mark(tt)
744.35/263.09	   active(U23(tt)) -> mark(tt)
744.35/263.09	   active(U36(tt)) -> mark(tt)
744.35/263.09	   active(U42(tt)) -> mark(tt)
744.35/263.09	   active(U51(tt)) -> mark(tt)
744.35/263.09	   active(U62(tt)) -> mark(tt)
744.35/263.09	   active(U92(tt)) -> mark(0)
744.35/263.09	   active(isNat(0)) -> mark(tt)
744.35/263.09	   active(isNatKind(0)) -> mark(tt)
744.35/263.09	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.09	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.09	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.09	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.09	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.09	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.09	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.09	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.09	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.09	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.09	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.09	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.09	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.09	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.09	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.09	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.09	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.09	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.09	   U16(active(X)) -> U16(X)
744.35/263.09	   U16(mark(X)) -> U16(X)
744.35/263.09	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.09	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.09	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.09	   U23(active(X)) -> U23(X)
744.35/263.09	   U23(mark(X)) -> U23(X)
744.35/263.09	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.09	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.09	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.09	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.09	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.09	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.09	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.09	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.09	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.09	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.09	   U36(active(X)) -> U36(X)
744.35/263.09	   U36(mark(X)) -> U36(X)
744.35/263.09	   U42(active(X)) -> U42(X)
744.35/263.09	   U42(mark(X)) -> U42(X)
744.35/263.09	   U62(active(X)) -> U62(X)
744.35/263.09	   U62(mark(X)) -> U62(X)
744.35/263.09	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.09	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.09	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.09	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.09	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.09	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.09	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.09	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.09	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.09	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.09	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.09	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.09	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.09	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.09	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.09	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.09	   s(active(X)) -> s(X)
744.35/263.09	   s(mark(X)) -> s(X)
744.35/263.09	   U92(active(X)) -> U92(X)
744.35/263.09	   U92(mark(X)) -> U92(X)
744.35/263.09	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.09	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.09	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.09	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.09	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.09	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.09	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.09	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.09	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.09	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.09	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.09	   U51(active(X)) -> U51(X)
744.35/263.09	   U51(mark(X)) -> U51(X)
744.35/263.09	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.09	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.09	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.09	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.09	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.09	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.09	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.09	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.09	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.09	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.09	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.09	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.09	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.09	   x(active(X1), X2) -> x(X1, X2)
744.35/263.09	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.09	
744.35/263.09	The set Q consists of the following terms:
744.35/263.09	
744.35/263.09	   active(U101(tt, x0, x1))
744.35/263.09	   active(U102(tt, x0, x1))
744.35/263.09	   active(U103(tt, x0, x1))
744.35/263.09	   active(U104(tt, x0, x1))
744.35/263.09	   active(U11(tt, x0, x1))
744.35/263.09	   active(U12(tt, x0, x1))
744.35/263.09	   active(U13(tt, x0, x1))
744.35/263.09	   active(U14(tt, x0, x1))
744.35/263.09	   active(U15(tt, x0))
744.35/263.09	   active(U16(tt))
744.35/263.09	   active(U21(tt, x0))
744.35/263.09	   active(U22(tt, x0))
744.35/263.09	   active(U23(tt))
744.35/263.09	   active(U31(tt, x0, x1))
744.35/263.09	   active(U32(tt, x0, x1))
744.35/263.09	   active(U33(tt, x0, x1))
744.35/263.09	   active(U34(tt, x0, x1))
744.35/263.09	   active(U35(tt, x0))
744.35/263.09	   active(U36(tt))
744.35/263.09	   active(U41(tt, x0))
744.35/263.09	   active(U42(tt))
744.35/263.09	   active(U51(tt))
744.35/263.09	   active(U61(tt, x0))
744.35/263.09	   active(U62(tt))
744.35/263.09	   active(U71(tt, x0))
744.35/263.09	   active(U72(tt, x0))
744.35/263.09	   active(U81(tt, x0, x1))
744.35/263.09	   active(U82(tt, x0, x1))
744.35/263.09	   active(U83(tt, x0, x1))
744.35/263.09	   active(U84(tt, x0, x1))
744.35/263.09	   active(U91(tt, x0))
744.35/263.09	   active(U92(tt))
744.35/263.09	   active(isNat(0))
744.35/263.09	   active(isNat(plus(x0, x1)))
744.35/263.09	   active(isNat(s(x0)))
744.35/263.09	   active(isNat(x(x0, x1)))
744.35/263.09	   active(isNatKind(0))
744.35/263.09	   active(isNatKind(plus(x0, x1)))
744.35/263.09	   active(isNatKind(s(x0)))
744.35/263.09	   active(isNatKind(x(x0, x1)))
744.35/263.09	   active(plus(x0, 0))
744.35/263.09	   active(plus(x0, s(x1)))
744.35/263.09	   active(x(x0, 0))
744.35/263.09	   active(x(x0, s(x1)))
744.35/263.09	   mark(U101(x0, x1, x2))
744.35/263.09	   mark(tt)
744.35/263.09	   mark(U102(x0, x1, x2))
744.35/263.09	   mark(isNatKind(x0))
744.35/263.09	   mark(U103(x0, x1, x2))
744.35/263.09	   mark(isNat(x0))
744.35/263.09	   mark(U104(x0, x1, x2))
744.35/263.09	   mark(plus(x0, x1))
744.35/263.09	   mark(x(x0, x1))
744.35/263.09	   mark(U11(x0, x1, x2))
744.35/263.09	   mark(U12(x0, x1, x2))
744.35/263.09	   mark(U13(x0, x1, x2))
744.35/263.09	   mark(U14(x0, x1, x2))
744.35/263.09	   mark(U15(x0, x1))
744.35/263.09	   mark(U16(x0))
744.35/263.09	   mark(U21(x0, x1))
744.35/263.09	   mark(U22(x0, x1))
744.35/263.09	   mark(U23(x0))
744.35/263.09	   mark(U31(x0, x1, x2))
744.35/263.09	   mark(U32(x0, x1, x2))
744.35/263.09	   mark(U33(x0, x1, x2))
744.35/263.09	   mark(U34(x0, x1, x2))
744.35/263.09	   mark(U35(x0, x1))
744.35/263.09	   mark(U36(x0))
744.35/263.09	   mark(U41(x0, x1))
744.35/263.09	   mark(U42(x0))
744.35/263.09	   mark(U51(x0))
744.35/263.09	   mark(U61(x0, x1))
744.35/263.09	   mark(U62(x0))
744.35/263.09	   mark(U71(x0, x1))
744.35/263.09	   mark(U72(x0, x1))
744.35/263.09	   mark(U81(x0, x1, x2))
744.35/263.09	   mark(U82(x0, x1, x2))
744.35/263.09	   mark(U83(x0, x1, x2))
744.35/263.09	   mark(U84(x0, x1, x2))
744.35/263.09	   mark(s(x0))
744.35/263.09	   mark(U91(x0, x1))
744.35/263.09	   mark(U92(x0))
744.35/263.09	   mark(0)
744.35/263.09	   U101(mark(x0), x1, x2)
744.35/263.09	   U101(x0, mark(x1), x2)
744.35/263.09	   U101(x0, x1, mark(x2))
744.35/263.09	   U101(active(x0), x1, x2)
744.35/263.09	   U101(x0, active(x1), x2)
744.35/263.09	   U101(x0, x1, active(x2))
744.35/263.09	   U102(mark(x0), x1, x2)
744.35/263.09	   U102(x0, mark(x1), x2)
744.35/263.09	   U102(x0, x1, mark(x2))
744.35/263.09	   U102(active(x0), x1, x2)
744.35/263.09	   U102(x0, active(x1), x2)
744.35/263.09	   U102(x0, x1, active(x2))
744.35/263.09	   isNatKind(mark(x0))
744.35/263.09	   isNatKind(active(x0))
744.35/263.09	   U103(mark(x0), x1, x2)
744.35/263.09	   U103(x0, mark(x1), x2)
744.35/263.09	   U103(x0, x1, mark(x2))
744.35/263.09	   U103(active(x0), x1, x2)
744.35/263.09	   U103(x0, active(x1), x2)
744.35/263.09	   U103(x0, x1, active(x2))
744.35/263.09	   isNat(mark(x0))
744.35/263.09	   isNat(active(x0))
744.35/263.09	   U104(mark(x0), x1, x2)
744.35/263.09	   U104(x0, mark(x1), x2)
744.35/263.09	   U104(x0, x1, mark(x2))
744.35/263.09	   U104(active(x0), x1, x2)
744.35/263.09	   U104(x0, active(x1), x2)
744.35/263.09	   U104(x0, x1, active(x2))
744.35/263.09	   plus(mark(x0), x1)
744.35/263.09	   plus(x0, mark(x1))
744.35/263.09	   plus(active(x0), x1)
744.35/263.09	   plus(x0, active(x1))
744.35/263.09	   x(mark(x0), x1)
744.35/263.09	   x(x0, mark(x1))
744.35/263.09	   x(active(x0), x1)
744.35/263.09	   x(x0, active(x1))
744.35/263.09	   U11(mark(x0), x1, x2)
744.35/263.09	   U11(x0, mark(x1), x2)
744.35/263.09	   U11(x0, x1, mark(x2))
744.35/263.09	   U11(active(x0), x1, x2)
744.35/263.09	   U11(x0, active(x1), x2)
744.35/263.09	   U11(x0, x1, active(x2))
744.35/263.09	   U12(mark(x0), x1, x2)
744.35/263.09	   U12(x0, mark(x1), x2)
744.35/263.09	   U12(x0, x1, mark(x2))
744.35/263.09	   U12(active(x0), x1, x2)
744.35/263.09	   U12(x0, active(x1), x2)
744.35/263.09	   U12(x0, x1, active(x2))
744.35/263.09	   U13(mark(x0), x1, x2)
744.35/263.09	   U13(x0, mark(x1), x2)
744.35/263.09	   U13(x0, x1, mark(x2))
744.35/263.09	   U13(active(x0), x1, x2)
744.35/263.09	   U13(x0, active(x1), x2)
744.35/263.09	   U13(x0, x1, active(x2))
744.35/263.09	   U14(mark(x0), x1, x2)
744.35/263.09	   U14(x0, mark(x1), x2)
744.35/263.09	   U14(x0, x1, mark(x2))
744.35/263.09	   U14(active(x0), x1, x2)
744.35/263.09	   U14(x0, active(x1), x2)
744.35/263.09	   U14(x0, x1, active(x2))
744.35/263.09	   U15(mark(x0), x1)
744.35/263.09	   U15(x0, mark(x1))
744.35/263.09	   U15(active(x0), x1)
744.35/263.09	   U15(x0, active(x1))
744.35/263.09	   U16(mark(x0))
744.35/263.09	   U16(active(x0))
744.35/263.09	   U21(mark(x0), x1)
744.35/263.09	   U21(x0, mark(x1))
744.35/263.09	   U21(active(x0), x1)
744.35/263.09	   U21(x0, active(x1))
744.35/263.09	   U22(mark(x0), x1)
744.35/263.09	   U22(x0, mark(x1))
744.35/263.09	   U22(active(x0), x1)
744.35/263.09	   U22(x0, active(x1))
744.35/263.09	   U23(mark(x0))
744.35/263.09	   U23(active(x0))
744.35/263.09	   U31(mark(x0), x1, x2)
744.35/263.09	   U31(x0, mark(x1), x2)
744.35/263.09	   U31(x0, x1, mark(x2))
744.35/263.09	   U31(active(x0), x1, x2)
744.35/263.09	   U31(x0, active(x1), x2)
744.35/263.09	   U31(x0, x1, active(x2))
744.35/263.09	   U32(mark(x0), x1, x2)
744.35/263.09	   U32(x0, mark(x1), x2)
744.35/263.09	   U32(x0, x1, mark(x2))
744.35/263.09	   U32(active(x0), x1, x2)
744.35/263.09	   U32(x0, active(x1), x2)
744.35/263.09	   U32(x0, x1, active(x2))
744.35/263.09	   U33(mark(x0), x1, x2)
744.35/263.09	   U33(x0, mark(x1), x2)
744.35/263.09	   U33(x0, x1, mark(x2))
744.35/263.09	   U33(active(x0), x1, x2)
744.35/263.09	   U33(x0, active(x1), x2)
744.35/263.09	   U33(x0, x1, active(x2))
744.35/263.09	   U34(mark(x0), x1, x2)
744.35/263.09	   U34(x0, mark(x1), x2)
744.35/263.09	   U34(x0, x1, mark(x2))
744.35/263.09	   U34(active(x0), x1, x2)
744.35/263.09	   U34(x0, active(x1), x2)
744.35/263.09	   U34(x0, x1, active(x2))
744.35/263.09	   U35(mark(x0), x1)
744.35/263.09	   U35(x0, mark(x1))
744.35/263.09	   U35(active(x0), x1)
744.35/263.09	   U35(x0, active(x1))
744.35/263.09	   U36(mark(x0))
744.35/263.09	   U36(active(x0))
744.35/263.09	   U41(mark(x0), x1)
744.35/263.09	   U41(x0, mark(x1))
744.35/263.09	   U41(active(x0), x1)
744.35/263.09	   U41(x0, active(x1))
744.35/263.09	   U42(mark(x0))
744.35/263.09	   U42(active(x0))
744.35/263.09	   U51(mark(x0))
744.35/263.09	   U51(active(x0))
744.35/263.09	   U61(mark(x0), x1)
744.35/263.09	   U61(x0, mark(x1))
744.35/263.09	   U61(active(x0), x1)
744.35/263.09	   U61(x0, active(x1))
744.35/263.09	   U62(mark(x0))
744.35/263.09	   U62(active(x0))
744.35/263.09	   U71(mark(x0), x1)
744.35/263.09	   U71(x0, mark(x1))
744.35/263.09	   U71(active(x0), x1)
744.35/263.09	   U71(x0, active(x1))
744.35/263.09	   U72(mark(x0), x1)
744.35/263.09	   U72(x0, mark(x1))
744.35/263.09	   U72(active(x0), x1)
744.35/263.09	   U72(x0, active(x1))
744.35/263.09	   U81(mark(x0), x1, x2)
744.35/263.09	   U81(x0, mark(x1), x2)
744.35/263.09	   U81(x0, x1, mark(x2))
744.35/263.09	   U81(active(x0), x1, x2)
744.35/263.09	   U81(x0, active(x1), x2)
744.35/263.09	   U81(x0, x1, active(x2))
744.35/263.09	   U82(mark(x0), x1, x2)
744.35/263.09	   U82(x0, mark(x1), x2)
744.35/263.09	   U82(x0, x1, mark(x2))
744.35/263.09	   U82(active(x0), x1, x2)
744.35/263.09	   U82(x0, active(x1), x2)
744.35/263.09	   U82(x0, x1, active(x2))
744.35/263.09	   U83(mark(x0), x1, x2)
744.35/263.09	   U83(x0, mark(x1), x2)
744.35/263.09	   U83(x0, x1, mark(x2))
744.35/263.09	   U83(active(x0), x1, x2)
744.35/263.09	   U83(x0, active(x1), x2)
744.35/263.09	   U83(x0, x1, active(x2))
744.35/263.09	   U84(mark(x0), x1, x2)
744.35/263.09	   U84(x0, mark(x1), x2)
744.35/263.09	   U84(x0, x1, mark(x2))
744.35/263.09	   U84(active(x0), x1, x2)
744.35/263.09	   U84(x0, active(x1), x2)
744.35/263.09	   U84(x0, x1, active(x2))
744.35/263.09	   s(mark(x0))
744.35/263.09	   s(active(x0))
744.35/263.09	   U91(mark(x0), x1)
744.35/263.09	   U91(x0, mark(x1))
744.35/263.09	   U91(active(x0), x1)
744.35/263.09	   U91(x0, active(x1))
744.35/263.09	   U92(mark(x0))
744.35/263.09	   U92(active(x0))
744.35/263.09	
744.35/263.09	We have to consider all minimal (P,Q,R)-chains.
744.35/263.09	----------------------------------------
744.35/263.09	
744.35/263.09	(331) QDPOrderProof (EQUIVALENT)
744.35/263.09	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.09	
744.35/263.09	
744.35/263.09	The following pairs can be oriented strictly and are deleted.
744.35/263.09	
744.35/263.09	   MARK(U33(X1, X2, X3)) -> ACTIVE(U33(mark(X1), X2, X3))
744.35/263.09	The remaining pairs can at least be oriented weakly.
744.35/263.09	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.09	
744.35/263.09	POL( ACTIVE_1(x_1) ) = max{0, x_1 - 1}
744.35/263.09	POL( U11_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U12_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U13_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U14_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U15_2(x_1, x_2) ) = 2
744.35/263.09	POL( U21_2(x_1, x_2) ) = 2
744.35/263.09	POL( U22_2(x_1, x_2) ) = 2
744.35/263.09	POL( U31_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U32_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U33_3(x_1, ..., x_3) ) = 0
744.35/263.09	POL( U41_2(x_1, x_2) ) = 2
744.35/263.09	POL( mark_1(x_1) ) = 2
744.35/263.09	POL( U102_3(x_1, ..., x_3) ) = max{0, x_3 - 2}
744.35/263.09	POL( active_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( U101_3(x_1, ..., x_3) ) = max{0, x_3 - 2}
744.35/263.09	POL( tt ) = 0
744.35/263.09	POL( isNatKind_1(x_1) ) = 2
744.35/263.09	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.09	POL( isNat_1(x_1) ) = 2
744.35/263.09	POL( U104_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( x_2(x_1, x_2) ) = max{0, -2}
744.35/263.09	POL( U16_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U23_1(x_1) ) = max{0, -2}
744.35/263.09	POL( U34_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( U35_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.35/263.09	POL( U36_1(x_1) ) = 2
744.35/263.09	POL( U42_1(x_1) ) = 2
744.35/263.09	POL( U61_2(x_1, x_2) ) = 2x_2 + 2
744.35/263.09	POL( U62_1(x_1) ) = 2
744.35/263.09	POL( U71_2(x_1, x_2) ) = x_2 + 2
744.35/263.09	POL( U72_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.09	POL( U81_3(x_1, ..., x_3) ) = 2
744.35/263.09	POL( U82_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + 2x_3 - 2}
744.35/263.09	POL( U83_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.09	POL( U84_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 + 2x_3 - 2}
744.35/263.09	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.35/263.09	POL( U91_2(x_1, x_2) ) = 2x_2 + 2
744.35/263.09	POL( U92_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.09	POL( U51_1(x_1) ) = max{0, -2}
744.35/263.09	POL( 0 ) = 0
744.35/263.09	POL( MARK_1(x_1) ) = 1
744.35/263.09	
744.35/263.09	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.09	
744.35/263.09	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.09	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.09	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.09	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.09	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.10	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.10	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.10	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.10	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.10	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.10	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.10	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.10	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.10	
744.35/263.10	
744.35/263.10	----------------------------------------
744.35/263.10	
744.35/263.10	(332)
744.35/263.10	Obligation:
744.35/263.10	Q DP problem:
744.35/263.10	The TRS P consists of the following rules:
744.35/263.10	
744.35/263.10	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.10	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.10	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.10	   MARK(U16(X)) -> MARK(X)
744.35/263.10	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.10	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.10	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.10	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.10	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.10	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.10	   MARK(U23(X)) -> MARK(X)
744.35/263.10	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.10	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.35/263.10	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.10	   MARK(U42(X)) -> MARK(X)
744.35/263.10	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.10	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.10	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.10	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.35/263.10	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U51(X)) -> MARK(X)
744.35/263.10	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.10	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.10	
744.35/263.10	The TRS R consists of the following rules:
744.35/263.10	
744.35/263.10	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.10	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.10	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.10	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.10	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.10	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.10	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.10	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.10	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.10	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.10	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.10	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.10	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.10	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.10	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.10	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.10	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.10	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.10	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.10	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.10	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.10	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.10	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.10	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.10	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.10	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.10	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.10	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.10	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.10	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.10	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.10	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.10	   active(U72(tt, N)) -> mark(N)
744.35/263.10	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.10	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.10	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.10	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.10	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.10	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.10	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.10	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.10	   mark(s(X)) -> active(s(mark(X)))
744.35/263.10	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.10	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.10	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.10	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.10	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.10	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.10	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.10	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.10	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.10	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.10	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.10	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.10	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.10	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.10	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.10	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.10	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.10	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.10	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.10	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.10	   mark(isNat(X)) -> active(isNat(X))
744.35/263.10	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.10	   mark(tt) -> active(tt)
744.35/263.10	   mark(0) -> active(0)
744.35/263.10	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.10	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.10	   active(U16(tt)) -> mark(tt)
744.35/263.10	   active(U23(tt)) -> mark(tt)
744.35/263.10	   active(U36(tt)) -> mark(tt)
744.35/263.10	   active(U42(tt)) -> mark(tt)
744.35/263.10	   active(U51(tt)) -> mark(tt)
744.35/263.10	   active(U62(tt)) -> mark(tt)
744.35/263.10	   active(U92(tt)) -> mark(0)
744.35/263.10	   active(isNat(0)) -> mark(tt)
744.35/263.10	   active(isNatKind(0)) -> mark(tt)
744.35/263.10	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.10	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.10	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.10	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.10	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.10	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.10	   U16(active(X)) -> U16(X)
744.35/263.10	   U16(mark(X)) -> U16(X)
744.35/263.10	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.10	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.10	   U23(active(X)) -> U23(X)
744.35/263.10	   U23(mark(X)) -> U23(X)
744.35/263.10	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.10	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.10	   U36(active(X)) -> U36(X)
744.35/263.10	   U36(mark(X)) -> U36(X)
744.35/263.10	   U42(active(X)) -> U42(X)
744.35/263.10	   U42(mark(X)) -> U42(X)
744.35/263.10	   U62(active(X)) -> U62(X)
744.35/263.10	   U62(mark(X)) -> U62(X)
744.35/263.10	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.10	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.10	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.10	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.10	   s(active(X)) -> s(X)
744.35/263.10	   s(mark(X)) -> s(X)
744.35/263.10	   U92(active(X)) -> U92(X)
744.35/263.10	   U92(mark(X)) -> U92(X)
744.35/263.10	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.10	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.10	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.10	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.10	   U51(active(X)) -> U51(X)
744.35/263.10	   U51(mark(X)) -> U51(X)
744.35/263.10	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.10	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.10	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.10	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.10	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.10	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.10	   x(active(X1), X2) -> x(X1, X2)
744.35/263.10	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.10	
744.35/263.10	The set Q consists of the following terms:
744.35/263.10	
744.35/263.10	   active(U101(tt, x0, x1))
744.35/263.10	   active(U102(tt, x0, x1))
744.35/263.10	   active(U103(tt, x0, x1))
744.35/263.10	   active(U104(tt, x0, x1))
744.35/263.10	   active(U11(tt, x0, x1))
744.35/263.10	   active(U12(tt, x0, x1))
744.35/263.10	   active(U13(tt, x0, x1))
744.35/263.10	   active(U14(tt, x0, x1))
744.35/263.10	   active(U15(tt, x0))
744.35/263.10	   active(U16(tt))
744.35/263.10	   active(U21(tt, x0))
744.35/263.10	   active(U22(tt, x0))
744.35/263.10	   active(U23(tt))
744.35/263.10	   active(U31(tt, x0, x1))
744.35/263.10	   active(U32(tt, x0, x1))
744.35/263.10	   active(U33(tt, x0, x1))
744.35/263.10	   active(U34(tt, x0, x1))
744.35/263.10	   active(U35(tt, x0))
744.35/263.10	   active(U36(tt))
744.35/263.10	   active(U41(tt, x0))
744.35/263.10	   active(U42(tt))
744.35/263.10	   active(U51(tt))
744.35/263.10	   active(U61(tt, x0))
744.35/263.10	   active(U62(tt))
744.35/263.10	   active(U71(tt, x0))
744.35/263.10	   active(U72(tt, x0))
744.35/263.10	   active(U81(tt, x0, x1))
744.35/263.10	   active(U82(tt, x0, x1))
744.35/263.10	   active(U83(tt, x0, x1))
744.35/263.10	   active(U84(tt, x0, x1))
744.35/263.10	   active(U91(tt, x0))
744.35/263.10	   active(U92(tt))
744.35/263.10	   active(isNat(0))
744.35/263.10	   active(isNat(plus(x0, x1)))
744.35/263.10	   active(isNat(s(x0)))
744.35/263.10	   active(isNat(x(x0, x1)))
744.35/263.10	   active(isNatKind(0))
744.35/263.10	   active(isNatKind(plus(x0, x1)))
744.35/263.10	   active(isNatKind(s(x0)))
744.35/263.10	   active(isNatKind(x(x0, x1)))
744.35/263.10	   active(plus(x0, 0))
744.35/263.10	   active(plus(x0, s(x1)))
744.35/263.10	   active(x(x0, 0))
744.35/263.10	   active(x(x0, s(x1)))
744.35/263.10	   mark(U101(x0, x1, x2))
744.35/263.10	   mark(tt)
744.35/263.10	   mark(U102(x0, x1, x2))
744.35/263.10	   mark(isNatKind(x0))
744.35/263.10	   mark(U103(x0, x1, x2))
744.35/263.10	   mark(isNat(x0))
744.35/263.10	   mark(U104(x0, x1, x2))
744.35/263.10	   mark(plus(x0, x1))
744.35/263.10	   mark(x(x0, x1))
744.35/263.10	   mark(U11(x0, x1, x2))
744.35/263.10	   mark(U12(x0, x1, x2))
744.35/263.10	   mark(U13(x0, x1, x2))
744.35/263.10	   mark(U14(x0, x1, x2))
744.35/263.10	   mark(U15(x0, x1))
744.35/263.10	   mark(U16(x0))
744.35/263.10	   mark(U21(x0, x1))
744.35/263.10	   mark(U22(x0, x1))
744.35/263.10	   mark(U23(x0))
744.35/263.10	   mark(U31(x0, x1, x2))
744.35/263.10	   mark(U32(x0, x1, x2))
744.35/263.10	   mark(U33(x0, x1, x2))
744.35/263.10	   mark(U34(x0, x1, x2))
744.35/263.10	   mark(U35(x0, x1))
744.35/263.10	   mark(U36(x0))
744.35/263.10	   mark(U41(x0, x1))
744.35/263.10	   mark(U42(x0))
744.35/263.10	   mark(U51(x0))
744.35/263.10	   mark(U61(x0, x1))
744.35/263.10	   mark(U62(x0))
744.35/263.10	   mark(U71(x0, x1))
744.35/263.10	   mark(U72(x0, x1))
744.35/263.10	   mark(U81(x0, x1, x2))
744.35/263.10	   mark(U82(x0, x1, x2))
744.35/263.10	   mark(U83(x0, x1, x2))
744.35/263.10	   mark(U84(x0, x1, x2))
744.35/263.10	   mark(s(x0))
744.35/263.10	   mark(U91(x0, x1))
744.35/263.10	   mark(U92(x0))
744.35/263.10	   mark(0)
744.35/263.10	   U101(mark(x0), x1, x2)
744.35/263.10	   U101(x0, mark(x1), x2)
744.35/263.10	   U101(x0, x1, mark(x2))
744.35/263.10	   U101(active(x0), x1, x2)
744.35/263.10	   U101(x0, active(x1), x2)
744.35/263.10	   U101(x0, x1, active(x2))
744.35/263.10	   U102(mark(x0), x1, x2)
744.35/263.10	   U102(x0, mark(x1), x2)
744.35/263.10	   U102(x0, x1, mark(x2))
744.35/263.10	   U102(active(x0), x1, x2)
744.35/263.10	   U102(x0, active(x1), x2)
744.35/263.10	   U102(x0, x1, active(x2))
744.35/263.10	   isNatKind(mark(x0))
744.35/263.10	   isNatKind(active(x0))
744.35/263.10	   U103(mark(x0), x1, x2)
744.35/263.10	   U103(x0, mark(x1), x2)
744.35/263.10	   U103(x0, x1, mark(x2))
744.35/263.10	   U103(active(x0), x1, x2)
744.35/263.10	   U103(x0, active(x1), x2)
744.35/263.10	   U103(x0, x1, active(x2))
744.35/263.10	   isNat(mark(x0))
744.35/263.10	   isNat(active(x0))
744.35/263.10	   U104(mark(x0), x1, x2)
744.35/263.10	   U104(x0, mark(x1), x2)
744.35/263.10	   U104(x0, x1, mark(x2))
744.35/263.10	   U104(active(x0), x1, x2)
744.35/263.10	   U104(x0, active(x1), x2)
744.35/263.10	   U104(x0, x1, active(x2))
744.35/263.10	   plus(mark(x0), x1)
744.35/263.10	   plus(x0, mark(x1))
744.35/263.10	   plus(active(x0), x1)
744.35/263.10	   plus(x0, active(x1))
744.35/263.10	   x(mark(x0), x1)
744.35/263.10	   x(x0, mark(x1))
744.35/263.10	   x(active(x0), x1)
744.35/263.10	   x(x0, active(x1))
744.35/263.10	   U11(mark(x0), x1, x2)
744.35/263.10	   U11(x0, mark(x1), x2)
744.35/263.10	   U11(x0, x1, mark(x2))
744.35/263.10	   U11(active(x0), x1, x2)
744.35/263.10	   U11(x0, active(x1), x2)
744.35/263.10	   U11(x0, x1, active(x2))
744.35/263.10	   U12(mark(x0), x1, x2)
744.35/263.10	   U12(x0, mark(x1), x2)
744.35/263.10	   U12(x0, x1, mark(x2))
744.35/263.10	   U12(active(x0), x1, x2)
744.35/263.10	   U12(x0, active(x1), x2)
744.35/263.10	   U12(x0, x1, active(x2))
744.35/263.10	   U13(mark(x0), x1, x2)
744.35/263.10	   U13(x0, mark(x1), x2)
744.35/263.10	   U13(x0, x1, mark(x2))
744.35/263.10	   U13(active(x0), x1, x2)
744.35/263.10	   U13(x0, active(x1), x2)
744.35/263.10	   U13(x0, x1, active(x2))
744.35/263.10	   U14(mark(x0), x1, x2)
744.35/263.10	   U14(x0, mark(x1), x2)
744.35/263.10	   U14(x0, x1, mark(x2))
744.35/263.10	   U14(active(x0), x1, x2)
744.35/263.10	   U14(x0, active(x1), x2)
744.35/263.10	   U14(x0, x1, active(x2))
744.35/263.10	   U15(mark(x0), x1)
744.35/263.10	   U15(x0, mark(x1))
744.35/263.10	   U15(active(x0), x1)
744.35/263.10	   U15(x0, active(x1))
744.35/263.10	   U16(mark(x0))
744.35/263.10	   U16(active(x0))
744.35/263.10	   U21(mark(x0), x1)
744.35/263.10	   U21(x0, mark(x1))
744.35/263.10	   U21(active(x0), x1)
744.35/263.10	   U21(x0, active(x1))
744.35/263.10	   U22(mark(x0), x1)
744.35/263.10	   U22(x0, mark(x1))
744.35/263.10	   U22(active(x0), x1)
744.35/263.10	   U22(x0, active(x1))
744.35/263.10	   U23(mark(x0))
744.35/263.10	   U23(active(x0))
744.35/263.10	   U31(mark(x0), x1, x2)
744.35/263.10	   U31(x0, mark(x1), x2)
744.35/263.10	   U31(x0, x1, mark(x2))
744.35/263.10	   U31(active(x0), x1, x2)
744.35/263.10	   U31(x0, active(x1), x2)
744.35/263.10	   U31(x0, x1, active(x2))
744.35/263.10	   U32(mark(x0), x1, x2)
744.35/263.10	   U32(x0, mark(x1), x2)
744.35/263.10	   U32(x0, x1, mark(x2))
744.35/263.10	   U32(active(x0), x1, x2)
744.35/263.10	   U32(x0, active(x1), x2)
744.35/263.10	   U32(x0, x1, active(x2))
744.35/263.10	   U33(mark(x0), x1, x2)
744.35/263.10	   U33(x0, mark(x1), x2)
744.35/263.10	   U33(x0, x1, mark(x2))
744.35/263.10	   U33(active(x0), x1, x2)
744.35/263.10	   U33(x0, active(x1), x2)
744.35/263.10	   U33(x0, x1, active(x2))
744.35/263.10	   U34(mark(x0), x1, x2)
744.35/263.10	   U34(x0, mark(x1), x2)
744.35/263.10	   U34(x0, x1, mark(x2))
744.35/263.10	   U34(active(x0), x1, x2)
744.35/263.10	   U34(x0, active(x1), x2)
744.35/263.10	   U34(x0, x1, active(x2))
744.35/263.10	   U35(mark(x0), x1)
744.35/263.10	   U35(x0, mark(x1))
744.35/263.10	   U35(active(x0), x1)
744.35/263.10	   U35(x0, active(x1))
744.35/263.10	   U36(mark(x0))
744.35/263.10	   U36(active(x0))
744.35/263.10	   U41(mark(x0), x1)
744.35/263.10	   U41(x0, mark(x1))
744.35/263.10	   U41(active(x0), x1)
744.35/263.10	   U41(x0, active(x1))
744.35/263.10	   U42(mark(x0))
744.35/263.10	   U42(active(x0))
744.35/263.10	   U51(mark(x0))
744.35/263.10	   U51(active(x0))
744.35/263.10	   U61(mark(x0), x1)
744.35/263.10	   U61(x0, mark(x1))
744.35/263.10	   U61(active(x0), x1)
744.35/263.10	   U61(x0, active(x1))
744.35/263.10	   U62(mark(x0))
744.35/263.10	   U62(active(x0))
744.35/263.10	   U71(mark(x0), x1)
744.35/263.10	   U71(x0, mark(x1))
744.35/263.10	   U71(active(x0), x1)
744.35/263.10	   U71(x0, active(x1))
744.35/263.10	   U72(mark(x0), x1)
744.35/263.10	   U72(x0, mark(x1))
744.35/263.10	   U72(active(x0), x1)
744.35/263.10	   U72(x0, active(x1))
744.35/263.10	   U81(mark(x0), x1, x2)
744.35/263.10	   U81(x0, mark(x1), x2)
744.35/263.10	   U81(x0, x1, mark(x2))
744.35/263.10	   U81(active(x0), x1, x2)
744.35/263.10	   U81(x0, active(x1), x2)
744.35/263.10	   U81(x0, x1, active(x2))
744.35/263.10	   U82(mark(x0), x1, x2)
744.35/263.10	   U82(x0, mark(x1), x2)
744.35/263.10	   U82(x0, x1, mark(x2))
744.35/263.10	   U82(active(x0), x1, x2)
744.35/263.10	   U82(x0, active(x1), x2)
744.35/263.10	   U82(x0, x1, active(x2))
744.35/263.10	   U83(mark(x0), x1, x2)
744.35/263.10	   U83(x0, mark(x1), x2)
744.35/263.10	   U83(x0, x1, mark(x2))
744.35/263.10	   U83(active(x0), x1, x2)
744.35/263.10	   U83(x0, active(x1), x2)
744.35/263.10	   U83(x0, x1, active(x2))
744.35/263.10	   U84(mark(x0), x1, x2)
744.35/263.10	   U84(x0, mark(x1), x2)
744.35/263.10	   U84(x0, x1, mark(x2))
744.35/263.10	   U84(active(x0), x1, x2)
744.35/263.10	   U84(x0, active(x1), x2)
744.35/263.10	   U84(x0, x1, active(x2))
744.35/263.10	   s(mark(x0))
744.35/263.10	   s(active(x0))
744.35/263.10	   U91(mark(x0), x1)
744.35/263.10	   U91(x0, mark(x1))
744.35/263.10	   U91(active(x0), x1)
744.35/263.10	   U91(x0, active(x1))
744.35/263.10	   U92(mark(x0))
744.35/263.10	   U92(active(x0))
744.35/263.10	
744.35/263.10	We have to consider all minimal (P,Q,R)-chains.
744.35/263.10	----------------------------------------
744.35/263.10	
744.35/263.10	(333) QDPOrderProof (EQUIVALENT)
744.35/263.10	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.10	
744.35/263.10	
744.35/263.10	The following pairs can be oriented strictly and are deleted.
744.35/263.10	
744.35/263.10	   ACTIVE(U32(tt, V1, V2)) -> MARK(U33(isNatKind(V2), V1, V2))
744.35/263.10	The remaining pairs can at least be oriented weakly.
744.35/263.10	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U11(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(tt) =  	[[0A]]
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U14(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(plus(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U21(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U31(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(x(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U103(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U34(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U62(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U81(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U82(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U91(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	   <<<
744.35/263.10	 POL(0) =  	[[0A]]
744.35/263.10	>>>
744.35/263.10	
744.35/263.10	
744.35/263.10	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.10	
744.35/263.10	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.10	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.10	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.10	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.10	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.10	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.10	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.10	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.10	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.10	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.10	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.10	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.10	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.10	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.10	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.10	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.10	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.10	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.10	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.10	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.10	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.10	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.10	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.10	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.10	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.10	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.10	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.10	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.10	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.10	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.10	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.10	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.10	   active(U72(tt, N)) -> mark(N)
744.35/263.10	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.10	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.10	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.10	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.10	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.10	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.10	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.10	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.10	   mark(s(X)) -> active(s(mark(X)))
744.35/263.10	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.10	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.10	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.10	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.10	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.10	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.10	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.10	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.10	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.10	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.10	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.10	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.10	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.10	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.10	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.10	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.10	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.10	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.10	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.10	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.10	   mark(isNat(X)) -> active(isNat(X))
744.35/263.10	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.10	   mark(tt) -> active(tt)
744.35/263.10	   mark(0) -> active(0)
744.35/263.10	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.10	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.10	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.10	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.10	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.10	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.10	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.10	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.10	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.10	   active(U16(tt)) -> mark(tt)
744.35/263.10	   active(U23(tt)) -> mark(tt)
744.35/263.10	   active(U36(tt)) -> mark(tt)
744.35/263.10	   active(U42(tt)) -> mark(tt)
744.35/263.10	   active(U51(tt)) -> mark(tt)
744.35/263.10	   active(U62(tt)) -> mark(tt)
744.35/263.10	   active(U92(tt)) -> mark(0)
744.35/263.10	   active(isNat(0)) -> mark(tt)
744.35/263.10	   active(isNatKind(0)) -> mark(tt)
744.35/263.10	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.10	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.10	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.10	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.10	   U16(active(X)) -> U16(X)
744.35/263.10	   U16(mark(X)) -> U16(X)
744.35/263.10	   U23(active(X)) -> U23(X)
744.35/263.10	   U23(mark(X)) -> U23(X)
744.35/263.10	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.10	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.10	   U36(active(X)) -> U36(X)
744.35/263.10	   U36(mark(X)) -> U36(X)
744.35/263.10	   U42(active(X)) -> U42(X)
744.35/263.10	   U42(mark(X)) -> U42(X)
744.35/263.10	   U62(active(X)) -> U62(X)
744.35/263.10	   U62(mark(X)) -> U62(X)
744.35/263.10	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.10	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.10	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.10	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.10	   s(active(X)) -> s(X)
744.35/263.10	   s(mark(X)) -> s(X)
744.35/263.10	   U92(active(X)) -> U92(X)
744.35/263.10	   U92(mark(X)) -> U92(X)
744.35/263.10	   U51(active(X)) -> U51(X)
744.35/263.10	   U51(mark(X)) -> U51(X)
744.35/263.10	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.10	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.10	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.10	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.10	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.10	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.10	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.10	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.10	   x(active(X1), X2) -> x(X1, X2)
744.35/263.10	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.10	
744.35/263.10	
744.35/263.10	----------------------------------------
744.35/263.10	
744.35/263.10	(334)
744.35/263.10	Obligation:
744.35/263.10	Q DP problem:
744.35/263.10	The TRS P consists of the following rules:
744.35/263.10	
744.35/263.10	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.10	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.10	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.10	   MARK(U16(X)) -> MARK(X)
744.35/263.10	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.10	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.10	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.10	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.10	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.10	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.10	   MARK(U23(X)) -> MARK(X)
744.35/263.10	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.10	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.10	   MARK(U42(X)) -> MARK(X)
744.35/263.10	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.10	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.10	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.10	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.35/263.10	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U51(X)) -> MARK(X)
744.35/263.10	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.10	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.10	
744.35/263.10	The TRS R consists of the following rules:
744.35/263.10	
744.35/263.10	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.10	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.10	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.10	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.10	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.10	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.10	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.10	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.10	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.10	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.10	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.10	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.10	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.10	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.10	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.10	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.10	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.10	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.10	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.10	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.10	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.10	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.10	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.10	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.10	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.10	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.10	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.10	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.10	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.10	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.10	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.10	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.10	   active(U72(tt, N)) -> mark(N)
744.35/263.10	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.10	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.10	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.10	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.10	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.10	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.10	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.10	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.10	   mark(s(X)) -> active(s(mark(X)))
744.35/263.10	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.10	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.10	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.10	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.10	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.10	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.10	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.10	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.10	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.10	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.10	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.10	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.10	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.10	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.10	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.10	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.10	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.10	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.10	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.10	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.10	   mark(isNat(X)) -> active(isNat(X))
744.35/263.10	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.10	   mark(tt) -> active(tt)
744.35/263.10	   mark(0) -> active(0)
744.35/263.10	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.10	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.10	   active(U16(tt)) -> mark(tt)
744.35/263.10	   active(U23(tt)) -> mark(tt)
744.35/263.10	   active(U36(tt)) -> mark(tt)
744.35/263.10	   active(U42(tt)) -> mark(tt)
744.35/263.10	   active(U51(tt)) -> mark(tt)
744.35/263.10	   active(U62(tt)) -> mark(tt)
744.35/263.10	   active(U92(tt)) -> mark(0)
744.35/263.10	   active(isNat(0)) -> mark(tt)
744.35/263.10	   active(isNatKind(0)) -> mark(tt)
744.35/263.10	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.10	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.10	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.10	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.10	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.10	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.10	   U16(active(X)) -> U16(X)
744.35/263.10	   U16(mark(X)) -> U16(X)
744.35/263.10	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.10	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.10	   U23(active(X)) -> U23(X)
744.35/263.10	   U23(mark(X)) -> U23(X)
744.35/263.10	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.10	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.10	   U36(active(X)) -> U36(X)
744.35/263.10	   U36(mark(X)) -> U36(X)
744.35/263.10	   U42(active(X)) -> U42(X)
744.35/263.10	   U42(mark(X)) -> U42(X)
744.35/263.10	   U62(active(X)) -> U62(X)
744.35/263.10	   U62(mark(X)) -> U62(X)
744.35/263.10	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.10	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.10	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.10	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.10	   s(active(X)) -> s(X)
744.35/263.10	   s(mark(X)) -> s(X)
744.35/263.10	   U92(active(X)) -> U92(X)
744.35/263.10	   U92(mark(X)) -> U92(X)
744.35/263.10	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.10	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.10	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.10	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.10	   U51(active(X)) -> U51(X)
744.35/263.10	   U51(mark(X)) -> U51(X)
744.35/263.10	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.10	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.10	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.10	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.10	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.10	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.10	   x(active(X1), X2) -> x(X1, X2)
744.35/263.10	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.10	
744.35/263.10	The set Q consists of the following terms:
744.35/263.10	
744.35/263.10	   active(U101(tt, x0, x1))
744.35/263.10	   active(U102(tt, x0, x1))
744.35/263.10	   active(U103(tt, x0, x1))
744.35/263.10	   active(U104(tt, x0, x1))
744.35/263.10	   active(U11(tt, x0, x1))
744.35/263.10	   active(U12(tt, x0, x1))
744.35/263.10	   active(U13(tt, x0, x1))
744.35/263.10	   active(U14(tt, x0, x1))
744.35/263.10	   active(U15(tt, x0))
744.35/263.10	   active(U16(tt))
744.35/263.10	   active(U21(tt, x0))
744.35/263.10	   active(U22(tt, x0))
744.35/263.10	   active(U23(tt))
744.35/263.10	   active(U31(tt, x0, x1))
744.35/263.10	   active(U32(tt, x0, x1))
744.35/263.10	   active(U33(tt, x0, x1))
744.35/263.10	   active(U34(tt, x0, x1))
744.35/263.10	   active(U35(tt, x0))
744.35/263.10	   active(U36(tt))
744.35/263.10	   active(U41(tt, x0))
744.35/263.10	   active(U42(tt))
744.35/263.10	   active(U51(tt))
744.35/263.10	   active(U61(tt, x0))
744.35/263.10	   active(U62(tt))
744.35/263.10	   active(U71(tt, x0))
744.35/263.10	   active(U72(tt, x0))
744.35/263.10	   active(U81(tt, x0, x1))
744.35/263.10	   active(U82(tt, x0, x1))
744.35/263.10	   active(U83(tt, x0, x1))
744.35/263.10	   active(U84(tt, x0, x1))
744.35/263.10	   active(U91(tt, x0))
744.35/263.10	   active(U92(tt))
744.35/263.10	   active(isNat(0))
744.35/263.10	   active(isNat(plus(x0, x1)))
744.35/263.10	   active(isNat(s(x0)))
744.35/263.10	   active(isNat(x(x0, x1)))
744.35/263.10	   active(isNatKind(0))
744.35/263.10	   active(isNatKind(plus(x0, x1)))
744.35/263.10	   active(isNatKind(s(x0)))
744.35/263.10	   active(isNatKind(x(x0, x1)))
744.35/263.10	   active(plus(x0, 0))
744.35/263.10	   active(plus(x0, s(x1)))
744.35/263.10	   active(x(x0, 0))
744.35/263.10	   active(x(x0, s(x1)))
744.35/263.10	   mark(U101(x0, x1, x2))
744.35/263.10	   mark(tt)
744.35/263.10	   mark(U102(x0, x1, x2))
744.35/263.10	   mark(isNatKind(x0))
744.35/263.10	   mark(U103(x0, x1, x2))
744.35/263.10	   mark(isNat(x0))
744.35/263.10	   mark(U104(x0, x1, x2))
744.35/263.10	   mark(plus(x0, x1))
744.35/263.10	   mark(x(x0, x1))
744.35/263.10	   mark(U11(x0, x1, x2))
744.35/263.10	   mark(U12(x0, x1, x2))
744.35/263.10	   mark(U13(x0, x1, x2))
744.35/263.10	   mark(U14(x0, x1, x2))
744.35/263.10	   mark(U15(x0, x1))
744.35/263.10	   mark(U16(x0))
744.35/263.10	   mark(U21(x0, x1))
744.35/263.10	   mark(U22(x0, x1))
744.35/263.10	   mark(U23(x0))
744.35/263.10	   mark(U31(x0, x1, x2))
744.35/263.10	   mark(U32(x0, x1, x2))
744.35/263.10	   mark(U33(x0, x1, x2))
744.35/263.10	   mark(U34(x0, x1, x2))
744.35/263.10	   mark(U35(x0, x1))
744.35/263.10	   mark(U36(x0))
744.35/263.10	   mark(U41(x0, x1))
744.35/263.10	   mark(U42(x0))
744.35/263.10	   mark(U51(x0))
744.35/263.10	   mark(U61(x0, x1))
744.35/263.10	   mark(U62(x0))
744.35/263.10	   mark(U71(x0, x1))
744.35/263.10	   mark(U72(x0, x1))
744.35/263.10	   mark(U81(x0, x1, x2))
744.35/263.10	   mark(U82(x0, x1, x2))
744.35/263.10	   mark(U83(x0, x1, x2))
744.35/263.10	   mark(U84(x0, x1, x2))
744.35/263.10	   mark(s(x0))
744.35/263.10	   mark(U91(x0, x1))
744.35/263.10	   mark(U92(x0))
744.35/263.10	   mark(0)
744.35/263.10	   U101(mark(x0), x1, x2)
744.35/263.10	   U101(x0, mark(x1), x2)
744.35/263.10	   U101(x0, x1, mark(x2))
744.35/263.10	   U101(active(x0), x1, x2)
744.35/263.10	   U101(x0, active(x1), x2)
744.35/263.10	   U101(x0, x1, active(x2))
744.35/263.10	   U102(mark(x0), x1, x2)
744.35/263.10	   U102(x0, mark(x1), x2)
744.35/263.10	   U102(x0, x1, mark(x2))
744.35/263.10	   U102(active(x0), x1, x2)
744.35/263.10	   U102(x0, active(x1), x2)
744.35/263.10	   U102(x0, x1, active(x2))
744.35/263.10	   isNatKind(mark(x0))
744.35/263.10	   isNatKind(active(x0))
744.35/263.10	   U103(mark(x0), x1, x2)
744.35/263.10	   U103(x0, mark(x1), x2)
744.35/263.10	   U103(x0, x1, mark(x2))
744.35/263.10	   U103(active(x0), x1, x2)
744.35/263.10	   U103(x0, active(x1), x2)
744.35/263.10	   U103(x0, x1, active(x2))
744.35/263.10	   isNat(mark(x0))
744.35/263.10	   isNat(active(x0))
744.35/263.10	   U104(mark(x0), x1, x2)
744.35/263.10	   U104(x0, mark(x1), x2)
744.35/263.10	   U104(x0, x1, mark(x2))
744.35/263.10	   U104(active(x0), x1, x2)
744.35/263.10	   U104(x0, active(x1), x2)
744.35/263.10	   U104(x0, x1, active(x2))
744.35/263.10	   plus(mark(x0), x1)
744.35/263.10	   plus(x0, mark(x1))
744.35/263.10	   plus(active(x0), x1)
744.35/263.10	   plus(x0, active(x1))
744.35/263.10	   x(mark(x0), x1)
744.35/263.10	   x(x0, mark(x1))
744.35/263.10	   x(active(x0), x1)
744.35/263.10	   x(x0, active(x1))
744.35/263.10	   U11(mark(x0), x1, x2)
744.35/263.10	   U11(x0, mark(x1), x2)
744.35/263.10	   U11(x0, x1, mark(x2))
744.35/263.10	   U11(active(x0), x1, x2)
744.35/263.10	   U11(x0, active(x1), x2)
744.35/263.10	   U11(x0, x1, active(x2))
744.35/263.10	   U12(mark(x0), x1, x2)
744.35/263.10	   U12(x0, mark(x1), x2)
744.35/263.10	   U12(x0, x1, mark(x2))
744.35/263.10	   U12(active(x0), x1, x2)
744.35/263.10	   U12(x0, active(x1), x2)
744.35/263.10	   U12(x0, x1, active(x2))
744.35/263.10	   U13(mark(x0), x1, x2)
744.35/263.10	   U13(x0, mark(x1), x2)
744.35/263.10	   U13(x0, x1, mark(x2))
744.35/263.10	   U13(active(x0), x1, x2)
744.35/263.10	   U13(x0, active(x1), x2)
744.35/263.10	   U13(x0, x1, active(x2))
744.35/263.10	   U14(mark(x0), x1, x2)
744.35/263.10	   U14(x0, mark(x1), x2)
744.35/263.10	   U14(x0, x1, mark(x2))
744.35/263.10	   U14(active(x0), x1, x2)
744.35/263.10	   U14(x0, active(x1), x2)
744.35/263.10	   U14(x0, x1, active(x2))
744.35/263.10	   U15(mark(x0), x1)
744.35/263.10	   U15(x0, mark(x1))
744.35/263.10	   U15(active(x0), x1)
744.35/263.10	   U15(x0, active(x1))
744.35/263.10	   U16(mark(x0))
744.35/263.10	   U16(active(x0))
744.35/263.10	   U21(mark(x0), x1)
744.35/263.10	   U21(x0, mark(x1))
744.35/263.10	   U21(active(x0), x1)
744.35/263.10	   U21(x0, active(x1))
744.35/263.10	   U22(mark(x0), x1)
744.35/263.10	   U22(x0, mark(x1))
744.35/263.10	   U22(active(x0), x1)
744.35/263.10	   U22(x0, active(x1))
744.35/263.10	   U23(mark(x0))
744.35/263.10	   U23(active(x0))
744.35/263.10	   U31(mark(x0), x1, x2)
744.35/263.10	   U31(x0, mark(x1), x2)
744.35/263.10	   U31(x0, x1, mark(x2))
744.35/263.10	   U31(active(x0), x1, x2)
744.35/263.10	   U31(x0, active(x1), x2)
744.35/263.10	   U31(x0, x1, active(x2))
744.35/263.10	   U32(mark(x0), x1, x2)
744.35/263.10	   U32(x0, mark(x1), x2)
744.35/263.10	   U32(x0, x1, mark(x2))
744.35/263.10	   U32(active(x0), x1, x2)
744.35/263.10	   U32(x0, active(x1), x2)
744.35/263.10	   U32(x0, x1, active(x2))
744.35/263.10	   U33(mark(x0), x1, x2)
744.35/263.10	   U33(x0, mark(x1), x2)
744.35/263.10	   U33(x0, x1, mark(x2))
744.35/263.10	   U33(active(x0), x1, x2)
744.35/263.10	   U33(x0, active(x1), x2)
744.35/263.10	   U33(x0, x1, active(x2))
744.35/263.10	   U34(mark(x0), x1, x2)
744.35/263.10	   U34(x0, mark(x1), x2)
744.35/263.10	   U34(x0, x1, mark(x2))
744.35/263.10	   U34(active(x0), x1, x2)
744.35/263.10	   U34(x0, active(x1), x2)
744.35/263.10	   U34(x0, x1, active(x2))
744.35/263.10	   U35(mark(x0), x1)
744.35/263.10	   U35(x0, mark(x1))
744.35/263.10	   U35(active(x0), x1)
744.35/263.10	   U35(x0, active(x1))
744.35/263.10	   U36(mark(x0))
744.35/263.10	   U36(active(x0))
744.35/263.10	   U41(mark(x0), x1)
744.35/263.10	   U41(x0, mark(x1))
744.35/263.10	   U41(active(x0), x1)
744.35/263.10	   U41(x0, active(x1))
744.35/263.10	   U42(mark(x0))
744.35/263.10	   U42(active(x0))
744.35/263.10	   U51(mark(x0))
744.35/263.10	   U51(active(x0))
744.35/263.10	   U61(mark(x0), x1)
744.35/263.10	   U61(x0, mark(x1))
744.35/263.10	   U61(active(x0), x1)
744.35/263.10	   U61(x0, active(x1))
744.35/263.10	   U62(mark(x0))
744.35/263.10	   U62(active(x0))
744.35/263.10	   U71(mark(x0), x1)
744.35/263.10	   U71(x0, mark(x1))
744.35/263.10	   U71(active(x0), x1)
744.35/263.10	   U71(x0, active(x1))
744.35/263.10	   U72(mark(x0), x1)
744.35/263.10	   U72(x0, mark(x1))
744.35/263.10	   U72(active(x0), x1)
744.35/263.10	   U72(x0, active(x1))
744.35/263.10	   U81(mark(x0), x1, x2)
744.35/263.10	   U81(x0, mark(x1), x2)
744.35/263.10	   U81(x0, x1, mark(x2))
744.35/263.10	   U81(active(x0), x1, x2)
744.35/263.10	   U81(x0, active(x1), x2)
744.35/263.10	   U81(x0, x1, active(x2))
744.35/263.10	   U82(mark(x0), x1, x2)
744.35/263.10	   U82(x0, mark(x1), x2)
744.35/263.10	   U82(x0, x1, mark(x2))
744.35/263.10	   U82(active(x0), x1, x2)
744.35/263.10	   U82(x0, active(x1), x2)
744.35/263.10	   U82(x0, x1, active(x2))
744.35/263.10	   U83(mark(x0), x1, x2)
744.35/263.10	   U83(x0, mark(x1), x2)
744.35/263.10	   U83(x0, x1, mark(x2))
744.35/263.10	   U83(active(x0), x1, x2)
744.35/263.10	   U83(x0, active(x1), x2)
744.35/263.10	   U83(x0, x1, active(x2))
744.35/263.10	   U84(mark(x0), x1, x2)
744.35/263.10	   U84(x0, mark(x1), x2)
744.35/263.10	   U84(x0, x1, mark(x2))
744.35/263.10	   U84(active(x0), x1, x2)
744.35/263.10	   U84(x0, active(x1), x2)
744.35/263.10	   U84(x0, x1, active(x2))
744.35/263.10	   s(mark(x0))
744.35/263.10	   s(active(x0))
744.35/263.10	   U91(mark(x0), x1)
744.35/263.10	   U91(x0, mark(x1))
744.35/263.10	   U91(active(x0), x1)
744.35/263.10	   U91(x0, active(x1))
744.35/263.10	   U92(mark(x0))
744.35/263.10	   U92(active(x0))
744.35/263.10	
744.35/263.10	We have to consider all minimal (P,Q,R)-chains.
744.35/263.10	----------------------------------------
744.35/263.10	
744.35/263.10	(335) QDPOrderProof (EQUIVALENT)
744.35/263.10	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.10	
744.35/263.10	
744.35/263.10	The following pairs can be oriented strictly and are deleted.
744.35/263.10	
744.35/263.10	   MARK(U33(X1, X2, X3)) -> MARK(X1)
744.35/263.10	The remaining pairs can at least be oriented weakly.
744.35/263.10	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.10	
744.35/263.10	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.35/263.10	POL( U11_3(x_1, ..., x_3) ) = 0
744.35/263.10	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.10	POL( U13_3(x_1, ..., x_3) ) = 1
744.35/263.10	POL( U14_3(x_1, ..., x_3) ) = x_1 + 1
744.35/263.10	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.35/263.10	POL( U21_2(x_1, x_2) ) = 0
744.35/263.10	POL( U22_2(x_1, x_2) ) = x_1 + 1
744.35/263.10	POL( U31_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.10	POL( U32_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.10	POL( U41_2(x_1, x_2) ) = x_1 + 1
744.35/263.10	POL( mark_1(x_1) ) = max{0, -2}
744.35/263.10	POL( U102_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_2 + x_3 - 2}
744.35/263.10	POL( active_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.10	POL( U101_3(x_1, ..., x_3) ) = x_2 + x_3 + 2
744.35/263.10	POL( tt ) = 0
744.35/263.10	POL( isNatKind_1(x_1) ) = 0
744.35/263.10	POL( U103_3(x_1, ..., x_3) ) = x_3 + 2
744.35/263.10	POL( isNat_1(x_1) ) = 0
744.35/263.10	POL( U104_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.10	POL( plus_2(x_1, x_2) ) = x_1 + 2
744.35/263.10	POL( x_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.35/263.10	POL( U16_1(x_1) ) = 2x_1 + 1
744.35/263.10	POL( U23_1(x_1) ) = x_1 + 1
744.35/263.10	POL( U33_3(x_1, ..., x_3) ) = x_1 + x_2 + 2
744.35/263.10	POL( U34_3(x_1, ..., x_3) ) = x_2 + x_3 + 2
744.35/263.10	POL( U35_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.10	POL( U36_1(x_1) ) = 1
744.35/263.10	POL( U42_1(x_1) ) = x_1 + 1
744.35/263.10	POL( U61_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.35/263.10	POL( U62_1(x_1) ) = 1
744.35/263.10	POL( U71_2(x_1, x_2) ) = 2
744.35/263.10	POL( U72_2(x_1, x_2) ) = 2
744.35/263.10	POL( U81_3(x_1, ..., x_3) ) = 2
744.35/263.10	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 2}
744.35/263.10	POL( U83_3(x_1, ..., x_3) ) = max{0, x_2 + 2x_3 - 2}
744.35/263.10	POL( U84_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.10	POL( s_1(x_1) ) = max{0, -2}
744.35/263.10	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.10	POL( U92_1(x_1) ) = 0
744.35/263.10	POL( U51_1(x_1) ) = x_1 + 1
744.35/263.10	POL( 0 ) = 0
744.35/263.10	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.35/263.10	
744.35/263.10	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.10	none
744.35/263.10	
744.35/263.10	
744.35/263.10	----------------------------------------
744.35/263.10	
744.35/263.10	(336)
744.35/263.10	Obligation:
744.35/263.10	Q DP problem:
744.35/263.10	The TRS P consists of the following rules:
744.35/263.10	
744.35/263.10	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.10	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.10	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.10	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.10	   MARK(U16(X)) -> MARK(X)
744.35/263.10	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.10	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.10	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.10	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.10	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.10	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.10	   MARK(U23(X)) -> MARK(X)
744.35/263.10	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.10	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.10	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.10	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.10	   MARK(U42(X)) -> MARK(X)
744.35/263.10	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.10	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.10	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.10	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.10	   MARK(U51(X)) -> MARK(X)
744.35/263.10	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.10	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.10	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.10	
744.35/263.10	The TRS R consists of the following rules:
744.35/263.10	
744.35/263.10	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.10	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.10	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.10	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.10	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.10	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.10	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.10	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.10	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.10	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.10	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.10	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.10	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.10	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.10	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.10	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.10	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.10	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.10	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.10	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.10	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.10	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.10	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.10	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.10	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.10	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.10	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.10	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.10	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.10	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.10	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.10	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.10	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.10	   active(U72(tt, N)) -> mark(N)
744.35/263.10	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.10	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.10	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.10	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.10	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.10	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.10	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.10	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.10	   mark(s(X)) -> active(s(mark(X)))
744.35/263.10	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.10	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.10	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.10	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.10	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.10	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.10	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.10	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.10	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.10	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.10	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.10	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.10	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.10	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.10	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.10	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.10	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.10	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.10	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.10	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.10	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.10	   mark(isNat(X)) -> active(isNat(X))
744.35/263.10	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.10	   mark(tt) -> active(tt)
744.35/263.10	   mark(0) -> active(0)
744.35/263.10	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.10	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.10	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.10	   active(U16(tt)) -> mark(tt)
744.35/263.10	   active(U23(tt)) -> mark(tt)
744.35/263.10	   active(U36(tt)) -> mark(tt)
744.35/263.10	   active(U42(tt)) -> mark(tt)
744.35/263.10	   active(U51(tt)) -> mark(tt)
744.35/263.10	   active(U62(tt)) -> mark(tt)
744.35/263.10	   active(U92(tt)) -> mark(0)
744.35/263.10	   active(isNat(0)) -> mark(tt)
744.35/263.10	   active(isNatKind(0)) -> mark(tt)
744.35/263.10	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.10	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.10	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.10	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.10	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.10	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.10	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.10	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.10	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.10	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.10	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.10	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.10	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.10	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.10	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.10	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.10	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.10	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.10	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.10	   U16(active(X)) -> U16(X)
744.35/263.10	   U16(mark(X)) -> U16(X)
744.35/263.10	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.10	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.10	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.10	   U23(active(X)) -> U23(X)
744.35/263.10	   U23(mark(X)) -> U23(X)
744.35/263.10	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.10	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.10	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.10	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.10	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.10	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.10	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.10	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.10	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.10	   U36(active(X)) -> U36(X)
744.35/263.10	   U36(mark(X)) -> U36(X)
744.35/263.10	   U42(active(X)) -> U42(X)
744.35/263.10	   U42(mark(X)) -> U42(X)
744.35/263.10	   U62(active(X)) -> U62(X)
744.35/263.10	   U62(mark(X)) -> U62(X)
744.35/263.10	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.10	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.10	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.10	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.10	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.10	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.10	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.10	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.10	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.10	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.10	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.10	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.10	   s(active(X)) -> s(X)
744.35/263.10	   s(mark(X)) -> s(X)
744.35/263.10	   U92(active(X)) -> U92(X)
744.35/263.10	   U92(mark(X)) -> U92(X)
744.35/263.10	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.10	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.10	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.10	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.10	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.10	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.10	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.10	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.10	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.10	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.10	   U51(active(X)) -> U51(X)
744.35/263.10	   U51(mark(X)) -> U51(X)
744.35/263.10	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.10	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.10	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.10	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.10	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.10	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.10	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.10	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.10	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.10	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.10	   x(active(X1), X2) -> x(X1, X2)
744.35/263.10	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.10	
744.35/263.10	The set Q consists of the following terms:
744.35/263.10	
744.35/263.10	   active(U101(tt, x0, x1))
744.35/263.10	   active(U102(tt, x0, x1))
744.35/263.10	   active(U103(tt, x0, x1))
744.35/263.10	   active(U104(tt, x0, x1))
744.35/263.10	   active(U11(tt, x0, x1))
744.35/263.10	   active(U12(tt, x0, x1))
744.35/263.10	   active(U13(tt, x0, x1))
744.35/263.10	   active(U14(tt, x0, x1))
744.35/263.10	   active(U15(tt, x0))
744.35/263.10	   active(U16(tt))
744.35/263.10	   active(U21(tt, x0))
744.35/263.10	   active(U22(tt, x0))
744.35/263.10	   active(U23(tt))
744.35/263.10	   active(U31(tt, x0, x1))
744.35/263.10	   active(U32(tt, x0, x1))
744.35/263.10	   active(U33(tt, x0, x1))
744.35/263.10	   active(U34(tt, x0, x1))
744.35/263.10	   active(U35(tt, x0))
744.35/263.10	   active(U36(tt))
744.35/263.10	   active(U41(tt, x0))
744.35/263.10	   active(U42(tt))
744.35/263.10	   active(U51(tt))
744.35/263.10	   active(U61(tt, x0))
744.35/263.10	   active(U62(tt))
744.35/263.10	   active(U71(tt, x0))
744.35/263.10	   active(U72(tt, x0))
744.35/263.10	   active(U81(tt, x0, x1))
744.35/263.10	   active(U82(tt, x0, x1))
744.35/263.10	   active(U83(tt, x0, x1))
744.35/263.10	   active(U84(tt, x0, x1))
744.35/263.10	   active(U91(tt, x0))
744.35/263.10	   active(U92(tt))
744.35/263.10	   active(isNat(0))
744.35/263.10	   active(isNat(plus(x0, x1)))
744.35/263.10	   active(isNat(s(x0)))
744.35/263.10	   active(isNat(x(x0, x1)))
744.35/263.10	   active(isNatKind(0))
744.35/263.10	   active(isNatKind(plus(x0, x1)))
744.35/263.10	   active(isNatKind(s(x0)))
744.35/263.10	   active(isNatKind(x(x0, x1)))
744.35/263.10	   active(plus(x0, 0))
744.35/263.10	   active(plus(x0, s(x1)))
744.35/263.10	   active(x(x0, 0))
744.35/263.10	   active(x(x0, s(x1)))
744.35/263.10	   mark(U101(x0, x1, x2))
744.35/263.10	   mark(tt)
744.35/263.10	   mark(U102(x0, x1, x2))
744.35/263.10	   mark(isNatKind(x0))
744.35/263.10	   mark(U103(x0, x1, x2))
744.35/263.10	   mark(isNat(x0))
744.35/263.10	   mark(U104(x0, x1, x2))
744.35/263.10	   mark(plus(x0, x1))
744.35/263.10	   mark(x(x0, x1))
744.35/263.10	   mark(U11(x0, x1, x2))
744.35/263.10	   mark(U12(x0, x1, x2))
744.35/263.10	   mark(U13(x0, x1, x2))
744.35/263.10	   mark(U14(x0, x1, x2))
744.35/263.10	   mark(U15(x0, x1))
744.35/263.10	   mark(U16(x0))
744.35/263.10	   mark(U21(x0, x1))
744.35/263.10	   mark(U22(x0, x1))
744.35/263.10	   mark(U23(x0))
744.35/263.10	   mark(U31(x0, x1, x2))
744.35/263.10	   mark(U32(x0, x1, x2))
744.35/263.10	   mark(U33(x0, x1, x2))
744.35/263.10	   mark(U34(x0, x1, x2))
744.35/263.10	   mark(U35(x0, x1))
744.35/263.10	   mark(U36(x0))
744.35/263.10	   mark(U41(x0, x1))
744.35/263.10	   mark(U42(x0))
744.35/263.10	   mark(U51(x0))
744.35/263.10	   mark(U61(x0, x1))
744.35/263.10	   mark(U62(x0))
744.35/263.10	   mark(U71(x0, x1))
744.35/263.10	   mark(U72(x0, x1))
744.35/263.10	   mark(U81(x0, x1, x2))
744.35/263.10	   mark(U82(x0, x1, x2))
744.35/263.10	   mark(U83(x0, x1, x2))
744.35/263.10	   mark(U84(x0, x1, x2))
744.35/263.10	   mark(s(x0))
744.35/263.10	   mark(U91(x0, x1))
744.35/263.10	   mark(U92(x0))
744.35/263.10	   mark(0)
744.35/263.10	   U101(mark(x0), x1, x2)
744.35/263.10	   U101(x0, mark(x1), x2)
744.35/263.10	   U101(x0, x1, mark(x2))
744.35/263.10	   U101(active(x0), x1, x2)
744.35/263.10	   U101(x0, active(x1), x2)
744.35/263.10	   U101(x0, x1, active(x2))
744.35/263.10	   U102(mark(x0), x1, x2)
744.35/263.10	   U102(x0, mark(x1), x2)
744.35/263.10	   U102(x0, x1, mark(x2))
744.35/263.10	   U102(active(x0), x1, x2)
744.35/263.10	   U102(x0, active(x1), x2)
744.35/263.10	   U102(x0, x1, active(x2))
744.35/263.10	   isNatKind(mark(x0))
744.35/263.10	   isNatKind(active(x0))
744.35/263.10	   U103(mark(x0), x1, x2)
744.35/263.10	   U103(x0, mark(x1), x2)
744.35/263.10	   U103(x0, x1, mark(x2))
744.35/263.10	   U103(active(x0), x1, x2)
744.35/263.10	   U103(x0, active(x1), x2)
744.35/263.10	   U103(x0, x1, active(x2))
744.35/263.10	   isNat(mark(x0))
744.35/263.10	   isNat(active(x0))
744.35/263.10	   U104(mark(x0), x1, x2)
744.35/263.10	   U104(x0, mark(x1), x2)
744.35/263.10	   U104(x0, x1, mark(x2))
744.35/263.10	   U104(active(x0), x1, x2)
744.35/263.10	   U104(x0, active(x1), x2)
744.35/263.10	   U104(x0, x1, active(x2))
744.35/263.10	   plus(mark(x0), x1)
744.35/263.10	   plus(x0, mark(x1))
744.35/263.10	   plus(active(x0), x1)
744.35/263.10	   plus(x0, active(x1))
744.35/263.10	   x(mark(x0), x1)
744.35/263.10	   x(x0, mark(x1))
744.35/263.10	   x(active(x0), x1)
744.35/263.10	   x(x0, active(x1))
744.35/263.10	   U11(mark(x0), x1, x2)
744.35/263.10	   U11(x0, mark(x1), x2)
744.35/263.10	   U11(x0, x1, mark(x2))
744.35/263.10	   U11(active(x0), x1, x2)
744.35/263.10	   U11(x0, active(x1), x2)
744.35/263.10	   U11(x0, x1, active(x2))
744.35/263.10	   U12(mark(x0), x1, x2)
744.35/263.10	   U12(x0, mark(x1), x2)
744.35/263.10	   U12(x0, x1, mark(x2))
744.35/263.10	   U12(active(x0), x1, x2)
744.35/263.10	   U12(x0, active(x1), x2)
744.35/263.10	   U12(x0, x1, active(x2))
744.35/263.10	   U13(mark(x0), x1, x2)
744.35/263.10	   U13(x0, mark(x1), x2)
744.35/263.10	   U13(x0, x1, mark(x2))
744.35/263.10	   U13(active(x0), x1, x2)
744.35/263.10	   U13(x0, active(x1), x2)
744.35/263.10	   U13(x0, x1, active(x2))
744.35/263.10	   U14(mark(x0), x1, x2)
744.35/263.10	   U14(x0, mark(x1), x2)
744.35/263.10	   U14(x0, x1, mark(x2))
744.35/263.10	   U14(active(x0), x1, x2)
744.35/263.10	   U14(x0, active(x1), x2)
744.35/263.10	   U14(x0, x1, active(x2))
744.35/263.10	   U15(mark(x0), x1)
744.35/263.10	   U15(x0, mark(x1))
744.35/263.10	   U15(active(x0), x1)
744.35/263.10	   U15(x0, active(x1))
744.35/263.10	   U16(mark(x0))
744.35/263.10	   U16(active(x0))
744.35/263.10	   U21(mark(x0), x1)
744.35/263.10	   U21(x0, mark(x1))
744.35/263.10	   U21(active(x0), x1)
744.35/263.10	   U21(x0, active(x1))
744.35/263.10	   U22(mark(x0), x1)
744.35/263.10	   U22(x0, mark(x1))
744.35/263.10	   U22(active(x0), x1)
744.35/263.10	   U22(x0, active(x1))
744.35/263.10	   U23(mark(x0))
744.35/263.10	   U23(active(x0))
744.35/263.10	   U31(mark(x0), x1, x2)
744.35/263.11	   U31(x0, mark(x1), x2)
744.35/263.11	   U31(x0, x1, mark(x2))
744.35/263.11	   U31(active(x0), x1, x2)
744.35/263.11	   U31(x0, active(x1), x2)
744.35/263.11	   U31(x0, x1, active(x2))
744.35/263.11	   U32(mark(x0), x1, x2)
744.35/263.11	   U32(x0, mark(x1), x2)
744.35/263.11	   U32(x0, x1, mark(x2))
744.35/263.11	   U32(active(x0), x1, x2)
744.35/263.11	   U32(x0, active(x1), x2)
744.35/263.11	   U32(x0, x1, active(x2))
744.35/263.11	   U33(mark(x0), x1, x2)
744.35/263.11	   U33(x0, mark(x1), x2)
744.35/263.11	   U33(x0, x1, mark(x2))
744.35/263.11	   U33(active(x0), x1, x2)
744.35/263.11	   U33(x0, active(x1), x2)
744.35/263.11	   U33(x0, x1, active(x2))
744.35/263.11	   U34(mark(x0), x1, x2)
744.35/263.11	   U34(x0, mark(x1), x2)
744.35/263.11	   U34(x0, x1, mark(x2))
744.35/263.11	   U34(active(x0), x1, x2)
744.35/263.11	   U34(x0, active(x1), x2)
744.35/263.11	   U34(x0, x1, active(x2))
744.35/263.11	   U35(mark(x0), x1)
744.35/263.11	   U35(x0, mark(x1))
744.35/263.11	   U35(active(x0), x1)
744.35/263.11	   U35(x0, active(x1))
744.35/263.11	   U36(mark(x0))
744.35/263.11	   U36(active(x0))
744.35/263.11	   U41(mark(x0), x1)
744.35/263.11	   U41(x0, mark(x1))
744.35/263.11	   U41(active(x0), x1)
744.35/263.11	   U41(x0, active(x1))
744.35/263.11	   U42(mark(x0))
744.35/263.11	   U42(active(x0))
744.35/263.11	   U51(mark(x0))
744.35/263.11	   U51(active(x0))
744.35/263.11	   U61(mark(x0), x1)
744.35/263.11	   U61(x0, mark(x1))
744.35/263.11	   U61(active(x0), x1)
744.35/263.11	   U61(x0, active(x1))
744.35/263.11	   U62(mark(x0))
744.35/263.11	   U62(active(x0))
744.35/263.11	   U71(mark(x0), x1)
744.35/263.11	   U71(x0, mark(x1))
744.35/263.11	   U71(active(x0), x1)
744.35/263.11	   U71(x0, active(x1))
744.35/263.11	   U72(mark(x0), x1)
744.35/263.11	   U72(x0, mark(x1))
744.35/263.11	   U72(active(x0), x1)
744.35/263.11	   U72(x0, active(x1))
744.35/263.11	   U81(mark(x0), x1, x2)
744.35/263.11	   U81(x0, mark(x1), x2)
744.35/263.11	   U81(x0, x1, mark(x2))
744.35/263.11	   U81(active(x0), x1, x2)
744.35/263.11	   U81(x0, active(x1), x2)
744.35/263.11	   U81(x0, x1, active(x2))
744.35/263.11	   U82(mark(x0), x1, x2)
744.35/263.11	   U82(x0, mark(x1), x2)
744.35/263.11	   U82(x0, x1, mark(x2))
744.35/263.11	   U82(active(x0), x1, x2)
744.35/263.11	   U82(x0, active(x1), x2)
744.35/263.11	   U82(x0, x1, active(x2))
744.35/263.11	   U83(mark(x0), x1, x2)
744.35/263.11	   U83(x0, mark(x1), x2)
744.35/263.11	   U83(x0, x1, mark(x2))
744.35/263.11	   U83(active(x0), x1, x2)
744.35/263.11	   U83(x0, active(x1), x2)
744.35/263.11	   U83(x0, x1, active(x2))
744.35/263.11	   U84(mark(x0), x1, x2)
744.35/263.11	   U84(x0, mark(x1), x2)
744.35/263.11	   U84(x0, x1, mark(x2))
744.35/263.11	   U84(active(x0), x1, x2)
744.35/263.11	   U84(x0, active(x1), x2)
744.35/263.11	   U84(x0, x1, active(x2))
744.35/263.11	   s(mark(x0))
744.35/263.11	   s(active(x0))
744.35/263.11	   U91(mark(x0), x1)
744.35/263.11	   U91(x0, mark(x1))
744.35/263.11	   U91(active(x0), x1)
744.35/263.11	   U91(x0, active(x1))
744.35/263.11	   U92(mark(x0))
744.35/263.11	   U92(active(x0))
744.35/263.11	
744.35/263.11	We have to consider all minimal (P,Q,R)-chains.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(337) QDPOrderProof (EQUIVALENT)
744.35/263.11	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.11	
744.35/263.11	
744.35/263.11	The following pairs can be oriented strictly and are deleted.
744.35/263.11	
744.35/263.11	   MARK(U32(X1, X2, X3)) -> ACTIVE(U32(mark(X1), X2, X3))
744.35/263.11	The remaining pairs can at least be oriented weakly.
744.35/263.11	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.11	
744.35/263.11	POL( ACTIVE_1(x_1) ) = x_1
744.35/263.11	POL( U11_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U12_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U13_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U14_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U15_2(x_1, x_2) ) = 2
744.35/263.11	POL( U21_2(x_1, x_2) ) = 2
744.35/263.11	POL( U22_2(x_1, x_2) ) = 2
744.35/263.11	POL( U31_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U32_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.11	POL( U41_2(x_1, x_2) ) = 2
744.35/263.11	POL( mark_1(x_1) ) = 2
744.35/263.11	POL( U102_3(x_1, ..., x_3) ) = x_2 + 2
744.35/263.11	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U101_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( tt ) = 0
744.35/263.11	POL( isNatKind_1(x_1) ) = 2
744.35/263.11	POL( U103_3(x_1, ..., x_3) ) = x_2 + 2
744.35/263.11	POL( isNat_1(x_1) ) = 2
744.35/263.11	POL( U104_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 2}
744.35/263.11	POL( plus_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2}
744.35/263.11	POL( x_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.11	POL( U16_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U23_1(x_1) ) = 2
744.35/263.11	POL( U33_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.35/263.11	POL( U34_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + 2x_3 - 2}
744.35/263.11	POL( U35_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2}
744.35/263.11	POL( U36_1(x_1) ) = 2
744.35/263.11	POL( U42_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U61_2(x_1, x_2) ) = 2x_1 + 2
744.35/263.11	POL( U62_1(x_1) ) = 0
744.35/263.11	POL( U71_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.11	POL( U72_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.11	POL( U81_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.35/263.11	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 1}
744.35/263.11	POL( U83_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.35/263.11	POL( U84_3(x_1, ..., x_3) ) = 2x_2 + 2
744.35/263.11	POL( s_1(x_1) ) = max{0, x_1 - 1}
744.35/263.11	POL( U91_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.11	POL( U92_1(x_1) ) = 2
744.35/263.11	POL( U51_1(x_1) ) = 0
744.35/263.11	POL( 0 ) = 0
744.35/263.11	POL( MARK_1(x_1) ) = 2
744.35/263.11	
744.35/263.11	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.11	
744.35/263.11	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.11	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.11	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.11	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.11	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.11	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.11	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.11	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.11	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.11	
744.35/263.11	
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(338)
744.35/263.11	Obligation:
744.35/263.11	Q DP problem:
744.35/263.11	The TRS P consists of the following rules:
744.35/263.11	
744.35/263.11	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.11	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.11	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.11	   MARK(U16(X)) -> MARK(X)
744.35/263.11	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.11	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.11	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.11	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.11	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.11	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.11	   MARK(U23(X)) -> MARK(X)
744.35/263.11	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.11	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U31(tt, V1, V2)) -> MARK(U32(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.11	   MARK(U42(X)) -> MARK(X)
744.35/263.11	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.11	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.11	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.11	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U51(X)) -> MARK(X)
744.35/263.11	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.11	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.11	
744.35/263.11	The TRS R consists of the following rules:
744.35/263.11	
744.35/263.11	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.11	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.11	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.11	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.11	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.11	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.11	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.11	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.11	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.11	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.11	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.11	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.11	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.11	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.11	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.11	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.11	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.11	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.11	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.11	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.11	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.11	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.11	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.11	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.11	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.11	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.11	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.11	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.11	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.11	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.11	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.11	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.11	   active(U72(tt, N)) -> mark(N)
744.35/263.11	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.11	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.11	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.11	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.11	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.11	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.11	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.11	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.11	   mark(s(X)) -> active(s(mark(X)))
744.35/263.11	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.11	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.11	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.11	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.11	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.11	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.11	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.11	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.11	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.11	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.11	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.11	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.11	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.11	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.11	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.11	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.11	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.11	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.11	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.11	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.11	   mark(isNat(X)) -> active(isNat(X))
744.35/263.11	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.11	   mark(tt) -> active(tt)
744.35/263.11	   mark(0) -> active(0)
744.35/263.11	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.11	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.11	   active(U16(tt)) -> mark(tt)
744.35/263.11	   active(U23(tt)) -> mark(tt)
744.35/263.11	   active(U36(tt)) -> mark(tt)
744.35/263.11	   active(U42(tt)) -> mark(tt)
744.35/263.11	   active(U51(tt)) -> mark(tt)
744.35/263.11	   active(U62(tt)) -> mark(tt)
744.35/263.11	   active(U92(tt)) -> mark(0)
744.35/263.11	   active(isNat(0)) -> mark(tt)
744.35/263.11	   active(isNatKind(0)) -> mark(tt)
744.35/263.11	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.11	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.11	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.11	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.11	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.11	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.11	   U16(active(X)) -> U16(X)
744.35/263.11	   U16(mark(X)) -> U16(X)
744.35/263.11	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.11	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.11	   U23(active(X)) -> U23(X)
744.35/263.11	   U23(mark(X)) -> U23(X)
744.35/263.11	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.11	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.11	   U36(active(X)) -> U36(X)
744.35/263.11	   U36(mark(X)) -> U36(X)
744.35/263.11	   U42(active(X)) -> U42(X)
744.35/263.11	   U42(mark(X)) -> U42(X)
744.35/263.11	   U62(active(X)) -> U62(X)
744.35/263.11	   U62(mark(X)) -> U62(X)
744.35/263.11	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.11	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.11	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.11	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.11	   s(active(X)) -> s(X)
744.35/263.11	   s(mark(X)) -> s(X)
744.35/263.11	   U92(active(X)) -> U92(X)
744.35/263.11	   U92(mark(X)) -> U92(X)
744.35/263.11	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.11	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.11	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.11	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.11	   U51(active(X)) -> U51(X)
744.35/263.11	   U51(mark(X)) -> U51(X)
744.35/263.11	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.11	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.11	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.11	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.11	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.11	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.11	   x(active(X1), X2) -> x(X1, X2)
744.35/263.11	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.11	
744.35/263.11	The set Q consists of the following terms:
744.35/263.11	
744.35/263.11	   active(U101(tt, x0, x1))
744.35/263.11	   active(U102(tt, x0, x1))
744.35/263.11	   active(U103(tt, x0, x1))
744.35/263.11	   active(U104(tt, x0, x1))
744.35/263.11	   active(U11(tt, x0, x1))
744.35/263.11	   active(U12(tt, x0, x1))
744.35/263.11	   active(U13(tt, x0, x1))
744.35/263.11	   active(U14(tt, x0, x1))
744.35/263.11	   active(U15(tt, x0))
744.35/263.11	   active(U16(tt))
744.35/263.11	   active(U21(tt, x0))
744.35/263.11	   active(U22(tt, x0))
744.35/263.11	   active(U23(tt))
744.35/263.11	   active(U31(tt, x0, x1))
744.35/263.11	   active(U32(tt, x0, x1))
744.35/263.11	   active(U33(tt, x0, x1))
744.35/263.11	   active(U34(tt, x0, x1))
744.35/263.11	   active(U35(tt, x0))
744.35/263.11	   active(U36(tt))
744.35/263.11	   active(U41(tt, x0))
744.35/263.11	   active(U42(tt))
744.35/263.11	   active(U51(tt))
744.35/263.11	   active(U61(tt, x0))
744.35/263.11	   active(U62(tt))
744.35/263.11	   active(U71(tt, x0))
744.35/263.11	   active(U72(tt, x0))
744.35/263.11	   active(U81(tt, x0, x1))
744.35/263.11	   active(U82(tt, x0, x1))
744.35/263.11	   active(U83(tt, x0, x1))
744.35/263.11	   active(U84(tt, x0, x1))
744.35/263.11	   active(U91(tt, x0))
744.35/263.11	   active(U92(tt))
744.35/263.11	   active(isNat(0))
744.35/263.11	   active(isNat(plus(x0, x1)))
744.35/263.11	   active(isNat(s(x0)))
744.35/263.11	   active(isNat(x(x0, x1)))
744.35/263.11	   active(isNatKind(0))
744.35/263.11	   active(isNatKind(plus(x0, x1)))
744.35/263.11	   active(isNatKind(s(x0)))
744.35/263.11	   active(isNatKind(x(x0, x1)))
744.35/263.11	   active(plus(x0, 0))
744.35/263.11	   active(plus(x0, s(x1)))
744.35/263.11	   active(x(x0, 0))
744.35/263.11	   active(x(x0, s(x1)))
744.35/263.11	   mark(U101(x0, x1, x2))
744.35/263.11	   mark(tt)
744.35/263.11	   mark(U102(x0, x1, x2))
744.35/263.11	   mark(isNatKind(x0))
744.35/263.11	   mark(U103(x0, x1, x2))
744.35/263.11	   mark(isNat(x0))
744.35/263.11	   mark(U104(x0, x1, x2))
744.35/263.11	   mark(plus(x0, x1))
744.35/263.11	   mark(x(x0, x1))
744.35/263.11	   mark(U11(x0, x1, x2))
744.35/263.11	   mark(U12(x0, x1, x2))
744.35/263.11	   mark(U13(x0, x1, x2))
744.35/263.11	   mark(U14(x0, x1, x2))
744.35/263.11	   mark(U15(x0, x1))
744.35/263.11	   mark(U16(x0))
744.35/263.11	   mark(U21(x0, x1))
744.35/263.11	   mark(U22(x0, x1))
744.35/263.11	   mark(U23(x0))
744.35/263.11	   mark(U31(x0, x1, x2))
744.35/263.11	   mark(U32(x0, x1, x2))
744.35/263.11	   mark(U33(x0, x1, x2))
744.35/263.11	   mark(U34(x0, x1, x2))
744.35/263.11	   mark(U35(x0, x1))
744.35/263.11	   mark(U36(x0))
744.35/263.11	   mark(U41(x0, x1))
744.35/263.11	   mark(U42(x0))
744.35/263.11	   mark(U51(x0))
744.35/263.11	   mark(U61(x0, x1))
744.35/263.11	   mark(U62(x0))
744.35/263.11	   mark(U71(x0, x1))
744.35/263.11	   mark(U72(x0, x1))
744.35/263.11	   mark(U81(x0, x1, x2))
744.35/263.11	   mark(U82(x0, x1, x2))
744.35/263.11	   mark(U83(x0, x1, x2))
744.35/263.11	   mark(U84(x0, x1, x2))
744.35/263.11	   mark(s(x0))
744.35/263.11	   mark(U91(x0, x1))
744.35/263.11	   mark(U92(x0))
744.35/263.11	   mark(0)
744.35/263.11	   U101(mark(x0), x1, x2)
744.35/263.11	   U101(x0, mark(x1), x2)
744.35/263.11	   U101(x0, x1, mark(x2))
744.35/263.11	   U101(active(x0), x1, x2)
744.35/263.11	   U101(x0, active(x1), x2)
744.35/263.11	   U101(x0, x1, active(x2))
744.35/263.11	   U102(mark(x0), x1, x2)
744.35/263.11	   U102(x0, mark(x1), x2)
744.35/263.11	   U102(x0, x1, mark(x2))
744.35/263.11	   U102(active(x0), x1, x2)
744.35/263.11	   U102(x0, active(x1), x2)
744.35/263.11	   U102(x0, x1, active(x2))
744.35/263.11	   isNatKind(mark(x0))
744.35/263.11	   isNatKind(active(x0))
744.35/263.11	   U103(mark(x0), x1, x2)
744.35/263.11	   U103(x0, mark(x1), x2)
744.35/263.11	   U103(x0, x1, mark(x2))
744.35/263.11	   U103(active(x0), x1, x2)
744.35/263.11	   U103(x0, active(x1), x2)
744.35/263.11	   U103(x0, x1, active(x2))
744.35/263.11	   isNat(mark(x0))
744.35/263.11	   isNat(active(x0))
744.35/263.11	   U104(mark(x0), x1, x2)
744.35/263.11	   U104(x0, mark(x1), x2)
744.35/263.11	   U104(x0, x1, mark(x2))
744.35/263.11	   U104(active(x0), x1, x2)
744.35/263.11	   U104(x0, active(x1), x2)
744.35/263.11	   U104(x0, x1, active(x2))
744.35/263.11	   plus(mark(x0), x1)
744.35/263.11	   plus(x0, mark(x1))
744.35/263.11	   plus(active(x0), x1)
744.35/263.11	   plus(x0, active(x1))
744.35/263.11	   x(mark(x0), x1)
744.35/263.11	   x(x0, mark(x1))
744.35/263.11	   x(active(x0), x1)
744.35/263.11	   x(x0, active(x1))
744.35/263.11	   U11(mark(x0), x1, x2)
744.35/263.11	   U11(x0, mark(x1), x2)
744.35/263.11	   U11(x0, x1, mark(x2))
744.35/263.11	   U11(active(x0), x1, x2)
744.35/263.11	   U11(x0, active(x1), x2)
744.35/263.11	   U11(x0, x1, active(x2))
744.35/263.11	   U12(mark(x0), x1, x2)
744.35/263.11	   U12(x0, mark(x1), x2)
744.35/263.11	   U12(x0, x1, mark(x2))
744.35/263.11	   U12(active(x0), x1, x2)
744.35/263.11	   U12(x0, active(x1), x2)
744.35/263.11	   U12(x0, x1, active(x2))
744.35/263.11	   U13(mark(x0), x1, x2)
744.35/263.11	   U13(x0, mark(x1), x2)
744.35/263.11	   U13(x0, x1, mark(x2))
744.35/263.11	   U13(active(x0), x1, x2)
744.35/263.11	   U13(x0, active(x1), x2)
744.35/263.11	   U13(x0, x1, active(x2))
744.35/263.11	   U14(mark(x0), x1, x2)
744.35/263.11	   U14(x0, mark(x1), x2)
744.35/263.11	   U14(x0, x1, mark(x2))
744.35/263.11	   U14(active(x0), x1, x2)
744.35/263.11	   U14(x0, active(x1), x2)
744.35/263.11	   U14(x0, x1, active(x2))
744.35/263.11	   U15(mark(x0), x1)
744.35/263.11	   U15(x0, mark(x1))
744.35/263.11	   U15(active(x0), x1)
744.35/263.11	   U15(x0, active(x1))
744.35/263.11	   U16(mark(x0))
744.35/263.11	   U16(active(x0))
744.35/263.11	   U21(mark(x0), x1)
744.35/263.11	   U21(x0, mark(x1))
744.35/263.11	   U21(active(x0), x1)
744.35/263.11	   U21(x0, active(x1))
744.35/263.11	   U22(mark(x0), x1)
744.35/263.11	   U22(x0, mark(x1))
744.35/263.11	   U22(active(x0), x1)
744.35/263.11	   U22(x0, active(x1))
744.35/263.11	   U23(mark(x0))
744.35/263.11	   U23(active(x0))
744.35/263.11	   U31(mark(x0), x1, x2)
744.35/263.11	   U31(x0, mark(x1), x2)
744.35/263.11	   U31(x0, x1, mark(x2))
744.35/263.11	   U31(active(x0), x1, x2)
744.35/263.11	   U31(x0, active(x1), x2)
744.35/263.11	   U31(x0, x1, active(x2))
744.35/263.11	   U32(mark(x0), x1, x2)
744.35/263.11	   U32(x0, mark(x1), x2)
744.35/263.11	   U32(x0, x1, mark(x2))
744.35/263.11	   U32(active(x0), x1, x2)
744.35/263.11	   U32(x0, active(x1), x2)
744.35/263.11	   U32(x0, x1, active(x2))
744.35/263.11	   U33(mark(x0), x1, x2)
744.35/263.11	   U33(x0, mark(x1), x2)
744.35/263.11	   U33(x0, x1, mark(x2))
744.35/263.11	   U33(active(x0), x1, x2)
744.35/263.11	   U33(x0, active(x1), x2)
744.35/263.11	   U33(x0, x1, active(x2))
744.35/263.11	   U34(mark(x0), x1, x2)
744.35/263.11	   U34(x0, mark(x1), x2)
744.35/263.11	   U34(x0, x1, mark(x2))
744.35/263.11	   U34(active(x0), x1, x2)
744.35/263.11	   U34(x0, active(x1), x2)
744.35/263.11	   U34(x0, x1, active(x2))
744.35/263.11	   U35(mark(x0), x1)
744.35/263.11	   U35(x0, mark(x1))
744.35/263.11	   U35(active(x0), x1)
744.35/263.11	   U35(x0, active(x1))
744.35/263.11	   U36(mark(x0))
744.35/263.11	   U36(active(x0))
744.35/263.11	   U41(mark(x0), x1)
744.35/263.11	   U41(x0, mark(x1))
744.35/263.11	   U41(active(x0), x1)
744.35/263.11	   U41(x0, active(x1))
744.35/263.11	   U42(mark(x0))
744.35/263.11	   U42(active(x0))
744.35/263.11	   U51(mark(x0))
744.35/263.11	   U51(active(x0))
744.35/263.11	   U61(mark(x0), x1)
744.35/263.11	   U61(x0, mark(x1))
744.35/263.11	   U61(active(x0), x1)
744.35/263.11	   U61(x0, active(x1))
744.35/263.11	   U62(mark(x0))
744.35/263.11	   U62(active(x0))
744.35/263.11	   U71(mark(x0), x1)
744.35/263.11	   U71(x0, mark(x1))
744.35/263.11	   U71(active(x0), x1)
744.35/263.11	   U71(x0, active(x1))
744.35/263.11	   U72(mark(x0), x1)
744.35/263.11	   U72(x0, mark(x1))
744.35/263.11	   U72(active(x0), x1)
744.35/263.11	   U72(x0, active(x1))
744.35/263.11	   U81(mark(x0), x1, x2)
744.35/263.11	   U81(x0, mark(x1), x2)
744.35/263.11	   U81(x0, x1, mark(x2))
744.35/263.11	   U81(active(x0), x1, x2)
744.35/263.11	   U81(x0, active(x1), x2)
744.35/263.11	   U81(x0, x1, active(x2))
744.35/263.11	   U82(mark(x0), x1, x2)
744.35/263.11	   U82(x0, mark(x1), x2)
744.35/263.11	   U82(x0, x1, mark(x2))
744.35/263.11	   U82(active(x0), x1, x2)
744.35/263.11	   U82(x0, active(x1), x2)
744.35/263.11	   U82(x0, x1, active(x2))
744.35/263.11	   U83(mark(x0), x1, x2)
744.35/263.11	   U83(x0, mark(x1), x2)
744.35/263.11	   U83(x0, x1, mark(x2))
744.35/263.11	   U83(active(x0), x1, x2)
744.35/263.11	   U83(x0, active(x1), x2)
744.35/263.11	   U83(x0, x1, active(x2))
744.35/263.11	   U84(mark(x0), x1, x2)
744.35/263.11	   U84(x0, mark(x1), x2)
744.35/263.11	   U84(x0, x1, mark(x2))
744.35/263.11	   U84(active(x0), x1, x2)
744.35/263.11	   U84(x0, active(x1), x2)
744.35/263.11	   U84(x0, x1, active(x2))
744.35/263.11	   s(mark(x0))
744.35/263.11	   s(active(x0))
744.35/263.11	   U91(mark(x0), x1)
744.35/263.11	   U91(x0, mark(x1))
744.35/263.11	   U91(active(x0), x1)
744.35/263.11	   U91(x0, active(x1))
744.35/263.11	   U92(mark(x0))
744.35/263.11	   U92(active(x0))
744.35/263.11	
744.35/263.11	We have to consider all minimal (P,Q,R)-chains.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(339) DependencyGraphProof (EQUIVALENT)
744.35/263.11	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(340)
744.35/263.11	Obligation:
744.35/263.11	Q DP problem:
744.35/263.11	The TRS P consists of the following rules:
744.35/263.11	
744.35/263.11	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.11	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.11	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.11	   MARK(U16(X)) -> MARK(X)
744.35/263.11	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.11	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.11	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.11	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.11	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.11	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.11	   MARK(U23(X)) -> MARK(X)
744.35/263.11	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.11	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.11	   MARK(U42(X)) -> MARK(X)
744.35/263.11	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.11	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.11	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.11	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U51(X)) -> MARK(X)
744.35/263.11	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.11	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.11	
744.35/263.11	The TRS R consists of the following rules:
744.35/263.11	
744.35/263.11	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.11	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.11	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.11	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.11	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.11	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.11	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.11	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.11	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.11	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.11	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.11	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.11	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.11	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.11	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.11	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.11	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.11	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.11	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.11	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.11	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.11	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.11	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.11	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.11	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.11	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.11	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.11	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.11	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.11	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.11	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.11	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.11	   active(U72(tt, N)) -> mark(N)
744.35/263.11	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.11	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.11	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.11	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.11	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.11	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.11	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.11	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.11	   mark(s(X)) -> active(s(mark(X)))
744.35/263.11	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.11	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.11	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.11	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.11	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.11	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.11	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.11	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.11	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.11	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.11	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.11	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.11	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.11	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.11	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.11	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.11	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.11	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.11	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.11	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.11	   mark(isNat(X)) -> active(isNat(X))
744.35/263.11	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.11	   mark(tt) -> active(tt)
744.35/263.11	   mark(0) -> active(0)
744.35/263.11	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.11	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.11	   active(U16(tt)) -> mark(tt)
744.35/263.11	   active(U23(tt)) -> mark(tt)
744.35/263.11	   active(U36(tt)) -> mark(tt)
744.35/263.11	   active(U42(tt)) -> mark(tt)
744.35/263.11	   active(U51(tt)) -> mark(tt)
744.35/263.11	   active(U62(tt)) -> mark(tt)
744.35/263.11	   active(U92(tt)) -> mark(0)
744.35/263.11	   active(isNat(0)) -> mark(tt)
744.35/263.11	   active(isNatKind(0)) -> mark(tt)
744.35/263.11	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.11	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.11	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.11	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.11	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.11	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.11	   U16(active(X)) -> U16(X)
744.35/263.11	   U16(mark(X)) -> U16(X)
744.35/263.11	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.11	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.11	   U23(active(X)) -> U23(X)
744.35/263.11	   U23(mark(X)) -> U23(X)
744.35/263.11	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.11	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.11	   U36(active(X)) -> U36(X)
744.35/263.11	   U36(mark(X)) -> U36(X)
744.35/263.11	   U42(active(X)) -> U42(X)
744.35/263.11	   U42(mark(X)) -> U42(X)
744.35/263.11	   U62(active(X)) -> U62(X)
744.35/263.11	   U62(mark(X)) -> U62(X)
744.35/263.11	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.11	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.11	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.11	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.11	   s(active(X)) -> s(X)
744.35/263.11	   s(mark(X)) -> s(X)
744.35/263.11	   U92(active(X)) -> U92(X)
744.35/263.11	   U92(mark(X)) -> U92(X)
744.35/263.11	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.11	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.11	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.11	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.11	   U51(active(X)) -> U51(X)
744.35/263.11	   U51(mark(X)) -> U51(X)
744.35/263.11	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.11	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.11	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.11	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.11	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.11	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.11	   x(active(X1), X2) -> x(X1, X2)
744.35/263.11	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.11	
744.35/263.11	The set Q consists of the following terms:
744.35/263.11	
744.35/263.11	   active(U101(tt, x0, x1))
744.35/263.11	   active(U102(tt, x0, x1))
744.35/263.11	   active(U103(tt, x0, x1))
744.35/263.11	   active(U104(tt, x0, x1))
744.35/263.11	   active(U11(tt, x0, x1))
744.35/263.11	   active(U12(tt, x0, x1))
744.35/263.11	   active(U13(tt, x0, x1))
744.35/263.11	   active(U14(tt, x0, x1))
744.35/263.11	   active(U15(tt, x0))
744.35/263.11	   active(U16(tt))
744.35/263.11	   active(U21(tt, x0))
744.35/263.11	   active(U22(tt, x0))
744.35/263.11	   active(U23(tt))
744.35/263.11	   active(U31(tt, x0, x1))
744.35/263.11	   active(U32(tt, x0, x1))
744.35/263.11	   active(U33(tt, x0, x1))
744.35/263.11	   active(U34(tt, x0, x1))
744.35/263.11	   active(U35(tt, x0))
744.35/263.11	   active(U36(tt))
744.35/263.11	   active(U41(tt, x0))
744.35/263.11	   active(U42(tt))
744.35/263.11	   active(U51(tt))
744.35/263.11	   active(U61(tt, x0))
744.35/263.11	   active(U62(tt))
744.35/263.11	   active(U71(tt, x0))
744.35/263.11	   active(U72(tt, x0))
744.35/263.11	   active(U81(tt, x0, x1))
744.35/263.11	   active(U82(tt, x0, x1))
744.35/263.11	   active(U83(tt, x0, x1))
744.35/263.11	   active(U84(tt, x0, x1))
744.35/263.11	   active(U91(tt, x0))
744.35/263.11	   active(U92(tt))
744.35/263.11	   active(isNat(0))
744.35/263.11	   active(isNat(plus(x0, x1)))
744.35/263.11	   active(isNat(s(x0)))
744.35/263.11	   active(isNat(x(x0, x1)))
744.35/263.11	   active(isNatKind(0))
744.35/263.11	   active(isNatKind(plus(x0, x1)))
744.35/263.11	   active(isNatKind(s(x0)))
744.35/263.11	   active(isNatKind(x(x0, x1)))
744.35/263.11	   active(plus(x0, 0))
744.35/263.11	   active(plus(x0, s(x1)))
744.35/263.11	   active(x(x0, 0))
744.35/263.11	   active(x(x0, s(x1)))
744.35/263.11	   mark(U101(x0, x1, x2))
744.35/263.11	   mark(tt)
744.35/263.11	   mark(U102(x0, x1, x2))
744.35/263.11	   mark(isNatKind(x0))
744.35/263.11	   mark(U103(x0, x1, x2))
744.35/263.11	   mark(isNat(x0))
744.35/263.11	   mark(U104(x0, x1, x2))
744.35/263.11	   mark(plus(x0, x1))
744.35/263.11	   mark(x(x0, x1))
744.35/263.11	   mark(U11(x0, x1, x2))
744.35/263.11	   mark(U12(x0, x1, x2))
744.35/263.11	   mark(U13(x0, x1, x2))
744.35/263.11	   mark(U14(x0, x1, x2))
744.35/263.11	   mark(U15(x0, x1))
744.35/263.11	   mark(U16(x0))
744.35/263.11	   mark(U21(x0, x1))
744.35/263.11	   mark(U22(x0, x1))
744.35/263.11	   mark(U23(x0))
744.35/263.11	   mark(U31(x0, x1, x2))
744.35/263.11	   mark(U32(x0, x1, x2))
744.35/263.11	   mark(U33(x0, x1, x2))
744.35/263.11	   mark(U34(x0, x1, x2))
744.35/263.11	   mark(U35(x0, x1))
744.35/263.11	   mark(U36(x0))
744.35/263.11	   mark(U41(x0, x1))
744.35/263.11	   mark(U42(x0))
744.35/263.11	   mark(U51(x0))
744.35/263.11	   mark(U61(x0, x1))
744.35/263.11	   mark(U62(x0))
744.35/263.11	   mark(U71(x0, x1))
744.35/263.11	   mark(U72(x0, x1))
744.35/263.11	   mark(U81(x0, x1, x2))
744.35/263.11	   mark(U82(x0, x1, x2))
744.35/263.11	   mark(U83(x0, x1, x2))
744.35/263.11	   mark(U84(x0, x1, x2))
744.35/263.11	   mark(s(x0))
744.35/263.11	   mark(U91(x0, x1))
744.35/263.11	   mark(U92(x0))
744.35/263.11	   mark(0)
744.35/263.11	   U101(mark(x0), x1, x2)
744.35/263.11	   U101(x0, mark(x1), x2)
744.35/263.11	   U101(x0, x1, mark(x2))
744.35/263.11	   U101(active(x0), x1, x2)
744.35/263.11	   U101(x0, active(x1), x2)
744.35/263.11	   U101(x0, x1, active(x2))
744.35/263.11	   U102(mark(x0), x1, x2)
744.35/263.11	   U102(x0, mark(x1), x2)
744.35/263.11	   U102(x0, x1, mark(x2))
744.35/263.11	   U102(active(x0), x1, x2)
744.35/263.11	   U102(x0, active(x1), x2)
744.35/263.11	   U102(x0, x1, active(x2))
744.35/263.11	   isNatKind(mark(x0))
744.35/263.11	   isNatKind(active(x0))
744.35/263.11	   U103(mark(x0), x1, x2)
744.35/263.11	   U103(x0, mark(x1), x2)
744.35/263.11	   U103(x0, x1, mark(x2))
744.35/263.11	   U103(active(x0), x1, x2)
744.35/263.11	   U103(x0, active(x1), x2)
744.35/263.11	   U103(x0, x1, active(x2))
744.35/263.11	   isNat(mark(x0))
744.35/263.11	   isNat(active(x0))
744.35/263.11	   U104(mark(x0), x1, x2)
744.35/263.11	   U104(x0, mark(x1), x2)
744.35/263.11	   U104(x0, x1, mark(x2))
744.35/263.11	   U104(active(x0), x1, x2)
744.35/263.11	   U104(x0, active(x1), x2)
744.35/263.11	   U104(x0, x1, active(x2))
744.35/263.11	   plus(mark(x0), x1)
744.35/263.11	   plus(x0, mark(x1))
744.35/263.11	   plus(active(x0), x1)
744.35/263.11	   plus(x0, active(x1))
744.35/263.11	   x(mark(x0), x1)
744.35/263.11	   x(x0, mark(x1))
744.35/263.11	   x(active(x0), x1)
744.35/263.11	   x(x0, active(x1))
744.35/263.11	   U11(mark(x0), x1, x2)
744.35/263.11	   U11(x0, mark(x1), x2)
744.35/263.11	   U11(x0, x1, mark(x2))
744.35/263.11	   U11(active(x0), x1, x2)
744.35/263.11	   U11(x0, active(x1), x2)
744.35/263.11	   U11(x0, x1, active(x2))
744.35/263.11	   U12(mark(x0), x1, x2)
744.35/263.11	   U12(x0, mark(x1), x2)
744.35/263.11	   U12(x0, x1, mark(x2))
744.35/263.11	   U12(active(x0), x1, x2)
744.35/263.11	   U12(x0, active(x1), x2)
744.35/263.11	   U12(x0, x1, active(x2))
744.35/263.11	   U13(mark(x0), x1, x2)
744.35/263.11	   U13(x0, mark(x1), x2)
744.35/263.11	   U13(x0, x1, mark(x2))
744.35/263.11	   U13(active(x0), x1, x2)
744.35/263.11	   U13(x0, active(x1), x2)
744.35/263.11	   U13(x0, x1, active(x2))
744.35/263.11	   U14(mark(x0), x1, x2)
744.35/263.11	   U14(x0, mark(x1), x2)
744.35/263.11	   U14(x0, x1, mark(x2))
744.35/263.11	   U14(active(x0), x1, x2)
744.35/263.11	   U14(x0, active(x1), x2)
744.35/263.11	   U14(x0, x1, active(x2))
744.35/263.11	   U15(mark(x0), x1)
744.35/263.11	   U15(x0, mark(x1))
744.35/263.11	   U15(active(x0), x1)
744.35/263.11	   U15(x0, active(x1))
744.35/263.11	   U16(mark(x0))
744.35/263.11	   U16(active(x0))
744.35/263.11	   U21(mark(x0), x1)
744.35/263.11	   U21(x0, mark(x1))
744.35/263.11	   U21(active(x0), x1)
744.35/263.11	   U21(x0, active(x1))
744.35/263.11	   U22(mark(x0), x1)
744.35/263.11	   U22(x0, mark(x1))
744.35/263.11	   U22(active(x0), x1)
744.35/263.11	   U22(x0, active(x1))
744.35/263.11	   U23(mark(x0))
744.35/263.11	   U23(active(x0))
744.35/263.11	   U31(mark(x0), x1, x2)
744.35/263.11	   U31(x0, mark(x1), x2)
744.35/263.11	   U31(x0, x1, mark(x2))
744.35/263.11	   U31(active(x0), x1, x2)
744.35/263.11	   U31(x0, active(x1), x2)
744.35/263.11	   U31(x0, x1, active(x2))
744.35/263.11	   U32(mark(x0), x1, x2)
744.35/263.11	   U32(x0, mark(x1), x2)
744.35/263.11	   U32(x0, x1, mark(x2))
744.35/263.11	   U32(active(x0), x1, x2)
744.35/263.11	   U32(x0, active(x1), x2)
744.35/263.11	   U32(x0, x1, active(x2))
744.35/263.11	   U33(mark(x0), x1, x2)
744.35/263.11	   U33(x0, mark(x1), x2)
744.35/263.11	   U33(x0, x1, mark(x2))
744.35/263.11	   U33(active(x0), x1, x2)
744.35/263.11	   U33(x0, active(x1), x2)
744.35/263.11	   U33(x0, x1, active(x2))
744.35/263.11	   U34(mark(x0), x1, x2)
744.35/263.11	   U34(x0, mark(x1), x2)
744.35/263.11	   U34(x0, x1, mark(x2))
744.35/263.11	   U34(active(x0), x1, x2)
744.35/263.11	   U34(x0, active(x1), x2)
744.35/263.11	   U34(x0, x1, active(x2))
744.35/263.11	   U35(mark(x0), x1)
744.35/263.11	   U35(x0, mark(x1))
744.35/263.11	   U35(active(x0), x1)
744.35/263.11	   U35(x0, active(x1))
744.35/263.11	   U36(mark(x0))
744.35/263.11	   U36(active(x0))
744.35/263.11	   U41(mark(x0), x1)
744.35/263.11	   U41(x0, mark(x1))
744.35/263.11	   U41(active(x0), x1)
744.35/263.11	   U41(x0, active(x1))
744.35/263.11	   U42(mark(x0))
744.35/263.11	   U42(active(x0))
744.35/263.11	   U51(mark(x0))
744.35/263.11	   U51(active(x0))
744.35/263.11	   U61(mark(x0), x1)
744.35/263.11	   U61(x0, mark(x1))
744.35/263.11	   U61(active(x0), x1)
744.35/263.11	   U61(x0, active(x1))
744.35/263.11	   U62(mark(x0))
744.35/263.11	   U62(active(x0))
744.35/263.11	   U71(mark(x0), x1)
744.35/263.11	   U71(x0, mark(x1))
744.35/263.11	   U71(active(x0), x1)
744.35/263.11	   U71(x0, active(x1))
744.35/263.11	   U72(mark(x0), x1)
744.35/263.11	   U72(x0, mark(x1))
744.35/263.11	   U72(active(x0), x1)
744.35/263.11	   U72(x0, active(x1))
744.35/263.11	   U81(mark(x0), x1, x2)
744.35/263.11	   U81(x0, mark(x1), x2)
744.35/263.11	   U81(x0, x1, mark(x2))
744.35/263.11	   U81(active(x0), x1, x2)
744.35/263.11	   U81(x0, active(x1), x2)
744.35/263.11	   U81(x0, x1, active(x2))
744.35/263.11	   U82(mark(x0), x1, x2)
744.35/263.11	   U82(x0, mark(x1), x2)
744.35/263.11	   U82(x0, x1, mark(x2))
744.35/263.11	   U82(active(x0), x1, x2)
744.35/263.11	   U82(x0, active(x1), x2)
744.35/263.11	   U82(x0, x1, active(x2))
744.35/263.11	   U83(mark(x0), x1, x2)
744.35/263.11	   U83(x0, mark(x1), x2)
744.35/263.11	   U83(x0, x1, mark(x2))
744.35/263.11	   U83(active(x0), x1, x2)
744.35/263.11	   U83(x0, active(x1), x2)
744.35/263.11	   U83(x0, x1, active(x2))
744.35/263.11	   U84(mark(x0), x1, x2)
744.35/263.11	   U84(x0, mark(x1), x2)
744.35/263.11	   U84(x0, x1, mark(x2))
744.35/263.11	   U84(active(x0), x1, x2)
744.35/263.11	   U84(x0, active(x1), x2)
744.35/263.11	   U84(x0, x1, active(x2))
744.35/263.11	   s(mark(x0))
744.35/263.11	   s(active(x0))
744.35/263.11	   U91(mark(x0), x1)
744.35/263.11	   U91(x0, mark(x1))
744.35/263.11	   U91(active(x0), x1)
744.35/263.11	   U91(x0, active(x1))
744.35/263.11	   U92(mark(x0))
744.35/263.11	   U92(active(x0))
744.35/263.11	
744.35/263.11	We have to consider all minimal (P,Q,R)-chains.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(341) QDPOrderProof (EQUIVALENT)
744.35/263.11	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.11	
744.35/263.11	
744.35/263.11	The following pairs can be oriented strictly and are deleted.
744.35/263.11	
744.35/263.11	   MARK(U31(X1, X2, X3)) -> ACTIVE(U31(mark(X1), X2, X3))
744.35/263.11	The remaining pairs can at least be oriented weakly.
744.35/263.11	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.11	
744.35/263.11	POL( ACTIVE_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.11	POL( U11_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U12_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U13_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U14_3(x_1, ..., x_3) ) = 2
744.35/263.11	POL( U15_2(x_1, x_2) ) = 2
744.35/263.11	POL( U21_2(x_1, x_2) ) = 2
744.35/263.11	POL( U22_2(x_1, x_2) ) = 2
744.35/263.11	POL( U31_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.11	POL( U41_2(x_1, x_2) ) = 2
744.35/263.11	POL( mark_1(x_1) ) = max{0, -2}
744.35/263.11	POL( U102_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_3 - 2}
744.35/263.11	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U101_3(x_1, ..., x_3) ) = 2x_1 + 2x_2 + 2
744.35/263.11	POL( tt ) = 0
744.35/263.11	POL( isNatKind_1(x_1) ) = 2
744.35/263.11	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_3 - 2}
744.35/263.11	POL( isNat_1(x_1) ) = 2
744.35/263.11	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_3 - 2}
744.35/263.11	POL( plus_2(x_1, x_2) ) = max{0, -2}
744.35/263.11	POL( x_2(x_1, x_2) ) = 2
744.35/263.11	POL( U16_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U23_1(x_1) ) = x_1 + 2
744.35/263.11	POL( U32_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + 2x_3 - 2}
744.35/263.11	POL( U33_3(x_1, ..., x_3) ) = x_1 + 2
744.35/263.11	POL( U34_3(x_1, ..., x_3) ) = x_1 + x_3 + 2
744.35/263.11	POL( U35_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.11	POL( U36_1(x_1) ) = 0
744.35/263.11	POL( U42_1(x_1) ) = max{0, -2}
744.35/263.11	POL( U61_2(x_1, x_2) ) = 2
744.35/263.11	POL( U62_1(x_1) ) = 0
744.35/263.11	POL( U71_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.11	POL( U72_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2}
744.35/263.11	POL( U81_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.35/263.11	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + x_3 - 2}
744.35/263.11	POL( U83_3(x_1, ..., x_3) ) = x_1 + x_2 + x_3 + 2
744.35/263.11	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.11	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.35/263.11	POL( U91_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.11	POL( U92_1(x_1) ) = 0
744.35/263.11	POL( U51_1(x_1) ) = 2
744.35/263.11	POL( 0 ) = 0
744.35/263.11	POL( MARK_1(x_1) ) = 2
744.35/263.11	
744.35/263.11	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.11	
744.35/263.11	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.11	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.11	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.11	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.11	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.11	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.11	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.11	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.11	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.11	
744.35/263.11	
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(342)
744.35/263.11	Obligation:
744.35/263.11	Q DP problem:
744.35/263.11	The TRS P consists of the following rules:
744.35/263.11	
744.35/263.11	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.11	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.11	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.11	   MARK(U16(X)) -> MARK(X)
744.35/263.11	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.11	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.11	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.11	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.11	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.11	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.11	   MARK(U23(X)) -> MARK(X)
744.35/263.11	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.11	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.11	   MARK(U42(X)) -> MARK(X)
744.35/263.11	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.11	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.11	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U51(X)) -> MARK(X)
744.35/263.11	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.11	   ACTIVE(isNat(x(V1, V2))) -> MARK(U31(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.11	
744.35/263.11	The TRS R consists of the following rules:
744.35/263.11	
744.35/263.11	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.11	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.11	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.11	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.11	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.11	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.11	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.11	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.11	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.11	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.11	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.11	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.11	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.11	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.11	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.11	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.11	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.11	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.11	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.11	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.11	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.11	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.11	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.11	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.11	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.11	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.11	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.11	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.11	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.11	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.11	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.11	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.11	   active(U72(tt, N)) -> mark(N)
744.35/263.11	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.11	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.11	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.11	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.11	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.11	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.11	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.11	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.11	   mark(s(X)) -> active(s(mark(X)))
744.35/263.11	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.11	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.11	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.11	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.11	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.11	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.11	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.11	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.11	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.11	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.11	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.11	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.11	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.11	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.11	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.11	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.11	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.11	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.11	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.11	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.11	   mark(isNat(X)) -> active(isNat(X))
744.35/263.11	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.11	   mark(tt) -> active(tt)
744.35/263.11	   mark(0) -> active(0)
744.35/263.11	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.11	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.11	   active(U16(tt)) -> mark(tt)
744.35/263.11	   active(U23(tt)) -> mark(tt)
744.35/263.11	   active(U36(tt)) -> mark(tt)
744.35/263.11	   active(U42(tt)) -> mark(tt)
744.35/263.11	   active(U51(tt)) -> mark(tt)
744.35/263.11	   active(U62(tt)) -> mark(tt)
744.35/263.11	   active(U92(tt)) -> mark(0)
744.35/263.11	   active(isNat(0)) -> mark(tt)
744.35/263.11	   active(isNatKind(0)) -> mark(tt)
744.35/263.11	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.11	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.11	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.11	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.11	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.11	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.11	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.11	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.11	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.11	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.11	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.11	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.11	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.11	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.11	   U16(active(X)) -> U16(X)
744.35/263.11	   U16(mark(X)) -> U16(X)
744.35/263.11	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.11	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.11	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.11	   U23(active(X)) -> U23(X)
744.35/263.11	   U23(mark(X)) -> U23(X)
744.35/263.11	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.11	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.11	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.11	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.11	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.11	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.11	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.11	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.11	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.11	   U36(active(X)) -> U36(X)
744.35/263.11	   U36(mark(X)) -> U36(X)
744.35/263.11	   U42(active(X)) -> U42(X)
744.35/263.11	   U42(mark(X)) -> U42(X)
744.35/263.11	   U62(active(X)) -> U62(X)
744.35/263.11	   U62(mark(X)) -> U62(X)
744.35/263.11	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.11	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.11	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.11	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.11	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.11	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.11	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.11	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.11	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.11	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.11	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.11	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.11	   s(active(X)) -> s(X)
744.35/263.11	   s(mark(X)) -> s(X)
744.35/263.11	   U92(active(X)) -> U92(X)
744.35/263.11	   U92(mark(X)) -> U92(X)
744.35/263.11	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.11	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.11	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.11	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.11	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.11	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.11	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.11	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.11	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.11	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.11	   U51(active(X)) -> U51(X)
744.35/263.11	   U51(mark(X)) -> U51(X)
744.35/263.11	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.11	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.11	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.11	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.11	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.11	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.11	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.11	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.11	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.11	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.11	   x(active(X1), X2) -> x(X1, X2)
744.35/263.11	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.11	
744.35/263.11	The set Q consists of the following terms:
744.35/263.11	
744.35/263.11	   active(U101(tt, x0, x1))
744.35/263.11	   active(U102(tt, x0, x1))
744.35/263.11	   active(U103(tt, x0, x1))
744.35/263.11	   active(U104(tt, x0, x1))
744.35/263.11	   active(U11(tt, x0, x1))
744.35/263.11	   active(U12(tt, x0, x1))
744.35/263.11	   active(U13(tt, x0, x1))
744.35/263.11	   active(U14(tt, x0, x1))
744.35/263.11	   active(U15(tt, x0))
744.35/263.11	   active(U16(tt))
744.35/263.11	   active(U21(tt, x0))
744.35/263.11	   active(U22(tt, x0))
744.35/263.11	   active(U23(tt))
744.35/263.11	   active(U31(tt, x0, x1))
744.35/263.11	   active(U32(tt, x0, x1))
744.35/263.11	   active(U33(tt, x0, x1))
744.35/263.11	   active(U34(tt, x0, x1))
744.35/263.11	   active(U35(tt, x0))
744.35/263.11	   active(U36(tt))
744.35/263.11	   active(U41(tt, x0))
744.35/263.11	   active(U42(tt))
744.35/263.11	   active(U51(tt))
744.35/263.11	   active(U61(tt, x0))
744.35/263.11	   active(U62(tt))
744.35/263.11	   active(U71(tt, x0))
744.35/263.11	   active(U72(tt, x0))
744.35/263.11	   active(U81(tt, x0, x1))
744.35/263.11	   active(U82(tt, x0, x1))
744.35/263.11	   active(U83(tt, x0, x1))
744.35/263.11	   active(U84(tt, x0, x1))
744.35/263.11	   active(U91(tt, x0))
744.35/263.11	   active(U92(tt))
744.35/263.11	   active(isNat(0))
744.35/263.11	   active(isNat(plus(x0, x1)))
744.35/263.11	   active(isNat(s(x0)))
744.35/263.11	   active(isNat(x(x0, x1)))
744.35/263.11	   active(isNatKind(0))
744.35/263.11	   active(isNatKind(plus(x0, x1)))
744.35/263.11	   active(isNatKind(s(x0)))
744.35/263.11	   active(isNatKind(x(x0, x1)))
744.35/263.11	   active(plus(x0, 0))
744.35/263.11	   active(plus(x0, s(x1)))
744.35/263.11	   active(x(x0, 0))
744.35/263.11	   active(x(x0, s(x1)))
744.35/263.11	   mark(U101(x0, x1, x2))
744.35/263.11	   mark(tt)
744.35/263.11	   mark(U102(x0, x1, x2))
744.35/263.11	   mark(isNatKind(x0))
744.35/263.11	   mark(U103(x0, x1, x2))
744.35/263.11	   mark(isNat(x0))
744.35/263.11	   mark(U104(x0, x1, x2))
744.35/263.11	   mark(plus(x0, x1))
744.35/263.11	   mark(x(x0, x1))
744.35/263.11	   mark(U11(x0, x1, x2))
744.35/263.11	   mark(U12(x0, x1, x2))
744.35/263.11	   mark(U13(x0, x1, x2))
744.35/263.11	   mark(U14(x0, x1, x2))
744.35/263.11	   mark(U15(x0, x1))
744.35/263.11	   mark(U16(x0))
744.35/263.11	   mark(U21(x0, x1))
744.35/263.11	   mark(U22(x0, x1))
744.35/263.11	   mark(U23(x0))
744.35/263.11	   mark(U31(x0, x1, x2))
744.35/263.11	   mark(U32(x0, x1, x2))
744.35/263.11	   mark(U33(x0, x1, x2))
744.35/263.11	   mark(U34(x0, x1, x2))
744.35/263.11	   mark(U35(x0, x1))
744.35/263.11	   mark(U36(x0))
744.35/263.11	   mark(U41(x0, x1))
744.35/263.11	   mark(U42(x0))
744.35/263.11	   mark(U51(x0))
744.35/263.11	   mark(U61(x0, x1))
744.35/263.11	   mark(U62(x0))
744.35/263.11	   mark(U71(x0, x1))
744.35/263.11	   mark(U72(x0, x1))
744.35/263.11	   mark(U81(x0, x1, x2))
744.35/263.11	   mark(U82(x0, x1, x2))
744.35/263.11	   mark(U83(x0, x1, x2))
744.35/263.11	   mark(U84(x0, x1, x2))
744.35/263.11	   mark(s(x0))
744.35/263.11	   mark(U91(x0, x1))
744.35/263.11	   mark(U92(x0))
744.35/263.11	   mark(0)
744.35/263.11	   U101(mark(x0), x1, x2)
744.35/263.11	   U101(x0, mark(x1), x2)
744.35/263.11	   U101(x0, x1, mark(x2))
744.35/263.11	   U101(active(x0), x1, x2)
744.35/263.11	   U101(x0, active(x1), x2)
744.35/263.11	   U101(x0, x1, active(x2))
744.35/263.11	   U102(mark(x0), x1, x2)
744.35/263.11	   U102(x0, mark(x1), x2)
744.35/263.11	   U102(x0, x1, mark(x2))
744.35/263.11	   U102(active(x0), x1, x2)
744.35/263.11	   U102(x0, active(x1), x2)
744.35/263.11	   U102(x0, x1, active(x2))
744.35/263.11	   isNatKind(mark(x0))
744.35/263.11	   isNatKind(active(x0))
744.35/263.11	   U103(mark(x0), x1, x2)
744.35/263.11	   U103(x0, mark(x1), x2)
744.35/263.11	   U103(x0, x1, mark(x2))
744.35/263.11	   U103(active(x0), x1, x2)
744.35/263.11	   U103(x0, active(x1), x2)
744.35/263.11	   U103(x0, x1, active(x2))
744.35/263.11	   isNat(mark(x0))
744.35/263.11	   isNat(active(x0))
744.35/263.11	   U104(mark(x0), x1, x2)
744.35/263.11	   U104(x0, mark(x1), x2)
744.35/263.11	   U104(x0, x1, mark(x2))
744.35/263.11	   U104(active(x0), x1, x2)
744.35/263.11	   U104(x0, active(x1), x2)
744.35/263.11	   U104(x0, x1, active(x2))
744.35/263.11	   plus(mark(x0), x1)
744.35/263.11	   plus(x0, mark(x1))
744.35/263.11	   plus(active(x0), x1)
744.35/263.11	   plus(x0, active(x1))
744.35/263.11	   x(mark(x0), x1)
744.35/263.11	   x(x0, mark(x1))
744.35/263.11	   x(active(x0), x1)
744.35/263.11	   x(x0, active(x1))
744.35/263.11	   U11(mark(x0), x1, x2)
744.35/263.11	   U11(x0, mark(x1), x2)
744.35/263.11	   U11(x0, x1, mark(x2))
744.35/263.11	   U11(active(x0), x1, x2)
744.35/263.11	   U11(x0, active(x1), x2)
744.35/263.11	   U11(x0, x1, active(x2))
744.35/263.11	   U12(mark(x0), x1, x2)
744.35/263.11	   U12(x0, mark(x1), x2)
744.35/263.11	   U12(x0, x1, mark(x2))
744.35/263.11	   U12(active(x0), x1, x2)
744.35/263.11	   U12(x0, active(x1), x2)
744.35/263.11	   U12(x0, x1, active(x2))
744.35/263.11	   U13(mark(x0), x1, x2)
744.35/263.11	   U13(x0, mark(x1), x2)
744.35/263.11	   U13(x0, x1, mark(x2))
744.35/263.11	   U13(active(x0), x1, x2)
744.35/263.11	   U13(x0, active(x1), x2)
744.35/263.11	   U13(x0, x1, active(x2))
744.35/263.11	   U14(mark(x0), x1, x2)
744.35/263.11	   U14(x0, mark(x1), x2)
744.35/263.11	   U14(x0, x1, mark(x2))
744.35/263.11	   U14(active(x0), x1, x2)
744.35/263.11	   U14(x0, active(x1), x2)
744.35/263.11	   U14(x0, x1, active(x2))
744.35/263.11	   U15(mark(x0), x1)
744.35/263.11	   U15(x0, mark(x1))
744.35/263.11	   U15(active(x0), x1)
744.35/263.11	   U15(x0, active(x1))
744.35/263.11	   U16(mark(x0))
744.35/263.11	   U16(active(x0))
744.35/263.11	   U21(mark(x0), x1)
744.35/263.11	   U21(x0, mark(x1))
744.35/263.11	   U21(active(x0), x1)
744.35/263.11	   U21(x0, active(x1))
744.35/263.11	   U22(mark(x0), x1)
744.35/263.11	   U22(x0, mark(x1))
744.35/263.11	   U22(active(x0), x1)
744.35/263.11	   U22(x0, active(x1))
744.35/263.11	   U23(mark(x0))
744.35/263.11	   U23(active(x0))
744.35/263.11	   U31(mark(x0), x1, x2)
744.35/263.11	   U31(x0, mark(x1), x2)
744.35/263.11	   U31(x0, x1, mark(x2))
744.35/263.11	   U31(active(x0), x1, x2)
744.35/263.11	   U31(x0, active(x1), x2)
744.35/263.11	   U31(x0, x1, active(x2))
744.35/263.11	   U32(mark(x0), x1, x2)
744.35/263.11	   U32(x0, mark(x1), x2)
744.35/263.11	   U32(x0, x1, mark(x2))
744.35/263.11	   U32(active(x0), x1, x2)
744.35/263.11	   U32(x0, active(x1), x2)
744.35/263.11	   U32(x0, x1, active(x2))
744.35/263.11	   U33(mark(x0), x1, x2)
744.35/263.11	   U33(x0, mark(x1), x2)
744.35/263.11	   U33(x0, x1, mark(x2))
744.35/263.11	   U33(active(x0), x1, x2)
744.35/263.11	   U33(x0, active(x1), x2)
744.35/263.11	   U33(x0, x1, active(x2))
744.35/263.11	   U34(mark(x0), x1, x2)
744.35/263.11	   U34(x0, mark(x1), x2)
744.35/263.11	   U34(x0, x1, mark(x2))
744.35/263.11	   U34(active(x0), x1, x2)
744.35/263.11	   U34(x0, active(x1), x2)
744.35/263.11	   U34(x0, x1, active(x2))
744.35/263.11	   U35(mark(x0), x1)
744.35/263.11	   U35(x0, mark(x1))
744.35/263.11	   U35(active(x0), x1)
744.35/263.11	   U35(x0, active(x1))
744.35/263.11	   U36(mark(x0))
744.35/263.11	   U36(active(x0))
744.35/263.11	   U41(mark(x0), x1)
744.35/263.11	   U41(x0, mark(x1))
744.35/263.11	   U41(active(x0), x1)
744.35/263.11	   U41(x0, active(x1))
744.35/263.11	   U42(mark(x0))
744.35/263.11	   U42(active(x0))
744.35/263.11	   U51(mark(x0))
744.35/263.11	   U51(active(x0))
744.35/263.11	   U61(mark(x0), x1)
744.35/263.11	   U61(x0, mark(x1))
744.35/263.11	   U61(active(x0), x1)
744.35/263.11	   U61(x0, active(x1))
744.35/263.11	   U62(mark(x0))
744.35/263.11	   U62(active(x0))
744.35/263.11	   U71(mark(x0), x1)
744.35/263.11	   U71(x0, mark(x1))
744.35/263.11	   U71(active(x0), x1)
744.35/263.11	   U71(x0, active(x1))
744.35/263.11	   U72(mark(x0), x1)
744.35/263.11	   U72(x0, mark(x1))
744.35/263.11	   U72(active(x0), x1)
744.35/263.11	   U72(x0, active(x1))
744.35/263.11	   U81(mark(x0), x1, x2)
744.35/263.11	   U81(x0, mark(x1), x2)
744.35/263.11	   U81(x0, x1, mark(x2))
744.35/263.11	   U81(active(x0), x1, x2)
744.35/263.11	   U81(x0, active(x1), x2)
744.35/263.11	   U81(x0, x1, active(x2))
744.35/263.11	   U82(mark(x0), x1, x2)
744.35/263.11	   U82(x0, mark(x1), x2)
744.35/263.11	   U82(x0, x1, mark(x2))
744.35/263.11	   U82(active(x0), x1, x2)
744.35/263.11	   U82(x0, active(x1), x2)
744.35/263.11	   U82(x0, x1, active(x2))
744.35/263.11	   U83(mark(x0), x1, x2)
744.35/263.11	   U83(x0, mark(x1), x2)
744.35/263.11	   U83(x0, x1, mark(x2))
744.35/263.11	   U83(active(x0), x1, x2)
744.35/263.11	   U83(x0, active(x1), x2)
744.35/263.11	   U83(x0, x1, active(x2))
744.35/263.11	   U84(mark(x0), x1, x2)
744.35/263.11	   U84(x0, mark(x1), x2)
744.35/263.11	   U84(x0, x1, mark(x2))
744.35/263.11	   U84(active(x0), x1, x2)
744.35/263.11	   U84(x0, active(x1), x2)
744.35/263.11	   U84(x0, x1, active(x2))
744.35/263.11	   s(mark(x0))
744.35/263.11	   s(active(x0))
744.35/263.11	   U91(mark(x0), x1)
744.35/263.11	   U91(x0, mark(x1))
744.35/263.11	   U91(active(x0), x1)
744.35/263.11	   U91(x0, active(x1))
744.35/263.11	   U92(mark(x0))
744.35/263.11	   U92(active(x0))
744.35/263.11	
744.35/263.11	We have to consider all minimal (P,Q,R)-chains.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(343) DependencyGraphProof (EQUIVALENT)
744.35/263.11	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.35/263.11	----------------------------------------
744.35/263.11	
744.35/263.11	(344)
744.35/263.11	Obligation:
744.35/263.11	Q DP problem:
744.35/263.11	The TRS P consists of the following rules:
744.35/263.11	
744.35/263.11	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.11	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.11	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.11	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.11	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.11	   MARK(U16(X)) -> MARK(X)
744.35/263.11	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.11	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.11	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.11	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.11	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.11	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.11	   MARK(U23(X)) -> MARK(X)
744.35/263.11	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.11	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.11	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.11	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.11	   MARK(U42(X)) -> MARK(X)
744.35/263.11	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.11	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.11	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.11	   MARK(U51(X)) -> MARK(X)
744.35/263.11	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.11	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.11	
744.35/263.11	The TRS R consists of the following rules:
744.35/263.11	
744.35/263.11	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.11	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.11	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.11	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.11	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.11	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.11	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.11	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.11	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.11	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.11	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.11	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.11	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.11	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.11	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.11	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.11	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.11	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.11	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.11	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.11	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.11	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.11	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.11	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.11	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.11	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.11	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.11	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.11	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.11	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.11	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.11	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.11	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.11	   active(U72(tt, N)) -> mark(N)
744.35/263.11	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.11	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.11	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.11	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.11	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.11	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.11	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.11	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.11	   mark(s(X)) -> active(s(mark(X)))
744.35/263.11	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.11	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.11	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.11	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.11	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.11	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.11	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.11	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.11	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.11	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.11	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.11	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.11	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.11	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.11	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.11	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.11	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.11	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.11	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.11	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.11	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.11	   mark(isNat(X)) -> active(isNat(X))
744.35/263.11	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.11	   mark(tt) -> active(tt)
744.35/263.11	   mark(0) -> active(0)
744.35/263.11	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.11	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.11	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.11	   active(U16(tt)) -> mark(tt)
744.35/263.11	   active(U23(tt)) -> mark(tt)
744.35/263.11	   active(U36(tt)) -> mark(tt)
744.35/263.11	   active(U42(tt)) -> mark(tt)
744.35/263.11	   active(U51(tt)) -> mark(tt)
744.35/263.11	   active(U62(tt)) -> mark(tt)
744.35/263.11	   active(U92(tt)) -> mark(0)
744.35/263.11	   active(isNat(0)) -> mark(tt)
744.35/263.11	   active(isNatKind(0)) -> mark(tt)
744.35/263.11	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.11	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.11	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.11	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.11	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.11	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.12	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.12	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.12	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.12	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.12	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.12	   U16(active(X)) -> U16(X)
744.35/263.12	   U16(mark(X)) -> U16(X)
744.35/263.12	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.12	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.12	   U23(active(X)) -> U23(X)
744.35/263.12	   U23(mark(X)) -> U23(X)
744.35/263.12	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.12	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.12	   U36(active(X)) -> U36(X)
744.35/263.12	   U36(mark(X)) -> U36(X)
744.35/263.12	   U42(active(X)) -> U42(X)
744.35/263.12	   U42(mark(X)) -> U42(X)
744.35/263.12	   U62(active(X)) -> U62(X)
744.35/263.12	   U62(mark(X)) -> U62(X)
744.35/263.12	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.12	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.12	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.12	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.12	   s(active(X)) -> s(X)
744.35/263.12	   s(mark(X)) -> s(X)
744.35/263.12	   U92(active(X)) -> U92(X)
744.35/263.12	   U92(mark(X)) -> U92(X)
744.35/263.12	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.12	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.12	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.12	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.12	   U51(active(X)) -> U51(X)
744.35/263.12	   U51(mark(X)) -> U51(X)
744.35/263.12	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.12	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.12	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.12	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.12	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.12	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.12	   x(active(X1), X2) -> x(X1, X2)
744.35/263.12	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.12	
744.35/263.12	The set Q consists of the following terms:
744.35/263.12	
744.35/263.12	   active(U101(tt, x0, x1))
744.35/263.12	   active(U102(tt, x0, x1))
744.35/263.12	   active(U103(tt, x0, x1))
744.35/263.12	   active(U104(tt, x0, x1))
744.35/263.12	   active(U11(tt, x0, x1))
744.35/263.12	   active(U12(tt, x0, x1))
744.35/263.12	   active(U13(tt, x0, x1))
744.35/263.12	   active(U14(tt, x0, x1))
744.35/263.12	   active(U15(tt, x0))
744.35/263.12	   active(U16(tt))
744.35/263.12	   active(U21(tt, x0))
744.35/263.12	   active(U22(tt, x0))
744.35/263.12	   active(U23(tt))
744.35/263.12	   active(U31(tt, x0, x1))
744.35/263.12	   active(U32(tt, x0, x1))
744.35/263.12	   active(U33(tt, x0, x1))
744.35/263.12	   active(U34(tt, x0, x1))
744.35/263.12	   active(U35(tt, x0))
744.35/263.12	   active(U36(tt))
744.35/263.12	   active(U41(tt, x0))
744.35/263.12	   active(U42(tt))
744.35/263.12	   active(U51(tt))
744.35/263.12	   active(U61(tt, x0))
744.35/263.12	   active(U62(tt))
744.35/263.12	   active(U71(tt, x0))
744.35/263.12	   active(U72(tt, x0))
744.35/263.12	   active(U81(tt, x0, x1))
744.35/263.12	   active(U82(tt, x0, x1))
744.35/263.12	   active(U83(tt, x0, x1))
744.35/263.12	   active(U84(tt, x0, x1))
744.35/263.12	   active(U91(tt, x0))
744.35/263.12	   active(U92(tt))
744.35/263.12	   active(isNat(0))
744.35/263.12	   active(isNat(plus(x0, x1)))
744.35/263.12	   active(isNat(s(x0)))
744.35/263.12	   active(isNat(x(x0, x1)))
744.35/263.12	   active(isNatKind(0))
744.35/263.12	   active(isNatKind(plus(x0, x1)))
744.35/263.12	   active(isNatKind(s(x0)))
744.35/263.12	   active(isNatKind(x(x0, x1)))
744.35/263.12	   active(plus(x0, 0))
744.35/263.12	   active(plus(x0, s(x1)))
744.35/263.12	   active(x(x0, 0))
744.35/263.12	   active(x(x0, s(x1)))
744.35/263.12	   mark(U101(x0, x1, x2))
744.35/263.12	   mark(tt)
744.35/263.12	   mark(U102(x0, x1, x2))
744.35/263.12	   mark(isNatKind(x0))
744.35/263.12	   mark(U103(x0, x1, x2))
744.35/263.12	   mark(isNat(x0))
744.35/263.12	   mark(U104(x0, x1, x2))
744.35/263.12	   mark(plus(x0, x1))
744.35/263.12	   mark(x(x0, x1))
744.35/263.12	   mark(U11(x0, x1, x2))
744.35/263.12	   mark(U12(x0, x1, x2))
744.35/263.12	   mark(U13(x0, x1, x2))
744.35/263.12	   mark(U14(x0, x1, x2))
744.35/263.12	   mark(U15(x0, x1))
744.35/263.12	   mark(U16(x0))
744.35/263.12	   mark(U21(x0, x1))
744.35/263.12	   mark(U22(x0, x1))
744.35/263.12	   mark(U23(x0))
744.35/263.12	   mark(U31(x0, x1, x2))
744.35/263.12	   mark(U32(x0, x1, x2))
744.35/263.12	   mark(U33(x0, x1, x2))
744.35/263.12	   mark(U34(x0, x1, x2))
744.35/263.12	   mark(U35(x0, x1))
744.35/263.12	   mark(U36(x0))
744.35/263.12	   mark(U41(x0, x1))
744.35/263.12	   mark(U42(x0))
744.35/263.12	   mark(U51(x0))
744.35/263.12	   mark(U61(x0, x1))
744.35/263.12	   mark(U62(x0))
744.35/263.12	   mark(U71(x0, x1))
744.35/263.12	   mark(U72(x0, x1))
744.35/263.12	   mark(U81(x0, x1, x2))
744.35/263.12	   mark(U82(x0, x1, x2))
744.35/263.12	   mark(U83(x0, x1, x2))
744.35/263.12	   mark(U84(x0, x1, x2))
744.35/263.12	   mark(s(x0))
744.35/263.12	   mark(U91(x0, x1))
744.35/263.12	   mark(U92(x0))
744.35/263.12	   mark(0)
744.35/263.12	   U101(mark(x0), x1, x2)
744.35/263.12	   U101(x0, mark(x1), x2)
744.35/263.12	   U101(x0, x1, mark(x2))
744.35/263.12	   U101(active(x0), x1, x2)
744.35/263.12	   U101(x0, active(x1), x2)
744.35/263.12	   U101(x0, x1, active(x2))
744.35/263.12	   U102(mark(x0), x1, x2)
744.35/263.12	   U102(x0, mark(x1), x2)
744.35/263.12	   U102(x0, x1, mark(x2))
744.35/263.12	   U102(active(x0), x1, x2)
744.35/263.12	   U102(x0, active(x1), x2)
744.35/263.12	   U102(x0, x1, active(x2))
744.35/263.12	   isNatKind(mark(x0))
744.35/263.12	   isNatKind(active(x0))
744.35/263.12	   U103(mark(x0), x1, x2)
744.35/263.12	   U103(x0, mark(x1), x2)
744.35/263.12	   U103(x0, x1, mark(x2))
744.35/263.12	   U103(active(x0), x1, x2)
744.35/263.12	   U103(x0, active(x1), x2)
744.35/263.12	   U103(x0, x1, active(x2))
744.35/263.12	   isNat(mark(x0))
744.35/263.12	   isNat(active(x0))
744.35/263.12	   U104(mark(x0), x1, x2)
744.35/263.12	   U104(x0, mark(x1), x2)
744.35/263.12	   U104(x0, x1, mark(x2))
744.35/263.12	   U104(active(x0), x1, x2)
744.35/263.12	   U104(x0, active(x1), x2)
744.35/263.12	   U104(x0, x1, active(x2))
744.35/263.12	   plus(mark(x0), x1)
744.35/263.12	   plus(x0, mark(x1))
744.35/263.12	   plus(active(x0), x1)
744.35/263.12	   plus(x0, active(x1))
744.35/263.12	   x(mark(x0), x1)
744.35/263.12	   x(x0, mark(x1))
744.35/263.12	   x(active(x0), x1)
744.35/263.12	   x(x0, active(x1))
744.35/263.12	   U11(mark(x0), x1, x2)
744.35/263.12	   U11(x0, mark(x1), x2)
744.35/263.12	   U11(x0, x1, mark(x2))
744.35/263.12	   U11(active(x0), x1, x2)
744.35/263.12	   U11(x0, active(x1), x2)
744.35/263.12	   U11(x0, x1, active(x2))
744.35/263.12	   U12(mark(x0), x1, x2)
744.35/263.12	   U12(x0, mark(x1), x2)
744.35/263.12	   U12(x0, x1, mark(x2))
744.35/263.12	   U12(active(x0), x1, x2)
744.35/263.12	   U12(x0, active(x1), x2)
744.35/263.12	   U12(x0, x1, active(x2))
744.35/263.12	   U13(mark(x0), x1, x2)
744.35/263.12	   U13(x0, mark(x1), x2)
744.35/263.12	   U13(x0, x1, mark(x2))
744.35/263.12	   U13(active(x0), x1, x2)
744.35/263.12	   U13(x0, active(x1), x2)
744.35/263.12	   U13(x0, x1, active(x2))
744.35/263.12	   U14(mark(x0), x1, x2)
744.35/263.12	   U14(x0, mark(x1), x2)
744.35/263.12	   U14(x0, x1, mark(x2))
744.35/263.12	   U14(active(x0), x1, x2)
744.35/263.12	   U14(x0, active(x1), x2)
744.35/263.12	   U14(x0, x1, active(x2))
744.35/263.12	   U15(mark(x0), x1)
744.35/263.12	   U15(x0, mark(x1))
744.35/263.12	   U15(active(x0), x1)
744.35/263.12	   U15(x0, active(x1))
744.35/263.12	   U16(mark(x0))
744.35/263.12	   U16(active(x0))
744.35/263.12	   U21(mark(x0), x1)
744.35/263.12	   U21(x0, mark(x1))
744.35/263.12	   U21(active(x0), x1)
744.35/263.12	   U21(x0, active(x1))
744.35/263.12	   U22(mark(x0), x1)
744.35/263.12	   U22(x0, mark(x1))
744.35/263.12	   U22(active(x0), x1)
744.35/263.12	   U22(x0, active(x1))
744.35/263.12	   U23(mark(x0))
744.35/263.12	   U23(active(x0))
744.35/263.12	   U31(mark(x0), x1, x2)
744.35/263.12	   U31(x0, mark(x1), x2)
744.35/263.12	   U31(x0, x1, mark(x2))
744.35/263.12	   U31(active(x0), x1, x2)
744.35/263.12	   U31(x0, active(x1), x2)
744.35/263.12	   U31(x0, x1, active(x2))
744.35/263.12	   U32(mark(x0), x1, x2)
744.35/263.12	   U32(x0, mark(x1), x2)
744.35/263.12	   U32(x0, x1, mark(x2))
744.35/263.12	   U32(active(x0), x1, x2)
744.35/263.12	   U32(x0, active(x1), x2)
744.35/263.12	   U32(x0, x1, active(x2))
744.35/263.12	   U33(mark(x0), x1, x2)
744.35/263.12	   U33(x0, mark(x1), x2)
744.35/263.12	   U33(x0, x1, mark(x2))
744.35/263.12	   U33(active(x0), x1, x2)
744.35/263.12	   U33(x0, active(x1), x2)
744.35/263.12	   U33(x0, x1, active(x2))
744.35/263.12	   U34(mark(x0), x1, x2)
744.35/263.12	   U34(x0, mark(x1), x2)
744.35/263.12	   U34(x0, x1, mark(x2))
744.35/263.12	   U34(active(x0), x1, x2)
744.35/263.12	   U34(x0, active(x1), x2)
744.35/263.12	   U34(x0, x1, active(x2))
744.35/263.12	   U35(mark(x0), x1)
744.35/263.12	   U35(x0, mark(x1))
744.35/263.12	   U35(active(x0), x1)
744.35/263.12	   U35(x0, active(x1))
744.35/263.12	   U36(mark(x0))
744.35/263.12	   U36(active(x0))
744.35/263.12	   U41(mark(x0), x1)
744.35/263.12	   U41(x0, mark(x1))
744.35/263.12	   U41(active(x0), x1)
744.35/263.12	   U41(x0, active(x1))
744.35/263.12	   U42(mark(x0))
744.35/263.12	   U42(active(x0))
744.35/263.12	   U51(mark(x0))
744.35/263.12	   U51(active(x0))
744.35/263.12	   U61(mark(x0), x1)
744.35/263.12	   U61(x0, mark(x1))
744.35/263.12	   U61(active(x0), x1)
744.35/263.12	   U61(x0, active(x1))
744.35/263.12	   U62(mark(x0))
744.35/263.12	   U62(active(x0))
744.35/263.12	   U71(mark(x0), x1)
744.35/263.12	   U71(x0, mark(x1))
744.35/263.12	   U71(active(x0), x1)
744.35/263.12	   U71(x0, active(x1))
744.35/263.12	   U72(mark(x0), x1)
744.35/263.12	   U72(x0, mark(x1))
744.35/263.12	   U72(active(x0), x1)
744.35/263.12	   U72(x0, active(x1))
744.35/263.12	   U81(mark(x0), x1, x2)
744.35/263.12	   U81(x0, mark(x1), x2)
744.35/263.12	   U81(x0, x1, mark(x2))
744.35/263.12	   U81(active(x0), x1, x2)
744.35/263.12	   U81(x0, active(x1), x2)
744.35/263.12	   U81(x0, x1, active(x2))
744.35/263.12	   U82(mark(x0), x1, x2)
744.35/263.12	   U82(x0, mark(x1), x2)
744.35/263.12	   U82(x0, x1, mark(x2))
744.35/263.12	   U82(active(x0), x1, x2)
744.35/263.12	   U82(x0, active(x1), x2)
744.35/263.12	   U82(x0, x1, active(x2))
744.35/263.12	   U83(mark(x0), x1, x2)
744.35/263.12	   U83(x0, mark(x1), x2)
744.35/263.12	   U83(x0, x1, mark(x2))
744.35/263.12	   U83(active(x0), x1, x2)
744.35/263.12	   U83(x0, active(x1), x2)
744.35/263.12	   U83(x0, x1, active(x2))
744.35/263.12	   U84(mark(x0), x1, x2)
744.35/263.12	   U84(x0, mark(x1), x2)
744.35/263.12	   U84(x0, x1, mark(x2))
744.35/263.12	   U84(active(x0), x1, x2)
744.35/263.12	   U84(x0, active(x1), x2)
744.35/263.12	   U84(x0, x1, active(x2))
744.35/263.12	   s(mark(x0))
744.35/263.12	   s(active(x0))
744.35/263.12	   U91(mark(x0), x1)
744.35/263.12	   U91(x0, mark(x1))
744.35/263.12	   U91(active(x0), x1)
744.35/263.12	   U91(x0, active(x1))
744.35/263.12	   U92(mark(x0))
744.35/263.12	   U92(active(x0))
744.35/263.12	
744.35/263.12	We have to consider all minimal (P,Q,R)-chains.
744.35/263.12	----------------------------------------
744.35/263.12	
744.35/263.12	(345) QDPOrderProof (EQUIVALENT)
744.35/263.12	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.12	
744.35/263.12	
744.35/263.12	The following pairs can be oriented strictly and are deleted.
744.35/263.12	
744.35/263.12	   MARK(U22(X1, X2)) -> MARK(X1)
744.35/263.12	The remaining pairs can at least be oriented weakly.
744.35/263.12	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(mark(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(tt) =  	[[0A]]
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U16(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U21(x_1, x_2)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U22(x_1, x_2)) =  	[[1A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(s(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(active(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U31(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U62(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U71(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U72(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(0) =  	[[0A]]
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	
744.35/263.12	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.12	
744.35/263.12	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.12	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.12	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.12	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.12	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.12	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.12	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.12	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.12	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.12	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.12	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.12	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.12	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.12	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.12	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.12	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.12	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.12	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.12	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.12	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.12	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.12	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.12	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.12	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.12	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.12	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.12	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.12	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.12	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.12	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.12	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.12	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.12	   active(U72(tt, N)) -> mark(N)
744.35/263.12	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.12	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.12	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.12	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.12	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.12	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.12	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.12	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.12	   mark(s(X)) -> active(s(mark(X)))
744.35/263.12	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.12	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.12	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.12	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.12	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.12	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.12	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.12	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.12	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.12	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.12	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.12	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.12	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.12	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.12	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.12	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.12	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.12	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.12	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.12	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.12	   mark(isNat(X)) -> active(isNat(X))
744.35/263.12	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.12	   mark(tt) -> active(tt)
744.35/263.12	   mark(0) -> active(0)
744.35/263.12	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.12	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.12	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.12	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.12	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.12	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.12	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.12	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.12	   active(U16(tt)) -> mark(tt)
744.35/263.12	   active(U23(tt)) -> mark(tt)
744.35/263.12	   active(U36(tt)) -> mark(tt)
744.35/263.12	   active(U42(tt)) -> mark(tt)
744.35/263.12	   active(U51(tt)) -> mark(tt)
744.35/263.12	   active(U62(tt)) -> mark(tt)
744.35/263.12	   active(U92(tt)) -> mark(0)
744.35/263.12	   active(isNat(0)) -> mark(tt)
744.35/263.12	   active(isNatKind(0)) -> mark(tt)
744.35/263.12	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.12	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.12	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.12	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.12	   U16(active(X)) -> U16(X)
744.35/263.12	   U16(mark(X)) -> U16(X)
744.35/263.12	   U23(active(X)) -> U23(X)
744.35/263.12	   U23(mark(X)) -> U23(X)
744.35/263.12	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.12	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.12	   U36(active(X)) -> U36(X)
744.35/263.12	   U36(mark(X)) -> U36(X)
744.35/263.12	   U42(active(X)) -> U42(X)
744.35/263.12	   U42(mark(X)) -> U42(X)
744.35/263.12	   U62(active(X)) -> U62(X)
744.35/263.12	   U62(mark(X)) -> U62(X)
744.35/263.12	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.12	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.12	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.12	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.12	   s(active(X)) -> s(X)
744.35/263.12	   s(mark(X)) -> s(X)
744.35/263.12	   U92(active(X)) -> U92(X)
744.35/263.12	   U92(mark(X)) -> U92(X)
744.35/263.12	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U51(active(X)) -> U51(X)
744.35/263.12	   U51(mark(X)) -> U51(X)
744.35/263.12	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.12	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.12	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.12	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.12	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.12	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.12	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.12	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.12	   x(active(X1), X2) -> x(X1, X2)
744.35/263.12	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.12	
744.35/263.12	
744.35/263.12	----------------------------------------
744.35/263.12	
744.35/263.12	(346)
744.35/263.12	Obligation:
744.35/263.12	Q DP problem:
744.35/263.12	The TRS P consists of the following rules:
744.35/263.12	
744.35/263.12	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.12	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.12	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.12	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.12	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.12	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.12	   MARK(U16(X)) -> MARK(X)
744.35/263.12	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.12	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.12	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.12	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.12	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.12	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.12	   MARK(U23(X)) -> MARK(X)
744.35/263.12	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.12	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.12	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.12	   MARK(U42(X)) -> MARK(X)
744.35/263.12	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.12	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.12	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.12	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.12	   MARK(U51(X)) -> MARK(X)
744.35/263.12	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.12	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.12	
744.35/263.12	The TRS R consists of the following rules:
744.35/263.12	
744.35/263.12	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.12	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.12	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.12	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.12	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.12	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.12	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.12	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.12	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.12	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.12	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.12	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.12	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.12	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.12	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.12	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.12	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.12	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.12	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.12	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.12	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.12	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.12	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.12	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.12	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.12	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.12	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.12	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.12	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.12	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.12	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.12	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.12	   active(U72(tt, N)) -> mark(N)
744.35/263.12	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.12	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.12	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.12	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.12	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.12	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.12	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.12	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.12	   mark(s(X)) -> active(s(mark(X)))
744.35/263.12	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.12	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.12	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.12	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.12	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.12	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.12	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.12	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.12	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.12	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.12	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.12	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.12	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.12	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.12	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.12	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.12	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.12	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.12	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.12	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.12	   mark(isNat(X)) -> active(isNat(X))
744.35/263.12	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.12	   mark(tt) -> active(tt)
744.35/263.12	   mark(0) -> active(0)
744.35/263.12	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.12	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.12	   active(U16(tt)) -> mark(tt)
744.35/263.12	   active(U23(tt)) -> mark(tt)
744.35/263.12	   active(U36(tt)) -> mark(tt)
744.35/263.12	   active(U42(tt)) -> mark(tt)
744.35/263.12	   active(U51(tt)) -> mark(tt)
744.35/263.12	   active(U62(tt)) -> mark(tt)
744.35/263.12	   active(U92(tt)) -> mark(0)
744.35/263.12	   active(isNat(0)) -> mark(tt)
744.35/263.12	   active(isNatKind(0)) -> mark(tt)
744.35/263.12	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.12	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.12	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.12	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.12	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.12	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.12	   U16(active(X)) -> U16(X)
744.35/263.12	   U16(mark(X)) -> U16(X)
744.35/263.12	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.12	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.12	   U23(active(X)) -> U23(X)
744.35/263.12	   U23(mark(X)) -> U23(X)
744.35/263.12	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.12	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.12	   U36(active(X)) -> U36(X)
744.35/263.12	   U36(mark(X)) -> U36(X)
744.35/263.12	   U42(active(X)) -> U42(X)
744.35/263.12	   U42(mark(X)) -> U42(X)
744.35/263.12	   U62(active(X)) -> U62(X)
744.35/263.12	   U62(mark(X)) -> U62(X)
744.35/263.12	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.12	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.12	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.12	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.12	   s(active(X)) -> s(X)
744.35/263.12	   s(mark(X)) -> s(X)
744.35/263.12	   U92(active(X)) -> U92(X)
744.35/263.12	   U92(mark(X)) -> U92(X)
744.35/263.12	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.12	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.12	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.12	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.12	   U51(active(X)) -> U51(X)
744.35/263.12	   U51(mark(X)) -> U51(X)
744.35/263.12	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.12	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.12	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.12	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.12	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.12	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.12	   x(active(X1), X2) -> x(X1, X2)
744.35/263.12	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.12	
744.35/263.12	The set Q consists of the following terms:
744.35/263.12	
744.35/263.12	   active(U101(tt, x0, x1))
744.35/263.12	   active(U102(tt, x0, x1))
744.35/263.12	   active(U103(tt, x0, x1))
744.35/263.12	   active(U104(tt, x0, x1))
744.35/263.12	   active(U11(tt, x0, x1))
744.35/263.12	   active(U12(tt, x0, x1))
744.35/263.12	   active(U13(tt, x0, x1))
744.35/263.12	   active(U14(tt, x0, x1))
744.35/263.12	   active(U15(tt, x0))
744.35/263.12	   active(U16(tt))
744.35/263.12	   active(U21(tt, x0))
744.35/263.12	   active(U22(tt, x0))
744.35/263.12	   active(U23(tt))
744.35/263.12	   active(U31(tt, x0, x1))
744.35/263.12	   active(U32(tt, x0, x1))
744.35/263.12	   active(U33(tt, x0, x1))
744.35/263.12	   active(U34(tt, x0, x1))
744.35/263.12	   active(U35(tt, x0))
744.35/263.12	   active(U36(tt))
744.35/263.12	   active(U41(tt, x0))
744.35/263.12	   active(U42(tt))
744.35/263.12	   active(U51(tt))
744.35/263.12	   active(U61(tt, x0))
744.35/263.12	   active(U62(tt))
744.35/263.12	   active(U71(tt, x0))
744.35/263.12	   active(U72(tt, x0))
744.35/263.12	   active(U81(tt, x0, x1))
744.35/263.12	   active(U82(tt, x0, x1))
744.35/263.12	   active(U83(tt, x0, x1))
744.35/263.12	   active(U84(tt, x0, x1))
744.35/263.12	   active(U91(tt, x0))
744.35/263.12	   active(U92(tt))
744.35/263.12	   active(isNat(0))
744.35/263.12	   active(isNat(plus(x0, x1)))
744.35/263.12	   active(isNat(s(x0)))
744.35/263.12	   active(isNat(x(x0, x1)))
744.35/263.12	   active(isNatKind(0))
744.35/263.12	   active(isNatKind(plus(x0, x1)))
744.35/263.12	   active(isNatKind(s(x0)))
744.35/263.12	   active(isNatKind(x(x0, x1)))
744.35/263.12	   active(plus(x0, 0))
744.35/263.12	   active(plus(x0, s(x1)))
744.35/263.12	   active(x(x0, 0))
744.35/263.12	   active(x(x0, s(x1)))
744.35/263.12	   mark(U101(x0, x1, x2))
744.35/263.12	   mark(tt)
744.35/263.12	   mark(U102(x0, x1, x2))
744.35/263.12	   mark(isNatKind(x0))
744.35/263.12	   mark(U103(x0, x1, x2))
744.35/263.12	   mark(isNat(x0))
744.35/263.12	   mark(U104(x0, x1, x2))
744.35/263.12	   mark(plus(x0, x1))
744.35/263.12	   mark(x(x0, x1))
744.35/263.12	   mark(U11(x0, x1, x2))
744.35/263.12	   mark(U12(x0, x1, x2))
744.35/263.12	   mark(U13(x0, x1, x2))
744.35/263.12	   mark(U14(x0, x1, x2))
744.35/263.12	   mark(U15(x0, x1))
744.35/263.12	   mark(U16(x0))
744.35/263.12	   mark(U21(x0, x1))
744.35/263.12	   mark(U22(x0, x1))
744.35/263.12	   mark(U23(x0))
744.35/263.12	   mark(U31(x0, x1, x2))
744.35/263.12	   mark(U32(x0, x1, x2))
744.35/263.12	   mark(U33(x0, x1, x2))
744.35/263.12	   mark(U34(x0, x1, x2))
744.35/263.12	   mark(U35(x0, x1))
744.35/263.12	   mark(U36(x0))
744.35/263.12	   mark(U41(x0, x1))
744.35/263.12	   mark(U42(x0))
744.35/263.12	   mark(U51(x0))
744.35/263.12	   mark(U61(x0, x1))
744.35/263.12	   mark(U62(x0))
744.35/263.12	   mark(U71(x0, x1))
744.35/263.12	   mark(U72(x0, x1))
744.35/263.12	   mark(U81(x0, x1, x2))
744.35/263.12	   mark(U82(x0, x1, x2))
744.35/263.12	   mark(U83(x0, x1, x2))
744.35/263.12	   mark(U84(x0, x1, x2))
744.35/263.12	   mark(s(x0))
744.35/263.12	   mark(U91(x0, x1))
744.35/263.12	   mark(U92(x0))
744.35/263.12	   mark(0)
744.35/263.12	   U101(mark(x0), x1, x2)
744.35/263.12	   U101(x0, mark(x1), x2)
744.35/263.12	   U101(x0, x1, mark(x2))
744.35/263.12	   U101(active(x0), x1, x2)
744.35/263.12	   U101(x0, active(x1), x2)
744.35/263.12	   U101(x0, x1, active(x2))
744.35/263.12	   U102(mark(x0), x1, x2)
744.35/263.12	   U102(x0, mark(x1), x2)
744.35/263.12	   U102(x0, x1, mark(x2))
744.35/263.12	   U102(active(x0), x1, x2)
744.35/263.12	   U102(x0, active(x1), x2)
744.35/263.12	   U102(x0, x1, active(x2))
744.35/263.12	   isNatKind(mark(x0))
744.35/263.12	   isNatKind(active(x0))
744.35/263.12	   U103(mark(x0), x1, x2)
744.35/263.12	   U103(x0, mark(x1), x2)
744.35/263.12	   U103(x0, x1, mark(x2))
744.35/263.12	   U103(active(x0), x1, x2)
744.35/263.12	   U103(x0, active(x1), x2)
744.35/263.12	   U103(x0, x1, active(x2))
744.35/263.12	   isNat(mark(x0))
744.35/263.12	   isNat(active(x0))
744.35/263.12	   U104(mark(x0), x1, x2)
744.35/263.12	   U104(x0, mark(x1), x2)
744.35/263.12	   U104(x0, x1, mark(x2))
744.35/263.12	   U104(active(x0), x1, x2)
744.35/263.12	   U104(x0, active(x1), x2)
744.35/263.12	   U104(x0, x1, active(x2))
744.35/263.12	   plus(mark(x0), x1)
744.35/263.12	   plus(x0, mark(x1))
744.35/263.12	   plus(active(x0), x1)
744.35/263.12	   plus(x0, active(x1))
744.35/263.12	   x(mark(x0), x1)
744.35/263.12	   x(x0, mark(x1))
744.35/263.12	   x(active(x0), x1)
744.35/263.12	   x(x0, active(x1))
744.35/263.12	   U11(mark(x0), x1, x2)
744.35/263.12	   U11(x0, mark(x1), x2)
744.35/263.12	   U11(x0, x1, mark(x2))
744.35/263.12	   U11(active(x0), x1, x2)
744.35/263.12	   U11(x0, active(x1), x2)
744.35/263.12	   U11(x0, x1, active(x2))
744.35/263.12	   U12(mark(x0), x1, x2)
744.35/263.12	   U12(x0, mark(x1), x2)
744.35/263.12	   U12(x0, x1, mark(x2))
744.35/263.12	   U12(active(x0), x1, x2)
744.35/263.12	   U12(x0, active(x1), x2)
744.35/263.12	   U12(x0, x1, active(x2))
744.35/263.12	   U13(mark(x0), x1, x2)
744.35/263.12	   U13(x0, mark(x1), x2)
744.35/263.12	   U13(x0, x1, mark(x2))
744.35/263.12	   U13(active(x0), x1, x2)
744.35/263.12	   U13(x0, active(x1), x2)
744.35/263.12	   U13(x0, x1, active(x2))
744.35/263.12	   U14(mark(x0), x1, x2)
744.35/263.12	   U14(x0, mark(x1), x2)
744.35/263.12	   U14(x0, x1, mark(x2))
744.35/263.12	   U14(active(x0), x1, x2)
744.35/263.12	   U14(x0, active(x1), x2)
744.35/263.12	   U14(x0, x1, active(x2))
744.35/263.12	   U15(mark(x0), x1)
744.35/263.12	   U15(x0, mark(x1))
744.35/263.12	   U15(active(x0), x1)
744.35/263.12	   U15(x0, active(x1))
744.35/263.12	   U16(mark(x0))
744.35/263.12	   U16(active(x0))
744.35/263.12	   U21(mark(x0), x1)
744.35/263.12	   U21(x0, mark(x1))
744.35/263.12	   U21(active(x0), x1)
744.35/263.12	   U21(x0, active(x1))
744.35/263.12	   U22(mark(x0), x1)
744.35/263.12	   U22(x0, mark(x1))
744.35/263.12	   U22(active(x0), x1)
744.35/263.12	   U22(x0, active(x1))
744.35/263.12	   U23(mark(x0))
744.35/263.12	   U23(active(x0))
744.35/263.12	   U31(mark(x0), x1, x2)
744.35/263.12	   U31(x0, mark(x1), x2)
744.35/263.12	   U31(x0, x1, mark(x2))
744.35/263.12	   U31(active(x0), x1, x2)
744.35/263.12	   U31(x0, active(x1), x2)
744.35/263.12	   U31(x0, x1, active(x2))
744.35/263.12	   U32(mark(x0), x1, x2)
744.35/263.12	   U32(x0, mark(x1), x2)
744.35/263.12	   U32(x0, x1, mark(x2))
744.35/263.12	   U32(active(x0), x1, x2)
744.35/263.12	   U32(x0, active(x1), x2)
744.35/263.12	   U32(x0, x1, active(x2))
744.35/263.12	   U33(mark(x0), x1, x2)
744.35/263.12	   U33(x0, mark(x1), x2)
744.35/263.12	   U33(x0, x1, mark(x2))
744.35/263.12	   U33(active(x0), x1, x2)
744.35/263.12	   U33(x0, active(x1), x2)
744.35/263.12	   U33(x0, x1, active(x2))
744.35/263.12	   U34(mark(x0), x1, x2)
744.35/263.12	   U34(x0, mark(x1), x2)
744.35/263.12	   U34(x0, x1, mark(x2))
744.35/263.12	   U34(active(x0), x1, x2)
744.35/263.12	   U34(x0, active(x1), x2)
744.35/263.12	   U34(x0, x1, active(x2))
744.35/263.12	   U35(mark(x0), x1)
744.35/263.12	   U35(x0, mark(x1))
744.35/263.12	   U35(active(x0), x1)
744.35/263.12	   U35(x0, active(x1))
744.35/263.12	   U36(mark(x0))
744.35/263.12	   U36(active(x0))
744.35/263.12	   U41(mark(x0), x1)
744.35/263.12	   U41(x0, mark(x1))
744.35/263.12	   U41(active(x0), x1)
744.35/263.12	   U41(x0, active(x1))
744.35/263.12	   U42(mark(x0))
744.35/263.12	   U42(active(x0))
744.35/263.12	   U51(mark(x0))
744.35/263.12	   U51(active(x0))
744.35/263.12	   U61(mark(x0), x1)
744.35/263.12	   U61(x0, mark(x1))
744.35/263.12	   U61(active(x0), x1)
744.35/263.12	   U61(x0, active(x1))
744.35/263.12	   U62(mark(x0))
744.35/263.12	   U62(active(x0))
744.35/263.12	   U71(mark(x0), x1)
744.35/263.12	   U71(x0, mark(x1))
744.35/263.12	   U71(active(x0), x1)
744.35/263.12	   U71(x0, active(x1))
744.35/263.12	   U72(mark(x0), x1)
744.35/263.12	   U72(x0, mark(x1))
744.35/263.12	   U72(active(x0), x1)
744.35/263.12	   U72(x0, active(x1))
744.35/263.12	   U81(mark(x0), x1, x2)
744.35/263.12	   U81(x0, mark(x1), x2)
744.35/263.12	   U81(x0, x1, mark(x2))
744.35/263.12	   U81(active(x0), x1, x2)
744.35/263.12	   U81(x0, active(x1), x2)
744.35/263.12	   U81(x0, x1, active(x2))
744.35/263.12	   U82(mark(x0), x1, x2)
744.35/263.12	   U82(x0, mark(x1), x2)
744.35/263.12	   U82(x0, x1, mark(x2))
744.35/263.12	   U82(active(x0), x1, x2)
744.35/263.12	   U82(x0, active(x1), x2)
744.35/263.12	   U82(x0, x1, active(x2))
744.35/263.12	   U83(mark(x0), x1, x2)
744.35/263.12	   U83(x0, mark(x1), x2)
744.35/263.12	   U83(x0, x1, mark(x2))
744.35/263.12	   U83(active(x0), x1, x2)
744.35/263.12	   U83(x0, active(x1), x2)
744.35/263.12	   U83(x0, x1, active(x2))
744.35/263.12	   U84(mark(x0), x1, x2)
744.35/263.12	   U84(x0, mark(x1), x2)
744.35/263.12	   U84(x0, x1, mark(x2))
744.35/263.12	   U84(active(x0), x1, x2)
744.35/263.12	   U84(x0, active(x1), x2)
744.35/263.12	   U84(x0, x1, active(x2))
744.35/263.12	   s(mark(x0))
744.35/263.12	   s(active(x0))
744.35/263.12	   U91(mark(x0), x1)
744.35/263.12	   U91(x0, mark(x1))
744.35/263.12	   U91(active(x0), x1)
744.35/263.12	   U91(x0, active(x1))
744.35/263.12	   U92(mark(x0))
744.35/263.12	   U92(active(x0))
744.35/263.12	
744.35/263.12	We have to consider all minimal (P,Q,R)-chains.
744.35/263.12	----------------------------------------
744.35/263.12	
744.35/263.12	(347) QDPOrderProof (EQUIVALENT)
744.35/263.12	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.12	
744.35/263.12	
744.35/263.12	The following pairs can be oriented strictly and are deleted.
744.35/263.12	
744.35/263.12	   MARK(U14(X1, X2, X3)) -> MARK(X1)
744.35/263.12	The remaining pairs can at least be oriented weakly.
744.35/263.12	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(MARK(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(ACTIVE(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U11(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(tt) =  	[[0A]]
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(isNatKind(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U13(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U15(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(isNat(x_1)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U41(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U21(x_1, x_2)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U22(x_1, x_2)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U42(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U51(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U102(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[2A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U101(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[2A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U103(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[2A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U104(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[2A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(x(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[2A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U31(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[2A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U32(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[2A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U33(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U34(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U35(x_1, x_2)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U61(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U71(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U83(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U84(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	   <<<
744.35/263.12	 POL(0) =  	[[0A]]
744.35/263.12	>>>
744.35/263.12	
744.35/263.12	
744.35/263.12	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.12	
744.35/263.12	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.12	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.12	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.12	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.12	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.12	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.12	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.12	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.12	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.12	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.12	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.12	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.12	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.12	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.12	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.12	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.12	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.12	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.12	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.12	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.12	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.12	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.12	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.12	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.12	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.12	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.12	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.12	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.12	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.12	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.12	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.12	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.12	   active(U72(tt, N)) -> mark(N)
744.35/263.12	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.12	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.12	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.12	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.12	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.12	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.12	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.12	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.12	   mark(s(X)) -> active(s(mark(X)))
744.35/263.12	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.12	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.12	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.12	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.12	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.12	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.12	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.12	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.12	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.12	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.12	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.12	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.12	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.12	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.12	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.12	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.12	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.12	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.12	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.12	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.12	   mark(isNat(X)) -> active(isNat(X))
744.35/263.12	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.12	   mark(tt) -> active(tt)
744.35/263.12	   mark(0) -> active(0)
744.35/263.12	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.12	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.12	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.12	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.12	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.12	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.12	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.12	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.12	   active(U16(tt)) -> mark(tt)
744.35/263.12	   active(U23(tt)) -> mark(tt)
744.35/263.12	   active(U36(tt)) -> mark(tt)
744.35/263.12	   active(U42(tt)) -> mark(tt)
744.35/263.12	   active(U51(tt)) -> mark(tt)
744.35/263.12	   active(U62(tt)) -> mark(tt)
744.35/263.12	   active(U92(tt)) -> mark(0)
744.35/263.12	   active(isNat(0)) -> mark(tt)
744.35/263.12	   active(isNatKind(0)) -> mark(tt)
744.35/263.12	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.12	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.12	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.12	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.12	   U16(active(X)) -> U16(X)
744.35/263.12	   U16(mark(X)) -> U16(X)
744.35/263.12	   U23(active(X)) -> U23(X)
744.35/263.12	   U23(mark(X)) -> U23(X)
744.35/263.12	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.12	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.12	   U36(active(X)) -> U36(X)
744.35/263.12	   U36(mark(X)) -> U36(X)
744.35/263.12	   U42(active(X)) -> U42(X)
744.35/263.12	   U42(mark(X)) -> U42(X)
744.35/263.12	   U62(active(X)) -> U62(X)
744.35/263.12	   U62(mark(X)) -> U62(X)
744.35/263.12	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.12	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.12	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.12	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.12	   s(active(X)) -> s(X)
744.35/263.12	   s(mark(X)) -> s(X)
744.35/263.12	   U92(active(X)) -> U92(X)
744.35/263.12	   U92(mark(X)) -> U92(X)
744.35/263.12	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U51(active(X)) -> U51(X)
744.35/263.12	   U51(mark(X)) -> U51(X)
744.35/263.12	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.12	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.12	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.12	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.12	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.12	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.12	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.12	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.12	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.12	   x(active(X1), X2) -> x(X1, X2)
744.35/263.12	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.12	
744.35/263.12	
744.35/263.12	----------------------------------------
744.35/263.12	
744.35/263.12	(348)
744.35/263.12	Obligation:
744.35/263.12	Q DP problem:
744.35/263.12	The TRS P consists of the following rules:
744.35/263.12	
744.35/263.12	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.12	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.12	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.12	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.12	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.12	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.12	   MARK(U16(X)) -> MARK(X)
744.35/263.12	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.12	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.12	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.12	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.12	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.12	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.12	   MARK(U23(X)) -> MARK(X)
744.35/263.12	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.12	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.12	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.12	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.12	   MARK(U42(X)) -> MARK(X)
744.35/263.12	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.12	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.12	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.12	   MARK(U51(X)) -> MARK(X)
744.35/263.12	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.12	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.12	
744.35/263.12	The TRS R consists of the following rules:
744.35/263.12	
744.35/263.12	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.12	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.12	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.12	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.12	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.12	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.12	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.12	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.12	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.12	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.12	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.12	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.12	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.12	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.12	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.12	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.12	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.12	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.12	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.12	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.12	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.12	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.12	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.12	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.12	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.12	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.12	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.12	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.12	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.12	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.12	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.12	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.12	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.12	   active(U72(tt, N)) -> mark(N)
744.35/263.12	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.12	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.12	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.12	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.12	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.12	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.12	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.12	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.12	   mark(s(X)) -> active(s(mark(X)))
744.35/263.12	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.12	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.12	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.12	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.12	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.12	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.12	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.12	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.12	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.12	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.12	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.12	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.12	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.12	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.12	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.12	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.12	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.12	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.12	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.12	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.12	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.12	   mark(isNat(X)) -> active(isNat(X))
744.35/263.12	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.12	   mark(tt) -> active(tt)
744.35/263.12	   mark(0) -> active(0)
744.35/263.12	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.12	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.12	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.12	   active(U16(tt)) -> mark(tt)
744.35/263.12	   active(U23(tt)) -> mark(tt)
744.35/263.12	   active(U36(tt)) -> mark(tt)
744.35/263.12	   active(U42(tt)) -> mark(tt)
744.35/263.12	   active(U51(tt)) -> mark(tt)
744.35/263.12	   active(U62(tt)) -> mark(tt)
744.35/263.12	   active(U92(tt)) -> mark(0)
744.35/263.12	   active(isNat(0)) -> mark(tt)
744.35/263.12	   active(isNatKind(0)) -> mark(tt)
744.35/263.12	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.12	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.12	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.12	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.12	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.12	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.12	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.12	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.12	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.12	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.12	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.12	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.12	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.12	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.12	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.12	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.12	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.12	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.12	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.12	   U16(active(X)) -> U16(X)
744.35/263.12	   U16(mark(X)) -> U16(X)
744.35/263.12	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.12	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.12	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.12	   U23(active(X)) -> U23(X)
744.35/263.12	   U23(mark(X)) -> U23(X)
744.35/263.12	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.12	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.12	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.12	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.12	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.12	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.12	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.12	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.12	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.12	   U36(active(X)) -> U36(X)
744.35/263.12	   U36(mark(X)) -> U36(X)
744.35/263.12	   U42(active(X)) -> U42(X)
744.35/263.12	   U42(mark(X)) -> U42(X)
744.35/263.12	   U62(active(X)) -> U62(X)
744.35/263.12	   U62(mark(X)) -> U62(X)
744.35/263.12	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.12	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.12	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.12	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.12	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.12	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.12	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.12	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.12	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.12	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.12	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.12	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.12	   s(active(X)) -> s(X)
744.35/263.12	   s(mark(X)) -> s(X)
744.35/263.12	   U92(active(X)) -> U92(X)
744.35/263.12	   U92(mark(X)) -> U92(X)
744.35/263.12	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.12	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.12	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.12	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.12	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.12	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.12	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.12	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.12	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.12	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.12	   U51(active(X)) -> U51(X)
744.35/263.12	   U51(mark(X)) -> U51(X)
744.35/263.12	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.12	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.12	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.12	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.12	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.12	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.13	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.13	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.13	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.13	   x(active(X1), X2) -> x(X1, X2)
744.35/263.13	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.13	
744.35/263.13	The set Q consists of the following terms:
744.35/263.13	
744.35/263.13	   active(U101(tt, x0, x1))
744.35/263.13	   active(U102(tt, x0, x1))
744.35/263.13	   active(U103(tt, x0, x1))
744.35/263.13	   active(U104(tt, x0, x1))
744.35/263.13	   active(U11(tt, x0, x1))
744.35/263.13	   active(U12(tt, x0, x1))
744.35/263.13	   active(U13(tt, x0, x1))
744.35/263.13	   active(U14(tt, x0, x1))
744.35/263.13	   active(U15(tt, x0))
744.35/263.13	   active(U16(tt))
744.35/263.13	   active(U21(tt, x0))
744.35/263.13	   active(U22(tt, x0))
744.35/263.13	   active(U23(tt))
744.35/263.13	   active(U31(tt, x0, x1))
744.35/263.13	   active(U32(tt, x0, x1))
744.35/263.13	   active(U33(tt, x0, x1))
744.35/263.13	   active(U34(tt, x0, x1))
744.35/263.13	   active(U35(tt, x0))
744.35/263.13	   active(U36(tt))
744.35/263.13	   active(U41(tt, x0))
744.35/263.13	   active(U42(tt))
744.35/263.13	   active(U51(tt))
744.35/263.13	   active(U61(tt, x0))
744.35/263.13	   active(U62(tt))
744.35/263.13	   active(U71(tt, x0))
744.35/263.13	   active(U72(tt, x0))
744.35/263.13	   active(U81(tt, x0, x1))
744.35/263.13	   active(U82(tt, x0, x1))
744.35/263.13	   active(U83(tt, x0, x1))
744.35/263.13	   active(U84(tt, x0, x1))
744.35/263.13	   active(U91(tt, x0))
744.35/263.13	   active(U92(tt))
744.35/263.13	   active(isNat(0))
744.35/263.13	   active(isNat(plus(x0, x1)))
744.35/263.13	   active(isNat(s(x0)))
744.35/263.13	   active(isNat(x(x0, x1)))
744.35/263.13	   active(isNatKind(0))
744.35/263.13	   active(isNatKind(plus(x0, x1)))
744.35/263.13	   active(isNatKind(s(x0)))
744.35/263.13	   active(isNatKind(x(x0, x1)))
744.35/263.13	   active(plus(x0, 0))
744.35/263.13	   active(plus(x0, s(x1)))
744.35/263.13	   active(x(x0, 0))
744.35/263.13	   active(x(x0, s(x1)))
744.35/263.13	   mark(U101(x0, x1, x2))
744.35/263.13	   mark(tt)
744.35/263.13	   mark(U102(x0, x1, x2))
744.35/263.13	   mark(isNatKind(x0))
744.35/263.13	   mark(U103(x0, x1, x2))
744.35/263.13	   mark(isNat(x0))
744.35/263.13	   mark(U104(x0, x1, x2))
744.35/263.13	   mark(plus(x0, x1))
744.35/263.13	   mark(x(x0, x1))
744.35/263.13	   mark(U11(x0, x1, x2))
744.35/263.13	   mark(U12(x0, x1, x2))
744.35/263.13	   mark(U13(x0, x1, x2))
744.35/263.13	   mark(U14(x0, x1, x2))
744.35/263.13	   mark(U15(x0, x1))
744.35/263.13	   mark(U16(x0))
744.35/263.13	   mark(U21(x0, x1))
744.35/263.13	   mark(U22(x0, x1))
744.35/263.13	   mark(U23(x0))
744.35/263.13	   mark(U31(x0, x1, x2))
744.35/263.13	   mark(U32(x0, x1, x2))
744.35/263.13	   mark(U33(x0, x1, x2))
744.35/263.13	   mark(U34(x0, x1, x2))
744.35/263.13	   mark(U35(x0, x1))
744.35/263.13	   mark(U36(x0))
744.35/263.13	   mark(U41(x0, x1))
744.35/263.13	   mark(U42(x0))
744.35/263.13	   mark(U51(x0))
744.35/263.13	   mark(U61(x0, x1))
744.35/263.13	   mark(U62(x0))
744.35/263.13	   mark(U71(x0, x1))
744.35/263.13	   mark(U72(x0, x1))
744.35/263.13	   mark(U81(x0, x1, x2))
744.35/263.13	   mark(U82(x0, x1, x2))
744.35/263.13	   mark(U83(x0, x1, x2))
744.35/263.13	   mark(U84(x0, x1, x2))
744.35/263.13	   mark(s(x0))
744.35/263.13	   mark(U91(x0, x1))
744.35/263.13	   mark(U92(x0))
744.35/263.13	   mark(0)
744.35/263.13	   U101(mark(x0), x1, x2)
744.35/263.13	   U101(x0, mark(x1), x2)
744.35/263.13	   U101(x0, x1, mark(x2))
744.35/263.13	   U101(active(x0), x1, x2)
744.35/263.13	   U101(x0, active(x1), x2)
744.35/263.13	   U101(x0, x1, active(x2))
744.35/263.13	   U102(mark(x0), x1, x2)
744.35/263.13	   U102(x0, mark(x1), x2)
744.35/263.13	   U102(x0, x1, mark(x2))
744.35/263.13	   U102(active(x0), x1, x2)
744.35/263.13	   U102(x0, active(x1), x2)
744.35/263.13	   U102(x0, x1, active(x2))
744.35/263.13	   isNatKind(mark(x0))
744.35/263.13	   isNatKind(active(x0))
744.35/263.13	   U103(mark(x0), x1, x2)
744.35/263.13	   U103(x0, mark(x1), x2)
744.35/263.13	   U103(x0, x1, mark(x2))
744.35/263.13	   U103(active(x0), x1, x2)
744.35/263.13	   U103(x0, active(x1), x2)
744.35/263.13	   U103(x0, x1, active(x2))
744.35/263.13	   isNat(mark(x0))
744.35/263.13	   isNat(active(x0))
744.35/263.13	   U104(mark(x0), x1, x2)
744.35/263.13	   U104(x0, mark(x1), x2)
744.35/263.13	   U104(x0, x1, mark(x2))
744.35/263.13	   U104(active(x0), x1, x2)
744.35/263.13	   U104(x0, active(x1), x2)
744.35/263.13	   U104(x0, x1, active(x2))
744.35/263.13	   plus(mark(x0), x1)
744.35/263.13	   plus(x0, mark(x1))
744.35/263.13	   plus(active(x0), x1)
744.35/263.13	   plus(x0, active(x1))
744.35/263.13	   x(mark(x0), x1)
744.35/263.13	   x(x0, mark(x1))
744.35/263.13	   x(active(x0), x1)
744.35/263.13	   x(x0, active(x1))
744.35/263.13	   U11(mark(x0), x1, x2)
744.35/263.13	   U11(x0, mark(x1), x2)
744.35/263.13	   U11(x0, x1, mark(x2))
744.35/263.13	   U11(active(x0), x1, x2)
744.35/263.13	   U11(x0, active(x1), x2)
744.35/263.13	   U11(x0, x1, active(x2))
744.35/263.13	   U12(mark(x0), x1, x2)
744.35/263.13	   U12(x0, mark(x1), x2)
744.35/263.13	   U12(x0, x1, mark(x2))
744.35/263.13	   U12(active(x0), x1, x2)
744.35/263.13	   U12(x0, active(x1), x2)
744.35/263.13	   U12(x0, x1, active(x2))
744.35/263.13	   U13(mark(x0), x1, x2)
744.35/263.13	   U13(x0, mark(x1), x2)
744.35/263.13	   U13(x0, x1, mark(x2))
744.35/263.13	   U13(active(x0), x1, x2)
744.35/263.13	   U13(x0, active(x1), x2)
744.35/263.13	   U13(x0, x1, active(x2))
744.35/263.13	   U14(mark(x0), x1, x2)
744.35/263.13	   U14(x0, mark(x1), x2)
744.35/263.13	   U14(x0, x1, mark(x2))
744.35/263.13	   U14(active(x0), x1, x2)
744.35/263.13	   U14(x0, active(x1), x2)
744.35/263.13	   U14(x0, x1, active(x2))
744.35/263.13	   U15(mark(x0), x1)
744.35/263.13	   U15(x0, mark(x1))
744.35/263.13	   U15(active(x0), x1)
744.35/263.13	   U15(x0, active(x1))
744.35/263.13	   U16(mark(x0))
744.35/263.13	   U16(active(x0))
744.35/263.13	   U21(mark(x0), x1)
744.35/263.13	   U21(x0, mark(x1))
744.35/263.13	   U21(active(x0), x1)
744.35/263.13	   U21(x0, active(x1))
744.35/263.13	   U22(mark(x0), x1)
744.35/263.13	   U22(x0, mark(x1))
744.35/263.13	   U22(active(x0), x1)
744.35/263.13	   U22(x0, active(x1))
744.35/263.13	   U23(mark(x0))
744.35/263.13	   U23(active(x0))
744.35/263.13	   U31(mark(x0), x1, x2)
744.35/263.13	   U31(x0, mark(x1), x2)
744.35/263.13	   U31(x0, x1, mark(x2))
744.35/263.13	   U31(active(x0), x1, x2)
744.35/263.13	   U31(x0, active(x1), x2)
744.35/263.13	   U31(x0, x1, active(x2))
744.35/263.13	   U32(mark(x0), x1, x2)
744.35/263.13	   U32(x0, mark(x1), x2)
744.35/263.13	   U32(x0, x1, mark(x2))
744.35/263.13	   U32(active(x0), x1, x2)
744.35/263.13	   U32(x0, active(x1), x2)
744.35/263.13	   U32(x0, x1, active(x2))
744.35/263.13	   U33(mark(x0), x1, x2)
744.35/263.13	   U33(x0, mark(x1), x2)
744.35/263.13	   U33(x0, x1, mark(x2))
744.35/263.13	   U33(active(x0), x1, x2)
744.35/263.13	   U33(x0, active(x1), x2)
744.35/263.13	   U33(x0, x1, active(x2))
744.35/263.13	   U34(mark(x0), x1, x2)
744.35/263.13	   U34(x0, mark(x1), x2)
744.35/263.13	   U34(x0, x1, mark(x2))
744.35/263.13	   U34(active(x0), x1, x2)
744.35/263.13	   U34(x0, active(x1), x2)
744.35/263.13	   U34(x0, x1, active(x2))
744.35/263.13	   U35(mark(x0), x1)
744.35/263.13	   U35(x0, mark(x1))
744.35/263.13	   U35(active(x0), x1)
744.35/263.13	   U35(x0, active(x1))
744.35/263.13	   U36(mark(x0))
744.35/263.13	   U36(active(x0))
744.35/263.13	   U41(mark(x0), x1)
744.35/263.13	   U41(x0, mark(x1))
744.35/263.13	   U41(active(x0), x1)
744.35/263.13	   U41(x0, active(x1))
744.35/263.13	   U42(mark(x0))
744.35/263.13	   U42(active(x0))
744.35/263.13	   U51(mark(x0))
744.35/263.13	   U51(active(x0))
744.35/263.13	   U61(mark(x0), x1)
744.35/263.13	   U61(x0, mark(x1))
744.35/263.13	   U61(active(x0), x1)
744.35/263.13	   U61(x0, active(x1))
744.35/263.13	   U62(mark(x0))
744.35/263.13	   U62(active(x0))
744.35/263.13	   U71(mark(x0), x1)
744.35/263.13	   U71(x0, mark(x1))
744.35/263.13	   U71(active(x0), x1)
744.35/263.13	   U71(x0, active(x1))
744.35/263.13	   U72(mark(x0), x1)
744.35/263.13	   U72(x0, mark(x1))
744.35/263.13	   U72(active(x0), x1)
744.35/263.13	   U72(x0, active(x1))
744.35/263.13	   U81(mark(x0), x1, x2)
744.35/263.13	   U81(x0, mark(x1), x2)
744.35/263.13	   U81(x0, x1, mark(x2))
744.35/263.13	   U81(active(x0), x1, x2)
744.35/263.13	   U81(x0, active(x1), x2)
744.35/263.13	   U81(x0, x1, active(x2))
744.35/263.13	   U82(mark(x0), x1, x2)
744.35/263.13	   U82(x0, mark(x1), x2)
744.35/263.13	   U82(x0, x1, mark(x2))
744.35/263.13	   U82(active(x0), x1, x2)
744.35/263.13	   U82(x0, active(x1), x2)
744.35/263.13	   U82(x0, x1, active(x2))
744.35/263.13	   U83(mark(x0), x1, x2)
744.35/263.13	   U83(x0, mark(x1), x2)
744.35/263.13	   U83(x0, x1, mark(x2))
744.35/263.13	   U83(active(x0), x1, x2)
744.35/263.13	   U83(x0, active(x1), x2)
744.35/263.13	   U83(x0, x1, active(x2))
744.35/263.13	   U84(mark(x0), x1, x2)
744.35/263.13	   U84(x0, mark(x1), x2)
744.35/263.13	   U84(x0, x1, mark(x2))
744.35/263.13	   U84(active(x0), x1, x2)
744.35/263.13	   U84(x0, active(x1), x2)
744.35/263.13	   U84(x0, x1, active(x2))
744.35/263.13	   s(mark(x0))
744.35/263.13	   s(active(x0))
744.35/263.13	   U91(mark(x0), x1)
744.35/263.13	   U91(x0, mark(x1))
744.35/263.13	   U91(active(x0), x1)
744.35/263.13	   U91(x0, active(x1))
744.35/263.13	   U92(mark(x0))
744.35/263.13	   U92(active(x0))
744.35/263.13	
744.35/263.13	We have to consider all minimal (P,Q,R)-chains.
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(349) QDPOrderProof (EQUIVALENT)
744.35/263.13	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.13	
744.35/263.13	
744.35/263.13	The following pairs can be oriented strictly and are deleted.
744.35/263.13	
744.35/263.13	   ACTIVE(U15(tt, V2)) -> MARK(U16(isNat(V2)))
744.35/263.13	The remaining pairs can at least be oriented weakly.
744.35/263.13	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(tt) =  	[[1A]]
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U13(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U14(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(isNat(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U21(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U51(x_1)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(s(x_1)) =  	[[1A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U103(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[1A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(x(x_1, x_2)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U31(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U32(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U34(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U35(x_1, x_2)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U62(x_1)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U81(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U82(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U83(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U84(x_1, x_2, x_3)) =  	[[1A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(U92(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	   <<<
744.35/263.13	 POL(0) =  	[[1A]]
744.35/263.13	>>>
744.35/263.13	
744.35/263.13	
744.35/263.13	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.13	
744.35/263.13	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.13	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.13	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.13	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.13	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.13	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.13	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.13	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.13	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.13	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.13	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.13	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.13	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.13	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.13	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.13	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.13	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.13	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.13	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.13	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.13	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.13	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.13	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.13	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.13	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.13	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.13	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.13	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.13	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.13	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.13	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.13	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.13	   active(U72(tt, N)) -> mark(N)
744.35/263.13	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.13	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.13	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.13	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.13	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.13	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.13	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.13	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.13	   mark(s(X)) -> active(s(mark(X)))
744.35/263.13	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.13	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.13	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.13	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.13	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.13	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.13	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.13	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.13	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.13	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.13	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.13	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.13	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.13	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.13	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.13	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.13	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.13	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.13	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.13	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.13	   mark(isNat(X)) -> active(isNat(X))
744.35/263.13	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.13	   mark(tt) -> active(tt)
744.35/263.13	   mark(0) -> active(0)
744.35/263.13	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.13	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.13	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.13	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.13	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.13	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.13	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.13	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.13	   active(U16(tt)) -> mark(tt)
744.35/263.13	   active(U23(tt)) -> mark(tt)
744.35/263.13	   active(U36(tt)) -> mark(tt)
744.35/263.13	   active(U42(tt)) -> mark(tt)
744.35/263.13	   active(U51(tt)) -> mark(tt)
744.35/263.13	   active(U62(tt)) -> mark(tt)
744.35/263.13	   active(U92(tt)) -> mark(0)
744.35/263.13	   active(isNat(0)) -> mark(tt)
744.35/263.13	   active(isNatKind(0)) -> mark(tt)
744.35/263.13	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.13	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.13	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.13	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.13	   U16(active(X)) -> U16(X)
744.35/263.13	   U16(mark(X)) -> U16(X)
744.35/263.13	   U23(active(X)) -> U23(X)
744.35/263.13	   U23(mark(X)) -> U23(X)
744.35/263.13	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.13	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.13	   U36(active(X)) -> U36(X)
744.35/263.13	   U36(mark(X)) -> U36(X)
744.35/263.13	   U42(active(X)) -> U42(X)
744.35/263.13	   U42(mark(X)) -> U42(X)
744.35/263.13	   U62(active(X)) -> U62(X)
744.35/263.13	   U62(mark(X)) -> U62(X)
744.35/263.13	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.13	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.13	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.13	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.13	   s(active(X)) -> s(X)
744.35/263.13	   s(mark(X)) -> s(X)
744.35/263.13	   U92(active(X)) -> U92(X)
744.35/263.13	   U92(mark(X)) -> U92(X)
744.35/263.13	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U51(active(X)) -> U51(X)
744.35/263.13	   U51(mark(X)) -> U51(X)
744.35/263.13	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.13	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.13	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.13	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.13	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.13	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.13	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.13	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.13	   x(active(X1), X2) -> x(X1, X2)
744.35/263.13	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.13	
744.35/263.13	
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(350)
744.35/263.13	Obligation:
744.35/263.13	Q DP problem:
744.35/263.13	The TRS P consists of the following rules:
744.35/263.13	
744.35/263.13	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.13	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.13	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.13	   MARK(U16(X)) -> MARK(X)
744.35/263.13	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.13	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.13	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.13	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.13	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.13	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.13	   MARK(U23(X)) -> MARK(X)
744.35/263.13	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.13	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.13	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.13	   MARK(U42(X)) -> MARK(X)
744.35/263.13	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.13	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U51(X)) -> MARK(X)
744.35/263.13	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.13	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.13	
744.35/263.13	The TRS R consists of the following rules:
744.35/263.13	
744.35/263.13	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.13	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.13	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.13	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.13	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.13	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.13	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.13	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.13	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.13	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.13	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.13	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.13	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.13	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.13	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.13	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.13	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.13	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.13	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.13	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.13	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.13	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.13	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.13	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.13	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.13	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.13	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.13	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.13	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.13	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.13	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.13	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.13	   active(U72(tt, N)) -> mark(N)
744.35/263.13	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.13	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.13	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.13	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.13	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.13	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.13	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.13	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.13	   mark(s(X)) -> active(s(mark(X)))
744.35/263.13	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.13	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.13	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.13	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.13	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.13	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.13	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.13	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.13	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.13	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.13	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.13	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.13	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.13	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.13	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.13	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.13	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.13	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.13	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.13	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.13	   mark(isNat(X)) -> active(isNat(X))
744.35/263.13	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.13	   mark(tt) -> active(tt)
744.35/263.13	   mark(0) -> active(0)
744.35/263.13	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.13	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.13	   active(U16(tt)) -> mark(tt)
744.35/263.13	   active(U23(tt)) -> mark(tt)
744.35/263.13	   active(U36(tt)) -> mark(tt)
744.35/263.13	   active(U42(tt)) -> mark(tt)
744.35/263.13	   active(U51(tt)) -> mark(tt)
744.35/263.13	   active(U62(tt)) -> mark(tt)
744.35/263.13	   active(U92(tt)) -> mark(0)
744.35/263.13	   active(isNat(0)) -> mark(tt)
744.35/263.13	   active(isNatKind(0)) -> mark(tt)
744.35/263.13	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.13	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.13	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.13	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.13	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.13	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.13	   U16(active(X)) -> U16(X)
744.35/263.13	   U16(mark(X)) -> U16(X)
744.35/263.13	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.13	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.13	   U23(active(X)) -> U23(X)
744.35/263.13	   U23(mark(X)) -> U23(X)
744.35/263.13	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.13	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.13	   U36(active(X)) -> U36(X)
744.35/263.13	   U36(mark(X)) -> U36(X)
744.35/263.13	   U42(active(X)) -> U42(X)
744.35/263.13	   U42(mark(X)) -> U42(X)
744.35/263.13	   U62(active(X)) -> U62(X)
744.35/263.13	   U62(mark(X)) -> U62(X)
744.35/263.13	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.13	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.13	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.13	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.13	   s(active(X)) -> s(X)
744.35/263.13	   s(mark(X)) -> s(X)
744.35/263.13	   U92(active(X)) -> U92(X)
744.35/263.13	   U92(mark(X)) -> U92(X)
744.35/263.13	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.13	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.13	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.13	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.13	   U51(active(X)) -> U51(X)
744.35/263.13	   U51(mark(X)) -> U51(X)
744.35/263.13	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.13	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.13	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.13	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.13	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.13	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.13	   x(active(X1), X2) -> x(X1, X2)
744.35/263.13	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.13	
744.35/263.13	The set Q consists of the following terms:
744.35/263.13	
744.35/263.13	   active(U101(tt, x0, x1))
744.35/263.13	   active(U102(tt, x0, x1))
744.35/263.13	   active(U103(tt, x0, x1))
744.35/263.13	   active(U104(tt, x0, x1))
744.35/263.13	   active(U11(tt, x0, x1))
744.35/263.13	   active(U12(tt, x0, x1))
744.35/263.13	   active(U13(tt, x0, x1))
744.35/263.13	   active(U14(tt, x0, x1))
744.35/263.13	   active(U15(tt, x0))
744.35/263.13	   active(U16(tt))
744.35/263.13	   active(U21(tt, x0))
744.35/263.13	   active(U22(tt, x0))
744.35/263.13	   active(U23(tt))
744.35/263.13	   active(U31(tt, x0, x1))
744.35/263.13	   active(U32(tt, x0, x1))
744.35/263.13	   active(U33(tt, x0, x1))
744.35/263.13	   active(U34(tt, x0, x1))
744.35/263.13	   active(U35(tt, x0))
744.35/263.13	   active(U36(tt))
744.35/263.13	   active(U41(tt, x0))
744.35/263.13	   active(U42(tt))
744.35/263.13	   active(U51(tt))
744.35/263.13	   active(U61(tt, x0))
744.35/263.13	   active(U62(tt))
744.35/263.13	   active(U71(tt, x0))
744.35/263.13	   active(U72(tt, x0))
744.35/263.13	   active(U81(tt, x0, x1))
744.35/263.13	   active(U82(tt, x0, x1))
744.35/263.13	   active(U83(tt, x0, x1))
744.35/263.13	   active(U84(tt, x0, x1))
744.35/263.13	   active(U91(tt, x0))
744.35/263.13	   active(U92(tt))
744.35/263.13	   active(isNat(0))
744.35/263.13	   active(isNat(plus(x0, x1)))
744.35/263.13	   active(isNat(s(x0)))
744.35/263.13	   active(isNat(x(x0, x1)))
744.35/263.13	   active(isNatKind(0))
744.35/263.13	   active(isNatKind(plus(x0, x1)))
744.35/263.13	   active(isNatKind(s(x0)))
744.35/263.13	   active(isNatKind(x(x0, x1)))
744.35/263.13	   active(plus(x0, 0))
744.35/263.13	   active(plus(x0, s(x1)))
744.35/263.13	   active(x(x0, 0))
744.35/263.13	   active(x(x0, s(x1)))
744.35/263.13	   mark(U101(x0, x1, x2))
744.35/263.13	   mark(tt)
744.35/263.13	   mark(U102(x0, x1, x2))
744.35/263.13	   mark(isNatKind(x0))
744.35/263.13	   mark(U103(x0, x1, x2))
744.35/263.13	   mark(isNat(x0))
744.35/263.13	   mark(U104(x0, x1, x2))
744.35/263.13	   mark(plus(x0, x1))
744.35/263.13	   mark(x(x0, x1))
744.35/263.13	   mark(U11(x0, x1, x2))
744.35/263.13	   mark(U12(x0, x1, x2))
744.35/263.13	   mark(U13(x0, x1, x2))
744.35/263.13	   mark(U14(x0, x1, x2))
744.35/263.13	   mark(U15(x0, x1))
744.35/263.13	   mark(U16(x0))
744.35/263.13	   mark(U21(x0, x1))
744.35/263.13	   mark(U22(x0, x1))
744.35/263.13	   mark(U23(x0))
744.35/263.13	   mark(U31(x0, x1, x2))
744.35/263.13	   mark(U32(x0, x1, x2))
744.35/263.13	   mark(U33(x0, x1, x2))
744.35/263.13	   mark(U34(x0, x1, x2))
744.35/263.13	   mark(U35(x0, x1))
744.35/263.13	   mark(U36(x0))
744.35/263.13	   mark(U41(x0, x1))
744.35/263.13	   mark(U42(x0))
744.35/263.13	   mark(U51(x0))
744.35/263.13	   mark(U61(x0, x1))
744.35/263.13	   mark(U62(x0))
744.35/263.13	   mark(U71(x0, x1))
744.35/263.13	   mark(U72(x0, x1))
744.35/263.13	   mark(U81(x0, x1, x2))
744.35/263.13	   mark(U82(x0, x1, x2))
744.35/263.13	   mark(U83(x0, x1, x2))
744.35/263.13	   mark(U84(x0, x1, x2))
744.35/263.13	   mark(s(x0))
744.35/263.13	   mark(U91(x0, x1))
744.35/263.13	   mark(U92(x0))
744.35/263.13	   mark(0)
744.35/263.13	   U101(mark(x0), x1, x2)
744.35/263.13	   U101(x0, mark(x1), x2)
744.35/263.13	   U101(x0, x1, mark(x2))
744.35/263.13	   U101(active(x0), x1, x2)
744.35/263.13	   U101(x0, active(x1), x2)
744.35/263.13	   U101(x0, x1, active(x2))
744.35/263.13	   U102(mark(x0), x1, x2)
744.35/263.13	   U102(x0, mark(x1), x2)
744.35/263.13	   U102(x0, x1, mark(x2))
744.35/263.13	   U102(active(x0), x1, x2)
744.35/263.13	   U102(x0, active(x1), x2)
744.35/263.13	   U102(x0, x1, active(x2))
744.35/263.13	   isNatKind(mark(x0))
744.35/263.13	   isNatKind(active(x0))
744.35/263.13	   U103(mark(x0), x1, x2)
744.35/263.13	   U103(x0, mark(x1), x2)
744.35/263.13	   U103(x0, x1, mark(x2))
744.35/263.13	   U103(active(x0), x1, x2)
744.35/263.13	   U103(x0, active(x1), x2)
744.35/263.13	   U103(x0, x1, active(x2))
744.35/263.13	   isNat(mark(x0))
744.35/263.13	   isNat(active(x0))
744.35/263.13	   U104(mark(x0), x1, x2)
744.35/263.13	   U104(x0, mark(x1), x2)
744.35/263.13	   U104(x0, x1, mark(x2))
744.35/263.13	   U104(active(x0), x1, x2)
744.35/263.13	   U104(x0, active(x1), x2)
744.35/263.13	   U104(x0, x1, active(x2))
744.35/263.13	   plus(mark(x0), x1)
744.35/263.13	   plus(x0, mark(x1))
744.35/263.13	   plus(active(x0), x1)
744.35/263.13	   plus(x0, active(x1))
744.35/263.13	   x(mark(x0), x1)
744.35/263.13	   x(x0, mark(x1))
744.35/263.13	   x(active(x0), x1)
744.35/263.13	   x(x0, active(x1))
744.35/263.13	   U11(mark(x0), x1, x2)
744.35/263.13	   U11(x0, mark(x1), x2)
744.35/263.13	   U11(x0, x1, mark(x2))
744.35/263.13	   U11(active(x0), x1, x2)
744.35/263.13	   U11(x0, active(x1), x2)
744.35/263.13	   U11(x0, x1, active(x2))
744.35/263.13	   U12(mark(x0), x1, x2)
744.35/263.13	   U12(x0, mark(x1), x2)
744.35/263.13	   U12(x0, x1, mark(x2))
744.35/263.13	   U12(active(x0), x1, x2)
744.35/263.13	   U12(x0, active(x1), x2)
744.35/263.13	   U12(x0, x1, active(x2))
744.35/263.13	   U13(mark(x0), x1, x2)
744.35/263.13	   U13(x0, mark(x1), x2)
744.35/263.13	   U13(x0, x1, mark(x2))
744.35/263.13	   U13(active(x0), x1, x2)
744.35/263.13	   U13(x0, active(x1), x2)
744.35/263.13	   U13(x0, x1, active(x2))
744.35/263.13	   U14(mark(x0), x1, x2)
744.35/263.13	   U14(x0, mark(x1), x2)
744.35/263.13	   U14(x0, x1, mark(x2))
744.35/263.13	   U14(active(x0), x1, x2)
744.35/263.13	   U14(x0, active(x1), x2)
744.35/263.13	   U14(x0, x1, active(x2))
744.35/263.13	   U15(mark(x0), x1)
744.35/263.13	   U15(x0, mark(x1))
744.35/263.13	   U15(active(x0), x1)
744.35/263.13	   U15(x0, active(x1))
744.35/263.13	   U16(mark(x0))
744.35/263.13	   U16(active(x0))
744.35/263.13	   U21(mark(x0), x1)
744.35/263.13	   U21(x0, mark(x1))
744.35/263.13	   U21(active(x0), x1)
744.35/263.13	   U21(x0, active(x1))
744.35/263.13	   U22(mark(x0), x1)
744.35/263.13	   U22(x0, mark(x1))
744.35/263.13	   U22(active(x0), x1)
744.35/263.13	   U22(x0, active(x1))
744.35/263.13	   U23(mark(x0))
744.35/263.13	   U23(active(x0))
744.35/263.13	   U31(mark(x0), x1, x2)
744.35/263.13	   U31(x0, mark(x1), x2)
744.35/263.13	   U31(x0, x1, mark(x2))
744.35/263.13	   U31(active(x0), x1, x2)
744.35/263.13	   U31(x0, active(x1), x2)
744.35/263.13	   U31(x0, x1, active(x2))
744.35/263.13	   U32(mark(x0), x1, x2)
744.35/263.13	   U32(x0, mark(x1), x2)
744.35/263.13	   U32(x0, x1, mark(x2))
744.35/263.13	   U32(active(x0), x1, x2)
744.35/263.13	   U32(x0, active(x1), x2)
744.35/263.13	   U32(x0, x1, active(x2))
744.35/263.13	   U33(mark(x0), x1, x2)
744.35/263.13	   U33(x0, mark(x1), x2)
744.35/263.13	   U33(x0, x1, mark(x2))
744.35/263.13	   U33(active(x0), x1, x2)
744.35/263.13	   U33(x0, active(x1), x2)
744.35/263.13	   U33(x0, x1, active(x2))
744.35/263.13	   U34(mark(x0), x1, x2)
744.35/263.13	   U34(x0, mark(x1), x2)
744.35/263.13	   U34(x0, x1, mark(x2))
744.35/263.13	   U34(active(x0), x1, x2)
744.35/263.13	   U34(x0, active(x1), x2)
744.35/263.13	   U34(x0, x1, active(x2))
744.35/263.13	   U35(mark(x0), x1)
744.35/263.13	   U35(x0, mark(x1))
744.35/263.13	   U35(active(x0), x1)
744.35/263.13	   U35(x0, active(x1))
744.35/263.13	   U36(mark(x0))
744.35/263.13	   U36(active(x0))
744.35/263.13	   U41(mark(x0), x1)
744.35/263.13	   U41(x0, mark(x1))
744.35/263.13	   U41(active(x0), x1)
744.35/263.13	   U41(x0, active(x1))
744.35/263.13	   U42(mark(x0))
744.35/263.13	   U42(active(x0))
744.35/263.13	   U51(mark(x0))
744.35/263.13	   U51(active(x0))
744.35/263.13	   U61(mark(x0), x1)
744.35/263.13	   U61(x0, mark(x1))
744.35/263.13	   U61(active(x0), x1)
744.35/263.13	   U61(x0, active(x1))
744.35/263.13	   U62(mark(x0))
744.35/263.13	   U62(active(x0))
744.35/263.13	   U71(mark(x0), x1)
744.35/263.13	   U71(x0, mark(x1))
744.35/263.13	   U71(active(x0), x1)
744.35/263.13	   U71(x0, active(x1))
744.35/263.13	   U72(mark(x0), x1)
744.35/263.13	   U72(x0, mark(x1))
744.35/263.13	   U72(active(x0), x1)
744.35/263.13	   U72(x0, active(x1))
744.35/263.13	   U81(mark(x0), x1, x2)
744.35/263.13	   U81(x0, mark(x1), x2)
744.35/263.13	   U81(x0, x1, mark(x2))
744.35/263.13	   U81(active(x0), x1, x2)
744.35/263.13	   U81(x0, active(x1), x2)
744.35/263.13	   U81(x0, x1, active(x2))
744.35/263.13	   U82(mark(x0), x1, x2)
744.35/263.13	   U82(x0, mark(x1), x2)
744.35/263.13	   U82(x0, x1, mark(x2))
744.35/263.13	   U82(active(x0), x1, x2)
744.35/263.13	   U82(x0, active(x1), x2)
744.35/263.13	   U82(x0, x1, active(x2))
744.35/263.13	   U83(mark(x0), x1, x2)
744.35/263.13	   U83(x0, mark(x1), x2)
744.35/263.13	   U83(x0, x1, mark(x2))
744.35/263.13	   U83(active(x0), x1, x2)
744.35/263.13	   U83(x0, active(x1), x2)
744.35/263.13	   U83(x0, x1, active(x2))
744.35/263.13	   U84(mark(x0), x1, x2)
744.35/263.13	   U84(x0, mark(x1), x2)
744.35/263.13	   U84(x0, x1, mark(x2))
744.35/263.13	   U84(active(x0), x1, x2)
744.35/263.13	   U84(x0, active(x1), x2)
744.35/263.13	   U84(x0, x1, active(x2))
744.35/263.13	   s(mark(x0))
744.35/263.13	   s(active(x0))
744.35/263.13	   U91(mark(x0), x1)
744.35/263.13	   U91(x0, mark(x1))
744.35/263.13	   U91(active(x0), x1)
744.35/263.13	   U91(x0, active(x1))
744.35/263.13	   U92(mark(x0))
744.35/263.13	   U92(active(x0))
744.35/263.13	
744.35/263.13	We have to consider all minimal (P,Q,R)-chains.
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(351) QDPQMonotonicMRRProof (EQUIVALENT)
744.35/263.13	By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain.
744.35/263.13	
744.35/263.13	Strictly oriented dependency pairs:
744.35/263.13	
744.35/263.13	   MARK(U15(X1, X2)) -> ACTIVE(U15(mark(X1), X2))
744.35/263.13	
744.35/263.13	
744.35/263.13	Used ordering: Polynomial interpretation [POLO]:
744.35/263.13	
744.35/263.13	   POL(0) = 0
744.35/263.13	   POL(ACTIVE(x_1)) = 2*x_1
744.35/263.13	   POL(MARK(x_1)) = 2
744.35/263.13	   POL(U101(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U102(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U103(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U104(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U11(x_1, x_2, x_3)) = 1
744.35/263.13	   POL(U12(x_1, x_2, x_3)) = 1
744.35/263.13	   POL(U13(x_1, x_2, x_3)) = 1
744.35/263.13	   POL(U14(x_1, x_2, x_3)) = 1
744.35/263.13	   POL(U15(x_1, x_2)) = 0
744.35/263.13	   POL(U16(x_1)) = 0
744.35/263.13	   POL(U21(x_1, x_2)) = 1
744.35/263.13	   POL(U22(x_1, x_2)) = 1
744.35/263.13	   POL(U23(x_1)) = 0
744.35/263.13	   POL(U31(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U32(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U33(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U34(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U35(x_1, x_2)) = 0
744.35/263.13	   POL(U36(x_1)) = 0
744.35/263.13	   POL(U41(x_1, x_2)) = 1
744.35/263.13	   POL(U42(x_1)) = 0
744.35/263.13	   POL(U51(x_1)) = 0
744.35/263.13	   POL(U61(x_1, x_2)) = 0
744.35/263.13	   POL(U62(x_1)) = 0
744.35/263.13	   POL(U71(x_1, x_2)) = 0
744.35/263.13	   POL(U72(x_1, x_2)) = 0
744.35/263.13	   POL(U81(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U82(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U83(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U84(x_1, x_2, x_3)) = 0
744.35/263.13	   POL(U91(x_1, x_2)) = 0
744.35/263.13	   POL(U92(x_1)) = 0
744.35/263.13	   POL(active(x_1)) = 0
744.35/263.13	   POL(isNat(x_1)) = 1
744.35/263.13	   POL(isNatKind(x_1)) = 1
744.35/263.13	   POL(mark(x_1)) = 0
744.35/263.13	   POL(plus(x_1, x_2)) = 0
744.35/263.13	   POL(s(x_1)) = 0
744.35/263.13	   POL(tt) = 0
744.35/263.13	   POL(x(x_1, x_2)) = 0
744.35/263.13	
744.35/263.13	
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(352)
744.35/263.13	Obligation:
744.35/263.13	Q DP problem:
744.35/263.13	The TRS P consists of the following rules:
744.35/263.13	
744.35/263.13	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.13	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.13	   MARK(U16(X)) -> MARK(X)
744.35/263.13	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.13	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.13	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.13	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.13	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.13	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.13	   MARK(U23(X)) -> MARK(X)
744.35/263.13	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.13	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.13	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.13	   MARK(U42(X)) -> MARK(X)
744.35/263.13	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.13	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U51(X)) -> MARK(X)
744.35/263.13	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.13	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.13	
744.35/263.13	The TRS R consists of the following rules:
744.35/263.13	
744.35/263.13	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.13	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.13	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.13	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.13	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.13	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.13	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.13	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.13	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.13	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.13	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.13	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.13	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.13	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.13	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.13	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.13	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.13	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.13	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.13	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.13	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.13	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.13	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.13	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.13	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.13	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.13	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.13	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.13	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.13	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.13	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.13	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.13	   active(U72(tt, N)) -> mark(N)
744.35/263.13	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.13	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.13	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.13	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.13	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.13	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.13	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.13	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.13	   mark(s(X)) -> active(s(mark(X)))
744.35/263.13	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.13	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.13	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.13	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.13	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.13	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.13	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.13	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.13	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.13	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.13	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.13	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.13	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.13	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.13	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.13	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.13	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.13	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.13	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.13	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.13	   mark(isNat(X)) -> active(isNat(X))
744.35/263.13	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.13	   mark(tt) -> active(tt)
744.35/263.13	   mark(0) -> active(0)
744.35/263.13	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.13	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.13	   active(U16(tt)) -> mark(tt)
744.35/263.13	   active(U23(tt)) -> mark(tt)
744.35/263.13	   active(U36(tt)) -> mark(tt)
744.35/263.13	   active(U42(tt)) -> mark(tt)
744.35/263.13	   active(U51(tt)) -> mark(tt)
744.35/263.13	   active(U62(tt)) -> mark(tt)
744.35/263.13	   active(U92(tt)) -> mark(0)
744.35/263.13	   active(isNat(0)) -> mark(tt)
744.35/263.13	   active(isNatKind(0)) -> mark(tt)
744.35/263.13	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.13	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.13	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.13	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.13	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.13	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.13	   U16(active(X)) -> U16(X)
744.35/263.13	   U16(mark(X)) -> U16(X)
744.35/263.13	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.13	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.13	   U23(active(X)) -> U23(X)
744.35/263.13	   U23(mark(X)) -> U23(X)
744.35/263.13	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.13	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.13	   U36(active(X)) -> U36(X)
744.35/263.13	   U36(mark(X)) -> U36(X)
744.35/263.13	   U42(active(X)) -> U42(X)
744.35/263.13	   U42(mark(X)) -> U42(X)
744.35/263.13	   U62(active(X)) -> U62(X)
744.35/263.13	   U62(mark(X)) -> U62(X)
744.35/263.13	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.13	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.13	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.13	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.13	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.13	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.13	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.13	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.13	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.13	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.13	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.13	   s(active(X)) -> s(X)
744.35/263.13	   s(mark(X)) -> s(X)
744.35/263.13	   U92(active(X)) -> U92(X)
744.35/263.13	   U92(mark(X)) -> U92(X)
744.35/263.13	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.13	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.13	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.13	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.13	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.13	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.13	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.13	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.13	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.13	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.13	   U51(active(X)) -> U51(X)
744.35/263.13	   U51(mark(X)) -> U51(X)
744.35/263.13	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.13	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.13	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.13	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.13	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.13	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.13	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.13	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.13	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.13	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.13	   x(active(X1), X2) -> x(X1, X2)
744.35/263.13	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.13	
744.35/263.13	The set Q consists of the following terms:
744.35/263.13	
744.35/263.13	   active(U101(tt, x0, x1))
744.35/263.13	   active(U102(tt, x0, x1))
744.35/263.13	   active(U103(tt, x0, x1))
744.35/263.13	   active(U104(tt, x0, x1))
744.35/263.13	   active(U11(tt, x0, x1))
744.35/263.13	   active(U12(tt, x0, x1))
744.35/263.13	   active(U13(tt, x0, x1))
744.35/263.13	   active(U14(tt, x0, x1))
744.35/263.13	   active(U15(tt, x0))
744.35/263.13	   active(U16(tt))
744.35/263.13	   active(U21(tt, x0))
744.35/263.13	   active(U22(tt, x0))
744.35/263.13	   active(U23(tt))
744.35/263.13	   active(U31(tt, x0, x1))
744.35/263.13	   active(U32(tt, x0, x1))
744.35/263.13	   active(U33(tt, x0, x1))
744.35/263.13	   active(U34(tt, x0, x1))
744.35/263.13	   active(U35(tt, x0))
744.35/263.13	   active(U36(tt))
744.35/263.13	   active(U41(tt, x0))
744.35/263.13	   active(U42(tt))
744.35/263.13	   active(U51(tt))
744.35/263.13	   active(U61(tt, x0))
744.35/263.13	   active(U62(tt))
744.35/263.13	   active(U71(tt, x0))
744.35/263.13	   active(U72(tt, x0))
744.35/263.13	   active(U81(tt, x0, x1))
744.35/263.13	   active(U82(tt, x0, x1))
744.35/263.13	   active(U83(tt, x0, x1))
744.35/263.13	   active(U84(tt, x0, x1))
744.35/263.13	   active(U91(tt, x0))
744.35/263.13	   active(U92(tt))
744.35/263.13	   active(isNat(0))
744.35/263.13	   active(isNat(plus(x0, x1)))
744.35/263.13	   active(isNat(s(x0)))
744.35/263.13	   active(isNat(x(x0, x1)))
744.35/263.13	   active(isNatKind(0))
744.35/263.13	   active(isNatKind(plus(x0, x1)))
744.35/263.13	   active(isNatKind(s(x0)))
744.35/263.13	   active(isNatKind(x(x0, x1)))
744.35/263.13	   active(plus(x0, 0))
744.35/263.13	   active(plus(x0, s(x1)))
744.35/263.13	   active(x(x0, 0))
744.35/263.13	   active(x(x0, s(x1)))
744.35/263.13	   mark(U101(x0, x1, x2))
744.35/263.13	   mark(tt)
744.35/263.13	   mark(U102(x0, x1, x2))
744.35/263.13	   mark(isNatKind(x0))
744.35/263.13	   mark(U103(x0, x1, x2))
744.35/263.13	   mark(isNat(x0))
744.35/263.13	   mark(U104(x0, x1, x2))
744.35/263.13	   mark(plus(x0, x1))
744.35/263.13	   mark(x(x0, x1))
744.35/263.13	   mark(U11(x0, x1, x2))
744.35/263.13	   mark(U12(x0, x1, x2))
744.35/263.13	   mark(U13(x0, x1, x2))
744.35/263.13	   mark(U14(x0, x1, x2))
744.35/263.13	   mark(U15(x0, x1))
744.35/263.13	   mark(U16(x0))
744.35/263.13	   mark(U21(x0, x1))
744.35/263.13	   mark(U22(x0, x1))
744.35/263.13	   mark(U23(x0))
744.35/263.13	   mark(U31(x0, x1, x2))
744.35/263.13	   mark(U32(x0, x1, x2))
744.35/263.13	   mark(U33(x0, x1, x2))
744.35/263.13	   mark(U34(x0, x1, x2))
744.35/263.13	   mark(U35(x0, x1))
744.35/263.13	   mark(U36(x0))
744.35/263.13	   mark(U41(x0, x1))
744.35/263.13	   mark(U42(x0))
744.35/263.13	   mark(U51(x0))
744.35/263.13	   mark(U61(x0, x1))
744.35/263.13	   mark(U62(x0))
744.35/263.13	   mark(U71(x0, x1))
744.35/263.13	   mark(U72(x0, x1))
744.35/263.13	   mark(U81(x0, x1, x2))
744.35/263.13	   mark(U82(x0, x1, x2))
744.35/263.13	   mark(U83(x0, x1, x2))
744.35/263.13	   mark(U84(x0, x1, x2))
744.35/263.13	   mark(s(x0))
744.35/263.13	   mark(U91(x0, x1))
744.35/263.13	   mark(U92(x0))
744.35/263.13	   mark(0)
744.35/263.13	   U101(mark(x0), x1, x2)
744.35/263.13	   U101(x0, mark(x1), x2)
744.35/263.13	   U101(x0, x1, mark(x2))
744.35/263.13	   U101(active(x0), x1, x2)
744.35/263.13	   U101(x0, active(x1), x2)
744.35/263.13	   U101(x0, x1, active(x2))
744.35/263.13	   U102(mark(x0), x1, x2)
744.35/263.13	   U102(x0, mark(x1), x2)
744.35/263.13	   U102(x0, x1, mark(x2))
744.35/263.13	   U102(active(x0), x1, x2)
744.35/263.13	   U102(x0, active(x1), x2)
744.35/263.13	   U102(x0, x1, active(x2))
744.35/263.13	   isNatKind(mark(x0))
744.35/263.13	   isNatKind(active(x0))
744.35/263.13	   U103(mark(x0), x1, x2)
744.35/263.13	   U103(x0, mark(x1), x2)
744.35/263.13	   U103(x0, x1, mark(x2))
744.35/263.13	   U103(active(x0), x1, x2)
744.35/263.13	   U103(x0, active(x1), x2)
744.35/263.13	   U103(x0, x1, active(x2))
744.35/263.13	   isNat(mark(x0))
744.35/263.13	   isNat(active(x0))
744.35/263.13	   U104(mark(x0), x1, x2)
744.35/263.13	   U104(x0, mark(x1), x2)
744.35/263.13	   U104(x0, x1, mark(x2))
744.35/263.13	   U104(active(x0), x1, x2)
744.35/263.13	   U104(x0, active(x1), x2)
744.35/263.13	   U104(x0, x1, active(x2))
744.35/263.13	   plus(mark(x0), x1)
744.35/263.13	   plus(x0, mark(x1))
744.35/263.13	   plus(active(x0), x1)
744.35/263.13	   plus(x0, active(x1))
744.35/263.13	   x(mark(x0), x1)
744.35/263.13	   x(x0, mark(x1))
744.35/263.13	   x(active(x0), x1)
744.35/263.13	   x(x0, active(x1))
744.35/263.13	   U11(mark(x0), x1, x2)
744.35/263.13	   U11(x0, mark(x1), x2)
744.35/263.13	   U11(x0, x1, mark(x2))
744.35/263.13	   U11(active(x0), x1, x2)
744.35/263.13	   U11(x0, active(x1), x2)
744.35/263.13	   U11(x0, x1, active(x2))
744.35/263.13	   U12(mark(x0), x1, x2)
744.35/263.13	   U12(x0, mark(x1), x2)
744.35/263.13	   U12(x0, x1, mark(x2))
744.35/263.13	   U12(active(x0), x1, x2)
744.35/263.13	   U12(x0, active(x1), x2)
744.35/263.13	   U12(x0, x1, active(x2))
744.35/263.13	   U13(mark(x0), x1, x2)
744.35/263.13	   U13(x0, mark(x1), x2)
744.35/263.13	   U13(x0, x1, mark(x2))
744.35/263.13	   U13(active(x0), x1, x2)
744.35/263.13	   U13(x0, active(x1), x2)
744.35/263.13	   U13(x0, x1, active(x2))
744.35/263.13	   U14(mark(x0), x1, x2)
744.35/263.13	   U14(x0, mark(x1), x2)
744.35/263.13	   U14(x0, x1, mark(x2))
744.35/263.13	   U14(active(x0), x1, x2)
744.35/263.13	   U14(x0, active(x1), x2)
744.35/263.13	   U14(x0, x1, active(x2))
744.35/263.13	   U15(mark(x0), x1)
744.35/263.13	   U15(x0, mark(x1))
744.35/263.13	   U15(active(x0), x1)
744.35/263.13	   U15(x0, active(x1))
744.35/263.13	   U16(mark(x0))
744.35/263.13	   U16(active(x0))
744.35/263.13	   U21(mark(x0), x1)
744.35/263.13	   U21(x0, mark(x1))
744.35/263.13	   U21(active(x0), x1)
744.35/263.13	   U21(x0, active(x1))
744.35/263.13	   U22(mark(x0), x1)
744.35/263.13	   U22(x0, mark(x1))
744.35/263.13	   U22(active(x0), x1)
744.35/263.13	   U22(x0, active(x1))
744.35/263.13	   U23(mark(x0))
744.35/263.13	   U23(active(x0))
744.35/263.13	   U31(mark(x0), x1, x2)
744.35/263.13	   U31(x0, mark(x1), x2)
744.35/263.13	   U31(x0, x1, mark(x2))
744.35/263.13	   U31(active(x0), x1, x2)
744.35/263.13	   U31(x0, active(x1), x2)
744.35/263.13	   U31(x0, x1, active(x2))
744.35/263.13	   U32(mark(x0), x1, x2)
744.35/263.13	   U32(x0, mark(x1), x2)
744.35/263.13	   U32(x0, x1, mark(x2))
744.35/263.13	   U32(active(x0), x1, x2)
744.35/263.13	   U32(x0, active(x1), x2)
744.35/263.13	   U32(x0, x1, active(x2))
744.35/263.13	   U33(mark(x0), x1, x2)
744.35/263.13	   U33(x0, mark(x1), x2)
744.35/263.13	   U33(x0, x1, mark(x2))
744.35/263.13	   U33(active(x0), x1, x2)
744.35/263.13	   U33(x0, active(x1), x2)
744.35/263.13	   U33(x0, x1, active(x2))
744.35/263.13	   U34(mark(x0), x1, x2)
744.35/263.13	   U34(x0, mark(x1), x2)
744.35/263.13	   U34(x0, x1, mark(x2))
744.35/263.13	   U34(active(x0), x1, x2)
744.35/263.13	   U34(x0, active(x1), x2)
744.35/263.13	   U34(x0, x1, active(x2))
744.35/263.13	   U35(mark(x0), x1)
744.35/263.13	   U35(x0, mark(x1))
744.35/263.13	   U35(active(x0), x1)
744.35/263.13	   U35(x0, active(x1))
744.35/263.13	   U36(mark(x0))
744.35/263.13	   U36(active(x0))
744.35/263.13	   U41(mark(x0), x1)
744.35/263.13	   U41(x0, mark(x1))
744.35/263.13	   U41(active(x0), x1)
744.35/263.13	   U41(x0, active(x1))
744.35/263.13	   U42(mark(x0))
744.35/263.13	   U42(active(x0))
744.35/263.13	   U51(mark(x0))
744.35/263.13	   U51(active(x0))
744.35/263.13	   U61(mark(x0), x1)
744.35/263.13	   U61(x0, mark(x1))
744.35/263.13	   U61(active(x0), x1)
744.35/263.13	   U61(x0, active(x1))
744.35/263.13	   U62(mark(x0))
744.35/263.13	   U62(active(x0))
744.35/263.13	   U71(mark(x0), x1)
744.35/263.13	   U71(x0, mark(x1))
744.35/263.13	   U71(active(x0), x1)
744.35/263.13	   U71(x0, active(x1))
744.35/263.13	   U72(mark(x0), x1)
744.35/263.13	   U72(x0, mark(x1))
744.35/263.13	   U72(active(x0), x1)
744.35/263.13	   U72(x0, active(x1))
744.35/263.13	   U81(mark(x0), x1, x2)
744.35/263.13	   U81(x0, mark(x1), x2)
744.35/263.13	   U81(x0, x1, mark(x2))
744.35/263.13	   U81(active(x0), x1, x2)
744.35/263.13	   U81(x0, active(x1), x2)
744.35/263.13	   U81(x0, x1, active(x2))
744.35/263.13	   U82(mark(x0), x1, x2)
744.35/263.13	   U82(x0, mark(x1), x2)
744.35/263.13	   U82(x0, x1, mark(x2))
744.35/263.13	   U82(active(x0), x1, x2)
744.35/263.13	   U82(x0, active(x1), x2)
744.35/263.13	   U82(x0, x1, active(x2))
744.35/263.13	   U83(mark(x0), x1, x2)
744.35/263.13	   U83(x0, mark(x1), x2)
744.35/263.13	   U83(x0, x1, mark(x2))
744.35/263.13	   U83(active(x0), x1, x2)
744.35/263.13	   U83(x0, active(x1), x2)
744.35/263.13	   U83(x0, x1, active(x2))
744.35/263.13	   U84(mark(x0), x1, x2)
744.35/263.13	   U84(x0, mark(x1), x2)
744.35/263.13	   U84(x0, x1, mark(x2))
744.35/263.13	   U84(active(x0), x1, x2)
744.35/263.13	   U84(x0, active(x1), x2)
744.35/263.13	   U84(x0, x1, active(x2))
744.35/263.13	   s(mark(x0))
744.35/263.13	   s(active(x0))
744.35/263.13	   U91(mark(x0), x1)
744.35/263.13	   U91(x0, mark(x1))
744.35/263.13	   U91(active(x0), x1)
744.35/263.13	   U91(x0, active(x1))
744.35/263.13	   U92(mark(x0))
744.35/263.13	   U92(active(x0))
744.35/263.13	
744.35/263.13	We have to consider all minimal (P,Q,R)-chains.
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(353) QDPOrderProof (EQUIVALENT)
744.35/263.13	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.13	
744.35/263.13	
744.35/263.13	The following pairs can be oriented strictly and are deleted.
744.35/263.13	
744.35/263.13	   MARK(U16(X)) -> MARK(X)
744.35/263.13	The remaining pairs can at least be oriented weakly.
744.35/263.13	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.13	
744.35/263.13	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.35/263.13	POL( U11_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.13	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.13	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.13	POL( U14_3(x_1, ..., x_3) ) = 1
744.35/263.13	POL( U21_2(x_1, x_2) ) = 0
744.35/263.13	POL( U22_2(x_1, x_2) ) = 0
744.35/263.13	POL( U41_2(x_1, x_2) ) = 2x_1 + 1
744.35/263.13	POL( mark_1(x_1) ) = max{0, -2}
744.35/263.13	POL( U102_3(x_1, ..., x_3) ) = 2x_3 + 2
744.35/263.13	POL( active_1(x_1) ) = 2
744.35/263.13	POL( U101_3(x_1, ..., x_3) ) = 2
744.35/263.13	POL( tt ) = 0
744.35/263.13	POL( isNatKind_1(x_1) ) = 0
744.35/263.13	POL( U103_3(x_1, ..., x_3) ) = max{0, x_3 - 2}
744.35/263.13	POL( isNat_1(x_1) ) = 0
744.35/263.13	POL( U104_3(x_1, ..., x_3) ) = 2x_3 + 2
744.35/263.13	POL( plus_2(x_1, x_2) ) = max{0, x_1 + x_2 - 1}
744.35/263.13	POL( x_2(x_1, x_2) ) = 2
744.35/263.13	POL( U15_2(x_1, x_2) ) = x_1 + 1
744.35/263.13	POL( U16_1(x_1) ) = 2x_1 + 2
744.35/263.13	POL( U23_1(x_1) ) = x_1 + 1
744.35/263.13	POL( U31_3(x_1, ..., x_3) ) = 2
744.35/263.13	POL( U32_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + 2x_3 - 2}
744.35/263.13	POL( U33_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.35/263.13	POL( U34_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.13	POL( U35_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.13	POL( U36_1(x_1) ) = 2
744.35/263.13	POL( U42_1(x_1) ) = x_1 + 1
744.35/263.13	POL( U61_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.13	POL( U62_1(x_1) ) = max{0, -2}
744.35/263.13	POL( U71_2(x_1, x_2) ) = 2
744.35/263.13	POL( U72_2(x_1, x_2) ) = 2
744.35/263.13	POL( U81_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.35/263.13	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 2}
744.35/263.13	POL( U83_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 + x_3 - 2}
744.35/263.13	POL( U84_3(x_1, ..., x_3) ) = x_1 + 2
744.35/263.13	POL( s_1(x_1) ) = 2
744.35/263.13	POL( U91_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.13	POL( U92_1(x_1) ) = 2
744.35/263.13	POL( U51_1(x_1) ) = 2x_1 + 1
744.35/263.13	POL( 0 ) = 0
744.35/263.13	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.35/263.13	
744.35/263.13	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.13	none
744.35/263.13	
744.35/263.13	
744.35/263.13	----------------------------------------
744.35/263.13	
744.35/263.13	(354)
744.35/263.13	Obligation:
744.35/263.13	Q DP problem:
744.35/263.13	The TRS P consists of the following rules:
744.35/263.13	
744.35/263.13	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.13	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.13	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.13	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.13	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.13	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.13	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.13	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.13	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.13	   MARK(U23(X)) -> MARK(X)
744.35/263.13	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.13	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.13	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.13	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.13	   MARK(U42(X)) -> MARK(X)
744.35/263.13	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.13	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.13	   MARK(U51(X)) -> MARK(X)
744.35/263.13	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.13	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.13	
744.35/263.13	The TRS R consists of the following rules:
744.35/263.13	
744.35/263.13	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.13	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.13	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.13	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.13	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.13	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.13	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.13	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.13	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.13	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.13	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.13	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.13	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.13	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.13	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.13	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.13	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.13	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.13	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.13	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.13	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.13	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.13	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.13	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.13	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.13	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.13	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.13	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.13	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.13	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.13	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.13	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.13	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.13	   active(U72(tt, N)) -> mark(N)
744.35/263.13	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.13	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.13	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.13	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.13	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.13	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.13	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.13	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.13	   mark(s(X)) -> active(s(mark(X)))
744.35/263.13	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.13	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.13	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.13	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.13	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.13	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.13	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.13	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.13	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.13	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.13	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.13	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.13	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.13	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.13	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.13	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.13	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.13	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.13	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.13	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.13	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.13	   mark(isNat(X)) -> active(isNat(X))
744.35/263.13	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.13	   mark(tt) -> active(tt)
744.35/263.13	   mark(0) -> active(0)
744.35/263.13	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.13	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.13	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.13	   active(U16(tt)) -> mark(tt)
744.35/263.13	   active(U23(tt)) -> mark(tt)
744.35/263.13	   active(U36(tt)) -> mark(tt)
744.35/263.13	   active(U42(tt)) -> mark(tt)
744.35/263.13	   active(U51(tt)) -> mark(tt)
744.35/263.13	   active(U62(tt)) -> mark(tt)
744.35/263.13	   active(U92(tt)) -> mark(0)
744.35/263.13	   active(isNat(0)) -> mark(tt)
744.35/263.13	   active(isNatKind(0)) -> mark(tt)
744.35/263.13	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.13	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.13	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.13	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.13	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.13	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.13	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.13	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.13	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.13	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.13	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.13	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.13	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.13	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.13	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.13	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.13	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.13	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.13	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.13	   U16(active(X)) -> U16(X)
744.35/263.13	   U16(mark(X)) -> U16(X)
744.35/263.13	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.13	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.13	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.13	   U23(active(X)) -> U23(X)
744.35/263.13	   U23(mark(X)) -> U23(X)
744.35/263.13	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.13	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.13	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.13	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.13	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.13	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.13	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.13	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.13	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.13	   U36(active(X)) -> U36(X)
744.35/263.13	   U36(mark(X)) -> U36(X)
744.35/263.13	   U42(active(X)) -> U42(X)
744.35/263.13	   U42(mark(X)) -> U42(X)
744.35/263.13	   U62(active(X)) -> U62(X)
744.35/263.13	   U62(mark(X)) -> U62(X)
744.35/263.13	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.13	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.13	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.13	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.14	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.14	   s(active(X)) -> s(X)
744.35/263.14	   s(mark(X)) -> s(X)
744.35/263.14	   U92(active(X)) -> U92(X)
744.35/263.14	   U92(mark(X)) -> U92(X)
744.35/263.14	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.14	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.14	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.14	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.14	   U51(active(X)) -> U51(X)
744.35/263.14	   U51(mark(X)) -> U51(X)
744.35/263.14	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.14	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.14	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.14	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.14	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.14	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.14	   x(active(X1), X2) -> x(X1, X2)
744.35/263.14	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.14	
744.35/263.14	The set Q consists of the following terms:
744.35/263.14	
744.35/263.14	   active(U101(tt, x0, x1))
744.35/263.14	   active(U102(tt, x0, x1))
744.35/263.14	   active(U103(tt, x0, x1))
744.35/263.14	   active(U104(tt, x0, x1))
744.35/263.14	   active(U11(tt, x0, x1))
744.35/263.14	   active(U12(tt, x0, x1))
744.35/263.14	   active(U13(tt, x0, x1))
744.35/263.14	   active(U14(tt, x0, x1))
744.35/263.14	   active(U15(tt, x0))
744.35/263.14	   active(U16(tt))
744.35/263.14	   active(U21(tt, x0))
744.35/263.14	   active(U22(tt, x0))
744.35/263.14	   active(U23(tt))
744.35/263.14	   active(U31(tt, x0, x1))
744.35/263.14	   active(U32(tt, x0, x1))
744.35/263.14	   active(U33(tt, x0, x1))
744.35/263.14	   active(U34(tt, x0, x1))
744.35/263.14	   active(U35(tt, x0))
744.35/263.14	   active(U36(tt))
744.35/263.14	   active(U41(tt, x0))
744.35/263.14	   active(U42(tt))
744.35/263.14	   active(U51(tt))
744.35/263.14	   active(U61(tt, x0))
744.35/263.14	   active(U62(tt))
744.35/263.14	   active(U71(tt, x0))
744.35/263.14	   active(U72(tt, x0))
744.35/263.14	   active(U81(tt, x0, x1))
744.35/263.14	   active(U82(tt, x0, x1))
744.35/263.14	   active(U83(tt, x0, x1))
744.35/263.14	   active(U84(tt, x0, x1))
744.35/263.14	   active(U91(tt, x0))
744.35/263.14	   active(U92(tt))
744.35/263.14	   active(isNat(0))
744.35/263.14	   active(isNat(plus(x0, x1)))
744.35/263.14	   active(isNat(s(x0)))
744.35/263.14	   active(isNat(x(x0, x1)))
744.35/263.14	   active(isNatKind(0))
744.35/263.14	   active(isNatKind(plus(x0, x1)))
744.35/263.14	   active(isNatKind(s(x0)))
744.35/263.14	   active(isNatKind(x(x0, x1)))
744.35/263.14	   active(plus(x0, 0))
744.35/263.14	   active(plus(x0, s(x1)))
744.35/263.14	   active(x(x0, 0))
744.35/263.14	   active(x(x0, s(x1)))
744.35/263.14	   mark(U101(x0, x1, x2))
744.35/263.14	   mark(tt)
744.35/263.14	   mark(U102(x0, x1, x2))
744.35/263.14	   mark(isNatKind(x0))
744.35/263.14	   mark(U103(x0, x1, x2))
744.35/263.14	   mark(isNat(x0))
744.35/263.14	   mark(U104(x0, x1, x2))
744.35/263.14	   mark(plus(x0, x1))
744.35/263.14	   mark(x(x0, x1))
744.35/263.14	   mark(U11(x0, x1, x2))
744.35/263.14	   mark(U12(x0, x1, x2))
744.35/263.14	   mark(U13(x0, x1, x2))
744.35/263.14	   mark(U14(x0, x1, x2))
744.35/263.14	   mark(U15(x0, x1))
744.35/263.14	   mark(U16(x0))
744.35/263.14	   mark(U21(x0, x1))
744.35/263.14	   mark(U22(x0, x1))
744.35/263.14	   mark(U23(x0))
744.35/263.14	   mark(U31(x0, x1, x2))
744.35/263.14	   mark(U32(x0, x1, x2))
744.35/263.14	   mark(U33(x0, x1, x2))
744.35/263.14	   mark(U34(x0, x1, x2))
744.35/263.14	   mark(U35(x0, x1))
744.35/263.14	   mark(U36(x0))
744.35/263.14	   mark(U41(x0, x1))
744.35/263.14	   mark(U42(x0))
744.35/263.14	   mark(U51(x0))
744.35/263.14	   mark(U61(x0, x1))
744.35/263.14	   mark(U62(x0))
744.35/263.14	   mark(U71(x0, x1))
744.35/263.14	   mark(U72(x0, x1))
744.35/263.14	   mark(U81(x0, x1, x2))
744.35/263.14	   mark(U82(x0, x1, x2))
744.35/263.14	   mark(U83(x0, x1, x2))
744.35/263.14	   mark(U84(x0, x1, x2))
744.35/263.14	   mark(s(x0))
744.35/263.14	   mark(U91(x0, x1))
744.35/263.14	   mark(U92(x0))
744.35/263.14	   mark(0)
744.35/263.14	   U101(mark(x0), x1, x2)
744.35/263.14	   U101(x0, mark(x1), x2)
744.35/263.14	   U101(x0, x1, mark(x2))
744.35/263.14	   U101(active(x0), x1, x2)
744.35/263.14	   U101(x0, active(x1), x2)
744.35/263.14	   U101(x0, x1, active(x2))
744.35/263.14	   U102(mark(x0), x1, x2)
744.35/263.14	   U102(x0, mark(x1), x2)
744.35/263.14	   U102(x0, x1, mark(x2))
744.35/263.14	   U102(active(x0), x1, x2)
744.35/263.14	   U102(x0, active(x1), x2)
744.35/263.14	   U102(x0, x1, active(x2))
744.35/263.14	   isNatKind(mark(x0))
744.35/263.14	   isNatKind(active(x0))
744.35/263.14	   U103(mark(x0), x1, x2)
744.35/263.14	   U103(x0, mark(x1), x2)
744.35/263.14	   U103(x0, x1, mark(x2))
744.35/263.14	   U103(active(x0), x1, x2)
744.35/263.14	   U103(x0, active(x1), x2)
744.35/263.14	   U103(x0, x1, active(x2))
744.35/263.14	   isNat(mark(x0))
744.35/263.14	   isNat(active(x0))
744.35/263.14	   U104(mark(x0), x1, x2)
744.35/263.14	   U104(x0, mark(x1), x2)
744.35/263.14	   U104(x0, x1, mark(x2))
744.35/263.14	   U104(active(x0), x1, x2)
744.35/263.14	   U104(x0, active(x1), x2)
744.35/263.14	   U104(x0, x1, active(x2))
744.35/263.14	   plus(mark(x0), x1)
744.35/263.14	   plus(x0, mark(x1))
744.35/263.14	   plus(active(x0), x1)
744.35/263.14	   plus(x0, active(x1))
744.35/263.14	   x(mark(x0), x1)
744.35/263.14	   x(x0, mark(x1))
744.35/263.14	   x(active(x0), x1)
744.35/263.14	   x(x0, active(x1))
744.35/263.14	   U11(mark(x0), x1, x2)
744.35/263.14	   U11(x0, mark(x1), x2)
744.35/263.14	   U11(x0, x1, mark(x2))
744.35/263.14	   U11(active(x0), x1, x2)
744.35/263.14	   U11(x0, active(x1), x2)
744.35/263.14	   U11(x0, x1, active(x2))
744.35/263.14	   U12(mark(x0), x1, x2)
744.35/263.14	   U12(x0, mark(x1), x2)
744.35/263.14	   U12(x0, x1, mark(x2))
744.35/263.14	   U12(active(x0), x1, x2)
744.35/263.14	   U12(x0, active(x1), x2)
744.35/263.14	   U12(x0, x1, active(x2))
744.35/263.14	   U13(mark(x0), x1, x2)
744.35/263.14	   U13(x0, mark(x1), x2)
744.35/263.14	   U13(x0, x1, mark(x2))
744.35/263.14	   U13(active(x0), x1, x2)
744.35/263.14	   U13(x0, active(x1), x2)
744.35/263.14	   U13(x0, x1, active(x2))
744.35/263.14	   U14(mark(x0), x1, x2)
744.35/263.14	   U14(x0, mark(x1), x2)
744.35/263.14	   U14(x0, x1, mark(x2))
744.35/263.14	   U14(active(x0), x1, x2)
744.35/263.14	   U14(x0, active(x1), x2)
744.35/263.14	   U14(x0, x1, active(x2))
744.35/263.14	   U15(mark(x0), x1)
744.35/263.14	   U15(x0, mark(x1))
744.35/263.14	   U15(active(x0), x1)
744.35/263.14	   U15(x0, active(x1))
744.35/263.14	   U16(mark(x0))
744.35/263.14	   U16(active(x0))
744.35/263.14	   U21(mark(x0), x1)
744.35/263.14	   U21(x0, mark(x1))
744.35/263.14	   U21(active(x0), x1)
744.35/263.14	   U21(x0, active(x1))
744.35/263.14	   U22(mark(x0), x1)
744.35/263.14	   U22(x0, mark(x1))
744.35/263.14	   U22(active(x0), x1)
744.35/263.14	   U22(x0, active(x1))
744.35/263.14	   U23(mark(x0))
744.35/263.14	   U23(active(x0))
744.35/263.14	   U31(mark(x0), x1, x2)
744.35/263.14	   U31(x0, mark(x1), x2)
744.35/263.14	   U31(x0, x1, mark(x2))
744.35/263.14	   U31(active(x0), x1, x2)
744.35/263.14	   U31(x0, active(x1), x2)
744.35/263.14	   U31(x0, x1, active(x2))
744.35/263.14	   U32(mark(x0), x1, x2)
744.35/263.14	   U32(x0, mark(x1), x2)
744.35/263.14	   U32(x0, x1, mark(x2))
744.35/263.14	   U32(active(x0), x1, x2)
744.35/263.14	   U32(x0, active(x1), x2)
744.35/263.14	   U32(x0, x1, active(x2))
744.35/263.14	   U33(mark(x0), x1, x2)
744.35/263.14	   U33(x0, mark(x1), x2)
744.35/263.14	   U33(x0, x1, mark(x2))
744.35/263.14	   U33(active(x0), x1, x2)
744.35/263.14	   U33(x0, active(x1), x2)
744.35/263.14	   U33(x0, x1, active(x2))
744.35/263.14	   U34(mark(x0), x1, x2)
744.35/263.14	   U34(x0, mark(x1), x2)
744.35/263.14	   U34(x0, x1, mark(x2))
744.35/263.14	   U34(active(x0), x1, x2)
744.35/263.14	   U34(x0, active(x1), x2)
744.35/263.14	   U34(x0, x1, active(x2))
744.35/263.14	   U35(mark(x0), x1)
744.35/263.14	   U35(x0, mark(x1))
744.35/263.14	   U35(active(x0), x1)
744.35/263.14	   U35(x0, active(x1))
744.35/263.14	   U36(mark(x0))
744.35/263.14	   U36(active(x0))
744.35/263.14	   U41(mark(x0), x1)
744.35/263.14	   U41(x0, mark(x1))
744.35/263.14	   U41(active(x0), x1)
744.35/263.14	   U41(x0, active(x1))
744.35/263.14	   U42(mark(x0))
744.35/263.14	   U42(active(x0))
744.35/263.14	   U51(mark(x0))
744.35/263.14	   U51(active(x0))
744.35/263.14	   U61(mark(x0), x1)
744.35/263.14	   U61(x0, mark(x1))
744.35/263.14	   U61(active(x0), x1)
744.35/263.14	   U61(x0, active(x1))
744.35/263.14	   U62(mark(x0))
744.35/263.14	   U62(active(x0))
744.35/263.14	   U71(mark(x0), x1)
744.35/263.14	   U71(x0, mark(x1))
744.35/263.14	   U71(active(x0), x1)
744.35/263.14	   U71(x0, active(x1))
744.35/263.14	   U72(mark(x0), x1)
744.35/263.14	   U72(x0, mark(x1))
744.35/263.14	   U72(active(x0), x1)
744.35/263.14	   U72(x0, active(x1))
744.35/263.14	   U81(mark(x0), x1, x2)
744.35/263.14	   U81(x0, mark(x1), x2)
744.35/263.14	   U81(x0, x1, mark(x2))
744.35/263.14	   U81(active(x0), x1, x2)
744.35/263.14	   U81(x0, active(x1), x2)
744.35/263.14	   U81(x0, x1, active(x2))
744.35/263.14	   U82(mark(x0), x1, x2)
744.35/263.14	   U82(x0, mark(x1), x2)
744.35/263.14	   U82(x0, x1, mark(x2))
744.35/263.14	   U82(active(x0), x1, x2)
744.35/263.14	   U82(x0, active(x1), x2)
744.35/263.14	   U82(x0, x1, active(x2))
744.35/263.14	   U83(mark(x0), x1, x2)
744.35/263.14	   U83(x0, mark(x1), x2)
744.35/263.14	   U83(x0, x1, mark(x2))
744.35/263.14	   U83(active(x0), x1, x2)
744.35/263.14	   U83(x0, active(x1), x2)
744.35/263.14	   U83(x0, x1, active(x2))
744.35/263.14	   U84(mark(x0), x1, x2)
744.35/263.14	   U84(x0, mark(x1), x2)
744.35/263.14	   U84(x0, x1, mark(x2))
744.35/263.14	   U84(active(x0), x1, x2)
744.35/263.14	   U84(x0, active(x1), x2)
744.35/263.14	   U84(x0, x1, active(x2))
744.35/263.14	   s(mark(x0))
744.35/263.14	   s(active(x0))
744.35/263.14	   U91(mark(x0), x1)
744.35/263.14	   U91(x0, mark(x1))
744.35/263.14	   U91(active(x0), x1)
744.35/263.14	   U91(x0, active(x1))
744.35/263.14	   U92(mark(x0))
744.35/263.14	   U92(active(x0))
744.35/263.14	
744.35/263.14	We have to consider all minimal (P,Q,R)-chains.
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(355) QDPOrderProof (EQUIVALENT)
744.35/263.14	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.14	
744.35/263.14	
744.35/263.14	The following pairs can be oriented strictly and are deleted.
744.35/263.14	
744.35/263.14	   ACTIVE(U41(tt, V2)) -> MARK(U42(isNatKind(V2)))
744.35/263.14	The remaining pairs can at least be oriented weakly.
744.35/263.14	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(MARK(x_1)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U12(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(ACTIVE(x_1)) =  	[[0A]] 	 +  	[[1A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(mark(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U11(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(tt) =  	[[0A]]
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(isNatKind(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U13(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U14(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U15(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(isNat(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(plus(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U41(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U21(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U22(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U23(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U42(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U51(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(s(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U102(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[5A]] 	* 	x_2 	 +  	[[3A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(active(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U101(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[5A]] 	* 	x_2 	 +  	[[3A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U103(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[5A]] 	* 	x_2 	 +  	[[3A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U104(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[2A]] 	* 	x_1 	 +  	[[5A]] 	* 	x_2 	 +  	[[3A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(x(x_1, x_2)) =  	[[2A]] 	 +  	[[3A]] 	* 	x_1 	 +  	[[5A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U16(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U31(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[5A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U32(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[5A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U33(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[5A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[3A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U34(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[2A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[-I]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U35(x_1, x_2)) =  	[[-I]] 	 +  	[[1A]] 	* 	x_1 	 +  	[[-I]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U36(x_1)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U61(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U62(x_1)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U71(x_1, x_2)) =  	[[0A]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U72(x_1, x_2)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[0A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U81(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U82(x_1, x_2, x_3)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U83(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U84(x_1, x_2, x_3)) =  	[[0A]] 	 +  	[[-I]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2 	 +  	[[0A]] 	* 	x_3
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U91(x_1, x_2)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1 	 +  	[[1A]] 	* 	x_2
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(U92(x_1)) =  	[[-I]] 	 +  	[[0A]] 	* 	x_1
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	   <<<
744.35/263.14	 POL(0) =  	[[0A]]
744.35/263.14	>>>
744.35/263.14	
744.35/263.14	
744.35/263.14	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.14	
744.35/263.14	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.14	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.14	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.14	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.14	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.14	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.14	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.14	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.14	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.14	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.14	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.14	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.14	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.14	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.14	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.14	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.14	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.14	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.14	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.14	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.14	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.14	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.14	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.14	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.14	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.14	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.14	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.14	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.14	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.14	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.14	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.14	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.14	   active(U72(tt, N)) -> mark(N)
744.35/263.14	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.14	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.14	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.14	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.14	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.14	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.14	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.14	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.14	   mark(s(X)) -> active(s(mark(X)))
744.35/263.14	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.14	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.14	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.14	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.14	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.14	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.14	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.14	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.14	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.14	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.14	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.14	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.14	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.14	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.14	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.14	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.14	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.14	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.14	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.14	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.14	   mark(isNat(X)) -> active(isNat(X))
744.35/263.14	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.14	   mark(tt) -> active(tt)
744.35/263.14	   mark(0) -> active(0)
744.35/263.14	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.14	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.14	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.14	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.14	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.14	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.14	   active(U16(tt)) -> mark(tt)
744.35/263.14	   active(U23(tt)) -> mark(tt)
744.35/263.14	   active(U36(tt)) -> mark(tt)
744.35/263.14	   active(U42(tt)) -> mark(tt)
744.35/263.14	   active(U51(tt)) -> mark(tt)
744.35/263.14	   active(U62(tt)) -> mark(tt)
744.35/263.14	   active(U92(tt)) -> mark(0)
744.35/263.14	   active(isNat(0)) -> mark(tt)
744.35/263.14	   active(isNatKind(0)) -> mark(tt)
744.35/263.14	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.14	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.14	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.14	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.14	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.14	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.14	   U16(active(X)) -> U16(X)
744.35/263.14	   U16(mark(X)) -> U16(X)
744.35/263.14	   U23(active(X)) -> U23(X)
744.35/263.14	   U23(mark(X)) -> U23(X)
744.35/263.14	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.14	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.14	   U36(active(X)) -> U36(X)
744.35/263.14	   U36(mark(X)) -> U36(X)
744.35/263.14	   U42(active(X)) -> U42(X)
744.35/263.14	   U42(mark(X)) -> U42(X)
744.35/263.14	   U62(active(X)) -> U62(X)
744.35/263.14	   U62(mark(X)) -> U62(X)
744.35/263.14	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.14	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.14	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.14	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.14	   s(active(X)) -> s(X)
744.35/263.14	   s(mark(X)) -> s(X)
744.35/263.14	   U92(active(X)) -> U92(X)
744.35/263.14	   U92(mark(X)) -> U92(X)
744.35/263.14	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U51(active(X)) -> U51(X)
744.35/263.14	   U51(mark(X)) -> U51(X)
744.35/263.14	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.14	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.14	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.14	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.14	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.14	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.14	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.14	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.14	   x(active(X1), X2) -> x(X1, X2)
744.35/263.14	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.14	
744.35/263.14	
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(356)
744.35/263.14	Obligation:
744.35/263.14	Q DP problem:
744.35/263.14	The TRS P consists of the following rules:
744.35/263.14	
744.35/263.14	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.14	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.14	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.14	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.14	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.14	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.14	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.14	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.14	   MARK(U23(X)) -> MARK(X)
744.35/263.14	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.14	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.14	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.14	   MARK(U42(X)) -> MARK(X)
744.35/263.14	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.14	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U51(X)) -> MARK(X)
744.35/263.14	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.14	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.14	
744.35/263.14	The TRS R consists of the following rules:
744.35/263.14	
744.35/263.14	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.14	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.14	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.14	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.14	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.14	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.14	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.14	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.14	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.14	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.14	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.14	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.14	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.14	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.14	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.14	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.14	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.14	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.14	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.14	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.14	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.14	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.14	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.14	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.14	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.14	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.14	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.14	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.14	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.14	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.14	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.14	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.14	   active(U72(tt, N)) -> mark(N)
744.35/263.14	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.14	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.14	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.14	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.14	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.14	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.14	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.14	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.14	   mark(s(X)) -> active(s(mark(X)))
744.35/263.14	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.14	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.14	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.14	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.14	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.14	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.14	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.14	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.14	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.14	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.14	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.14	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.14	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.14	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.14	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.14	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.14	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.14	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.14	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.14	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.14	   mark(isNat(X)) -> active(isNat(X))
744.35/263.14	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.14	   mark(tt) -> active(tt)
744.35/263.14	   mark(0) -> active(0)
744.35/263.14	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.14	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.14	   active(U16(tt)) -> mark(tt)
744.35/263.14	   active(U23(tt)) -> mark(tt)
744.35/263.14	   active(U36(tt)) -> mark(tt)
744.35/263.14	   active(U42(tt)) -> mark(tt)
744.35/263.14	   active(U51(tt)) -> mark(tt)
744.35/263.14	   active(U62(tt)) -> mark(tt)
744.35/263.14	   active(U92(tt)) -> mark(0)
744.35/263.14	   active(isNat(0)) -> mark(tt)
744.35/263.14	   active(isNatKind(0)) -> mark(tt)
744.35/263.14	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.14	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.14	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.14	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.14	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.14	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.14	   U16(active(X)) -> U16(X)
744.35/263.14	   U16(mark(X)) -> U16(X)
744.35/263.14	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.14	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.14	   U23(active(X)) -> U23(X)
744.35/263.14	   U23(mark(X)) -> U23(X)
744.35/263.14	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.14	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.14	   U36(active(X)) -> U36(X)
744.35/263.14	   U36(mark(X)) -> U36(X)
744.35/263.14	   U42(active(X)) -> U42(X)
744.35/263.14	   U42(mark(X)) -> U42(X)
744.35/263.14	   U62(active(X)) -> U62(X)
744.35/263.14	   U62(mark(X)) -> U62(X)
744.35/263.14	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.14	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.14	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.14	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.14	   s(active(X)) -> s(X)
744.35/263.14	   s(mark(X)) -> s(X)
744.35/263.14	   U92(active(X)) -> U92(X)
744.35/263.14	   U92(mark(X)) -> U92(X)
744.35/263.14	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.14	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.14	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.14	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.14	   U51(active(X)) -> U51(X)
744.35/263.14	   U51(mark(X)) -> U51(X)
744.35/263.14	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.14	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.14	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.14	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.14	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.14	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.14	   x(active(X1), X2) -> x(X1, X2)
744.35/263.14	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.14	
744.35/263.14	The set Q consists of the following terms:
744.35/263.14	
744.35/263.14	   active(U101(tt, x0, x1))
744.35/263.14	   active(U102(tt, x0, x1))
744.35/263.14	   active(U103(tt, x0, x1))
744.35/263.14	   active(U104(tt, x0, x1))
744.35/263.14	   active(U11(tt, x0, x1))
744.35/263.14	   active(U12(tt, x0, x1))
744.35/263.14	   active(U13(tt, x0, x1))
744.35/263.14	   active(U14(tt, x0, x1))
744.35/263.14	   active(U15(tt, x0))
744.35/263.14	   active(U16(tt))
744.35/263.14	   active(U21(tt, x0))
744.35/263.14	   active(U22(tt, x0))
744.35/263.14	   active(U23(tt))
744.35/263.14	   active(U31(tt, x0, x1))
744.35/263.14	   active(U32(tt, x0, x1))
744.35/263.14	   active(U33(tt, x0, x1))
744.35/263.14	   active(U34(tt, x0, x1))
744.35/263.14	   active(U35(tt, x0))
744.35/263.14	   active(U36(tt))
744.35/263.14	   active(U41(tt, x0))
744.35/263.14	   active(U42(tt))
744.35/263.14	   active(U51(tt))
744.35/263.14	   active(U61(tt, x0))
744.35/263.14	   active(U62(tt))
744.35/263.14	   active(U71(tt, x0))
744.35/263.14	   active(U72(tt, x0))
744.35/263.14	   active(U81(tt, x0, x1))
744.35/263.14	   active(U82(tt, x0, x1))
744.35/263.14	   active(U83(tt, x0, x1))
744.35/263.14	   active(U84(tt, x0, x1))
744.35/263.14	   active(U91(tt, x0))
744.35/263.14	   active(U92(tt))
744.35/263.14	   active(isNat(0))
744.35/263.14	   active(isNat(plus(x0, x1)))
744.35/263.14	   active(isNat(s(x0)))
744.35/263.14	   active(isNat(x(x0, x1)))
744.35/263.14	   active(isNatKind(0))
744.35/263.14	   active(isNatKind(plus(x0, x1)))
744.35/263.14	   active(isNatKind(s(x0)))
744.35/263.14	   active(isNatKind(x(x0, x1)))
744.35/263.14	   active(plus(x0, 0))
744.35/263.14	   active(plus(x0, s(x1)))
744.35/263.14	   active(x(x0, 0))
744.35/263.14	   active(x(x0, s(x1)))
744.35/263.14	   mark(U101(x0, x1, x2))
744.35/263.14	   mark(tt)
744.35/263.14	   mark(U102(x0, x1, x2))
744.35/263.14	   mark(isNatKind(x0))
744.35/263.14	   mark(U103(x0, x1, x2))
744.35/263.14	   mark(isNat(x0))
744.35/263.14	   mark(U104(x0, x1, x2))
744.35/263.14	   mark(plus(x0, x1))
744.35/263.14	   mark(x(x0, x1))
744.35/263.14	   mark(U11(x0, x1, x2))
744.35/263.14	   mark(U12(x0, x1, x2))
744.35/263.14	   mark(U13(x0, x1, x2))
744.35/263.14	   mark(U14(x0, x1, x2))
744.35/263.14	   mark(U15(x0, x1))
744.35/263.14	   mark(U16(x0))
744.35/263.14	   mark(U21(x0, x1))
744.35/263.14	   mark(U22(x0, x1))
744.35/263.14	   mark(U23(x0))
744.35/263.14	   mark(U31(x0, x1, x2))
744.35/263.14	   mark(U32(x0, x1, x2))
744.35/263.14	   mark(U33(x0, x1, x2))
744.35/263.14	   mark(U34(x0, x1, x2))
744.35/263.14	   mark(U35(x0, x1))
744.35/263.14	   mark(U36(x0))
744.35/263.14	   mark(U41(x0, x1))
744.35/263.14	   mark(U42(x0))
744.35/263.14	   mark(U51(x0))
744.35/263.14	   mark(U61(x0, x1))
744.35/263.14	   mark(U62(x0))
744.35/263.14	   mark(U71(x0, x1))
744.35/263.14	   mark(U72(x0, x1))
744.35/263.14	   mark(U81(x0, x1, x2))
744.35/263.14	   mark(U82(x0, x1, x2))
744.35/263.14	   mark(U83(x0, x1, x2))
744.35/263.14	   mark(U84(x0, x1, x2))
744.35/263.14	   mark(s(x0))
744.35/263.14	   mark(U91(x0, x1))
744.35/263.14	   mark(U92(x0))
744.35/263.14	   mark(0)
744.35/263.14	   U101(mark(x0), x1, x2)
744.35/263.14	   U101(x0, mark(x1), x2)
744.35/263.14	   U101(x0, x1, mark(x2))
744.35/263.14	   U101(active(x0), x1, x2)
744.35/263.14	   U101(x0, active(x1), x2)
744.35/263.14	   U101(x0, x1, active(x2))
744.35/263.14	   U102(mark(x0), x1, x2)
744.35/263.14	   U102(x0, mark(x1), x2)
744.35/263.14	   U102(x0, x1, mark(x2))
744.35/263.14	   U102(active(x0), x1, x2)
744.35/263.14	   U102(x0, active(x1), x2)
744.35/263.14	   U102(x0, x1, active(x2))
744.35/263.14	   isNatKind(mark(x0))
744.35/263.14	   isNatKind(active(x0))
744.35/263.14	   U103(mark(x0), x1, x2)
744.35/263.14	   U103(x0, mark(x1), x2)
744.35/263.14	   U103(x0, x1, mark(x2))
744.35/263.14	   U103(active(x0), x1, x2)
744.35/263.14	   U103(x0, active(x1), x2)
744.35/263.14	   U103(x0, x1, active(x2))
744.35/263.14	   isNat(mark(x0))
744.35/263.14	   isNat(active(x0))
744.35/263.14	   U104(mark(x0), x1, x2)
744.35/263.14	   U104(x0, mark(x1), x2)
744.35/263.14	   U104(x0, x1, mark(x2))
744.35/263.14	   U104(active(x0), x1, x2)
744.35/263.14	   U104(x0, active(x1), x2)
744.35/263.14	   U104(x0, x1, active(x2))
744.35/263.14	   plus(mark(x0), x1)
744.35/263.14	   plus(x0, mark(x1))
744.35/263.14	   plus(active(x0), x1)
744.35/263.14	   plus(x0, active(x1))
744.35/263.14	   x(mark(x0), x1)
744.35/263.14	   x(x0, mark(x1))
744.35/263.14	   x(active(x0), x1)
744.35/263.14	   x(x0, active(x1))
744.35/263.14	   U11(mark(x0), x1, x2)
744.35/263.14	   U11(x0, mark(x1), x2)
744.35/263.14	   U11(x0, x1, mark(x2))
744.35/263.14	   U11(active(x0), x1, x2)
744.35/263.14	   U11(x0, active(x1), x2)
744.35/263.14	   U11(x0, x1, active(x2))
744.35/263.14	   U12(mark(x0), x1, x2)
744.35/263.14	   U12(x0, mark(x1), x2)
744.35/263.14	   U12(x0, x1, mark(x2))
744.35/263.14	   U12(active(x0), x1, x2)
744.35/263.14	   U12(x0, active(x1), x2)
744.35/263.14	   U12(x0, x1, active(x2))
744.35/263.14	   U13(mark(x0), x1, x2)
744.35/263.14	   U13(x0, mark(x1), x2)
744.35/263.14	   U13(x0, x1, mark(x2))
744.35/263.14	   U13(active(x0), x1, x2)
744.35/263.14	   U13(x0, active(x1), x2)
744.35/263.14	   U13(x0, x1, active(x2))
744.35/263.14	   U14(mark(x0), x1, x2)
744.35/263.14	   U14(x0, mark(x1), x2)
744.35/263.14	   U14(x0, x1, mark(x2))
744.35/263.14	   U14(active(x0), x1, x2)
744.35/263.14	   U14(x0, active(x1), x2)
744.35/263.14	   U14(x0, x1, active(x2))
744.35/263.14	   U15(mark(x0), x1)
744.35/263.14	   U15(x0, mark(x1))
744.35/263.14	   U15(active(x0), x1)
744.35/263.14	   U15(x0, active(x1))
744.35/263.14	   U16(mark(x0))
744.35/263.14	   U16(active(x0))
744.35/263.14	   U21(mark(x0), x1)
744.35/263.14	   U21(x0, mark(x1))
744.35/263.14	   U21(active(x0), x1)
744.35/263.14	   U21(x0, active(x1))
744.35/263.14	   U22(mark(x0), x1)
744.35/263.14	   U22(x0, mark(x1))
744.35/263.14	   U22(active(x0), x1)
744.35/263.14	   U22(x0, active(x1))
744.35/263.14	   U23(mark(x0))
744.35/263.14	   U23(active(x0))
744.35/263.14	   U31(mark(x0), x1, x2)
744.35/263.14	   U31(x0, mark(x1), x2)
744.35/263.14	   U31(x0, x1, mark(x2))
744.35/263.14	   U31(active(x0), x1, x2)
744.35/263.14	   U31(x0, active(x1), x2)
744.35/263.14	   U31(x0, x1, active(x2))
744.35/263.14	   U32(mark(x0), x1, x2)
744.35/263.14	   U32(x0, mark(x1), x2)
744.35/263.14	   U32(x0, x1, mark(x2))
744.35/263.14	   U32(active(x0), x1, x2)
744.35/263.14	   U32(x0, active(x1), x2)
744.35/263.14	   U32(x0, x1, active(x2))
744.35/263.14	   U33(mark(x0), x1, x2)
744.35/263.14	   U33(x0, mark(x1), x2)
744.35/263.14	   U33(x0, x1, mark(x2))
744.35/263.14	   U33(active(x0), x1, x2)
744.35/263.14	   U33(x0, active(x1), x2)
744.35/263.14	   U33(x0, x1, active(x2))
744.35/263.14	   U34(mark(x0), x1, x2)
744.35/263.14	   U34(x0, mark(x1), x2)
744.35/263.14	   U34(x0, x1, mark(x2))
744.35/263.14	   U34(active(x0), x1, x2)
744.35/263.14	   U34(x0, active(x1), x2)
744.35/263.14	   U34(x0, x1, active(x2))
744.35/263.14	   U35(mark(x0), x1)
744.35/263.14	   U35(x0, mark(x1))
744.35/263.14	   U35(active(x0), x1)
744.35/263.14	   U35(x0, active(x1))
744.35/263.14	   U36(mark(x0))
744.35/263.14	   U36(active(x0))
744.35/263.14	   U41(mark(x0), x1)
744.35/263.14	   U41(x0, mark(x1))
744.35/263.14	   U41(active(x0), x1)
744.35/263.14	   U41(x0, active(x1))
744.35/263.14	   U42(mark(x0))
744.35/263.14	   U42(active(x0))
744.35/263.14	   U51(mark(x0))
744.35/263.14	   U51(active(x0))
744.35/263.14	   U61(mark(x0), x1)
744.35/263.14	   U61(x0, mark(x1))
744.35/263.14	   U61(active(x0), x1)
744.35/263.14	   U61(x0, active(x1))
744.35/263.14	   U62(mark(x0))
744.35/263.14	   U62(active(x0))
744.35/263.14	   U71(mark(x0), x1)
744.35/263.14	   U71(x0, mark(x1))
744.35/263.14	   U71(active(x0), x1)
744.35/263.14	   U71(x0, active(x1))
744.35/263.14	   U72(mark(x0), x1)
744.35/263.14	   U72(x0, mark(x1))
744.35/263.14	   U72(active(x0), x1)
744.35/263.14	   U72(x0, active(x1))
744.35/263.14	   U81(mark(x0), x1, x2)
744.35/263.14	   U81(x0, mark(x1), x2)
744.35/263.14	   U81(x0, x1, mark(x2))
744.35/263.14	   U81(active(x0), x1, x2)
744.35/263.14	   U81(x0, active(x1), x2)
744.35/263.14	   U81(x0, x1, active(x2))
744.35/263.14	   U82(mark(x0), x1, x2)
744.35/263.14	   U82(x0, mark(x1), x2)
744.35/263.14	   U82(x0, x1, mark(x2))
744.35/263.14	   U82(active(x0), x1, x2)
744.35/263.14	   U82(x0, active(x1), x2)
744.35/263.14	   U82(x0, x1, active(x2))
744.35/263.14	   U83(mark(x0), x1, x2)
744.35/263.14	   U83(x0, mark(x1), x2)
744.35/263.14	   U83(x0, x1, mark(x2))
744.35/263.14	   U83(active(x0), x1, x2)
744.35/263.14	   U83(x0, active(x1), x2)
744.35/263.14	   U83(x0, x1, active(x2))
744.35/263.14	   U84(mark(x0), x1, x2)
744.35/263.14	   U84(x0, mark(x1), x2)
744.35/263.14	   U84(x0, x1, mark(x2))
744.35/263.14	   U84(active(x0), x1, x2)
744.35/263.14	   U84(x0, active(x1), x2)
744.35/263.14	   U84(x0, x1, active(x2))
744.35/263.14	   s(mark(x0))
744.35/263.14	   s(active(x0))
744.35/263.14	   U91(mark(x0), x1)
744.35/263.14	   U91(x0, mark(x1))
744.35/263.14	   U91(active(x0), x1)
744.35/263.14	   U91(x0, active(x1))
744.35/263.14	   U92(mark(x0))
744.35/263.14	   U92(active(x0))
744.35/263.14	
744.35/263.14	We have to consider all minimal (P,Q,R)-chains.
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(357) QDPQMonotonicMRRProof (EQUIVALENT)
744.35/263.14	By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain.
744.35/263.14	
744.35/263.14	Strictly oriented dependency pairs:
744.35/263.14	
744.35/263.14	   MARK(U41(X1, X2)) -> ACTIVE(U41(mark(X1), X2))
744.35/263.14	
744.35/263.14	
744.35/263.14	Used ordering: Polynomial interpretation [POLO]:
744.35/263.14	
744.35/263.14	   POL(0) = 0
744.35/263.14	   POL(ACTIVE(x_1)) = 2*x_1
744.35/263.14	   POL(MARK(x_1)) = 2
744.35/263.14	   POL(U101(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U102(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U103(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U104(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U11(x_1, x_2, x_3)) = 1
744.35/263.14	   POL(U12(x_1, x_2, x_3)) = 1
744.35/263.14	   POL(U13(x_1, x_2, x_3)) = 1
744.35/263.14	   POL(U14(x_1, x_2, x_3)) = 1
744.35/263.14	   POL(U15(x_1, x_2)) = 0
744.35/263.14	   POL(U16(x_1)) = 0
744.35/263.14	   POL(U21(x_1, x_2)) = 1
744.35/263.14	   POL(U22(x_1, x_2)) = 1
744.35/263.14	   POL(U23(x_1)) = 0
744.35/263.14	   POL(U31(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U32(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U33(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U34(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U35(x_1, x_2)) = 0
744.35/263.14	   POL(U36(x_1)) = 0
744.35/263.14	   POL(U41(x_1, x_2)) = 0
744.35/263.14	   POL(U42(x_1)) = 0
744.35/263.14	   POL(U51(x_1)) = 0
744.35/263.14	   POL(U61(x_1, x_2)) = 0
744.35/263.14	   POL(U62(x_1)) = 0
744.35/263.14	   POL(U71(x_1, x_2)) = 0
744.35/263.14	   POL(U72(x_1, x_2)) = 0
744.35/263.14	   POL(U81(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U82(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U83(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U84(x_1, x_2, x_3)) = 0
744.35/263.14	   POL(U91(x_1, x_2)) = 0
744.35/263.14	   POL(U92(x_1)) = 0
744.35/263.14	   POL(active(x_1)) = 0
744.35/263.14	   POL(isNat(x_1)) = 1
744.35/263.14	   POL(isNatKind(x_1)) = 1
744.35/263.14	   POL(mark(x_1)) = 0
744.35/263.14	   POL(plus(x_1, x_2)) = 0
744.35/263.14	   POL(s(x_1)) = 0
744.35/263.14	   POL(tt) = 0
744.35/263.14	   POL(x(x_1, x_2)) = 0
744.35/263.14	
744.35/263.14	
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(358)
744.35/263.14	Obligation:
744.35/263.14	Q DP problem:
744.35/263.14	The TRS P consists of the following rules:
744.35/263.14	
744.35/263.14	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.14	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.14	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.14	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.14	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.14	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.14	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.14	   MARK(U23(X)) -> MARK(X)
744.35/263.14	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.14	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.14	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.14	   MARK(U42(X)) -> MARK(X)
744.35/263.14	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.14	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U51(X)) -> MARK(X)
744.35/263.14	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.14	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.14	
744.35/263.14	The TRS R consists of the following rules:
744.35/263.14	
744.35/263.14	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.14	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.14	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.14	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.14	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.14	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.14	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.14	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.14	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.14	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.14	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.14	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.14	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.14	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.14	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.14	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.14	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.14	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.14	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.14	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.14	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.14	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.14	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.14	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.14	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.14	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.14	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.14	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.14	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.14	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.14	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.14	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.14	   active(U72(tt, N)) -> mark(N)
744.35/263.14	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.14	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.14	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.14	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.14	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.14	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.14	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.14	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.14	   mark(s(X)) -> active(s(mark(X)))
744.35/263.14	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.14	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.14	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.14	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.14	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.14	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.14	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.14	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.14	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.14	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.14	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.14	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.14	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.14	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.14	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.14	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.14	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.14	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.14	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.14	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.14	   mark(isNat(X)) -> active(isNat(X))
744.35/263.14	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.14	   mark(tt) -> active(tt)
744.35/263.14	   mark(0) -> active(0)
744.35/263.14	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.14	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.14	   active(U16(tt)) -> mark(tt)
744.35/263.14	   active(U23(tt)) -> mark(tt)
744.35/263.14	   active(U36(tt)) -> mark(tt)
744.35/263.14	   active(U42(tt)) -> mark(tt)
744.35/263.14	   active(U51(tt)) -> mark(tt)
744.35/263.14	   active(U62(tt)) -> mark(tt)
744.35/263.14	   active(U92(tt)) -> mark(0)
744.35/263.14	   active(isNat(0)) -> mark(tt)
744.35/263.14	   active(isNatKind(0)) -> mark(tt)
744.35/263.14	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.14	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.14	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.14	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.14	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.14	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.14	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.14	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.14	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.14	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.14	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.14	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.14	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.14	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.14	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.14	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.14	   U16(active(X)) -> U16(X)
744.35/263.14	   U16(mark(X)) -> U16(X)
744.35/263.14	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.14	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.14	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.14	   U23(active(X)) -> U23(X)
744.35/263.14	   U23(mark(X)) -> U23(X)
744.35/263.14	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.14	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.14	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.14	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.14	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.14	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.14	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.14	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.14	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.14	   U36(active(X)) -> U36(X)
744.35/263.14	   U36(mark(X)) -> U36(X)
744.35/263.14	   U42(active(X)) -> U42(X)
744.35/263.14	   U42(mark(X)) -> U42(X)
744.35/263.14	   U62(active(X)) -> U62(X)
744.35/263.14	   U62(mark(X)) -> U62(X)
744.35/263.14	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.14	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.14	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.14	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.14	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.14	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.14	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.14	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.14	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.14	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.14	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.14	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.14	   s(active(X)) -> s(X)
744.35/263.14	   s(mark(X)) -> s(X)
744.35/263.14	   U92(active(X)) -> U92(X)
744.35/263.14	   U92(mark(X)) -> U92(X)
744.35/263.14	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.14	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.14	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.14	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.14	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.14	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.14	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.14	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.14	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.14	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.14	   U51(active(X)) -> U51(X)
744.35/263.14	   U51(mark(X)) -> U51(X)
744.35/263.14	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.14	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.14	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.14	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.14	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.14	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.14	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.14	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.14	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.14	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.14	   x(active(X1), X2) -> x(X1, X2)
744.35/263.14	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.14	
744.35/263.14	The set Q consists of the following terms:
744.35/263.14	
744.35/263.14	   active(U101(tt, x0, x1))
744.35/263.14	   active(U102(tt, x0, x1))
744.35/263.14	   active(U103(tt, x0, x1))
744.35/263.14	   active(U104(tt, x0, x1))
744.35/263.14	   active(U11(tt, x0, x1))
744.35/263.14	   active(U12(tt, x0, x1))
744.35/263.14	   active(U13(tt, x0, x1))
744.35/263.14	   active(U14(tt, x0, x1))
744.35/263.14	   active(U15(tt, x0))
744.35/263.14	   active(U16(tt))
744.35/263.14	   active(U21(tt, x0))
744.35/263.14	   active(U22(tt, x0))
744.35/263.14	   active(U23(tt))
744.35/263.14	   active(U31(tt, x0, x1))
744.35/263.14	   active(U32(tt, x0, x1))
744.35/263.14	   active(U33(tt, x0, x1))
744.35/263.14	   active(U34(tt, x0, x1))
744.35/263.14	   active(U35(tt, x0))
744.35/263.14	   active(U36(tt))
744.35/263.14	   active(U41(tt, x0))
744.35/263.14	   active(U42(tt))
744.35/263.14	   active(U51(tt))
744.35/263.14	   active(U61(tt, x0))
744.35/263.14	   active(U62(tt))
744.35/263.14	   active(U71(tt, x0))
744.35/263.14	   active(U72(tt, x0))
744.35/263.14	   active(U81(tt, x0, x1))
744.35/263.14	   active(U82(tt, x0, x1))
744.35/263.14	   active(U83(tt, x0, x1))
744.35/263.14	   active(U84(tt, x0, x1))
744.35/263.14	   active(U91(tt, x0))
744.35/263.14	   active(U92(tt))
744.35/263.14	   active(isNat(0))
744.35/263.14	   active(isNat(plus(x0, x1)))
744.35/263.14	   active(isNat(s(x0)))
744.35/263.14	   active(isNat(x(x0, x1)))
744.35/263.14	   active(isNatKind(0))
744.35/263.14	   active(isNatKind(plus(x0, x1)))
744.35/263.14	   active(isNatKind(s(x0)))
744.35/263.14	   active(isNatKind(x(x0, x1)))
744.35/263.14	   active(plus(x0, 0))
744.35/263.14	   active(plus(x0, s(x1)))
744.35/263.14	   active(x(x0, 0))
744.35/263.14	   active(x(x0, s(x1)))
744.35/263.14	   mark(U101(x0, x1, x2))
744.35/263.14	   mark(tt)
744.35/263.14	   mark(U102(x0, x1, x2))
744.35/263.14	   mark(isNatKind(x0))
744.35/263.14	   mark(U103(x0, x1, x2))
744.35/263.14	   mark(isNat(x0))
744.35/263.14	   mark(U104(x0, x1, x2))
744.35/263.14	   mark(plus(x0, x1))
744.35/263.14	   mark(x(x0, x1))
744.35/263.14	   mark(U11(x0, x1, x2))
744.35/263.14	   mark(U12(x0, x1, x2))
744.35/263.14	   mark(U13(x0, x1, x2))
744.35/263.14	   mark(U14(x0, x1, x2))
744.35/263.14	   mark(U15(x0, x1))
744.35/263.14	   mark(U16(x0))
744.35/263.14	   mark(U21(x0, x1))
744.35/263.14	   mark(U22(x0, x1))
744.35/263.14	   mark(U23(x0))
744.35/263.14	   mark(U31(x0, x1, x2))
744.35/263.14	   mark(U32(x0, x1, x2))
744.35/263.14	   mark(U33(x0, x1, x2))
744.35/263.14	   mark(U34(x0, x1, x2))
744.35/263.14	   mark(U35(x0, x1))
744.35/263.14	   mark(U36(x0))
744.35/263.14	   mark(U41(x0, x1))
744.35/263.14	   mark(U42(x0))
744.35/263.14	   mark(U51(x0))
744.35/263.14	   mark(U61(x0, x1))
744.35/263.14	   mark(U62(x0))
744.35/263.14	   mark(U71(x0, x1))
744.35/263.14	   mark(U72(x0, x1))
744.35/263.14	   mark(U81(x0, x1, x2))
744.35/263.14	   mark(U82(x0, x1, x2))
744.35/263.14	   mark(U83(x0, x1, x2))
744.35/263.14	   mark(U84(x0, x1, x2))
744.35/263.14	   mark(s(x0))
744.35/263.14	   mark(U91(x0, x1))
744.35/263.14	   mark(U92(x0))
744.35/263.14	   mark(0)
744.35/263.14	   U101(mark(x0), x1, x2)
744.35/263.14	   U101(x0, mark(x1), x2)
744.35/263.14	   U101(x0, x1, mark(x2))
744.35/263.14	   U101(active(x0), x1, x2)
744.35/263.14	   U101(x0, active(x1), x2)
744.35/263.14	   U101(x0, x1, active(x2))
744.35/263.14	   U102(mark(x0), x1, x2)
744.35/263.14	   U102(x0, mark(x1), x2)
744.35/263.14	   U102(x0, x1, mark(x2))
744.35/263.14	   U102(active(x0), x1, x2)
744.35/263.14	   U102(x0, active(x1), x2)
744.35/263.14	   U102(x0, x1, active(x2))
744.35/263.14	   isNatKind(mark(x0))
744.35/263.14	   isNatKind(active(x0))
744.35/263.14	   U103(mark(x0), x1, x2)
744.35/263.14	   U103(x0, mark(x1), x2)
744.35/263.14	   U103(x0, x1, mark(x2))
744.35/263.14	   U103(active(x0), x1, x2)
744.35/263.14	   U103(x0, active(x1), x2)
744.35/263.14	   U103(x0, x1, active(x2))
744.35/263.14	   isNat(mark(x0))
744.35/263.14	   isNat(active(x0))
744.35/263.14	   U104(mark(x0), x1, x2)
744.35/263.14	   U104(x0, mark(x1), x2)
744.35/263.14	   U104(x0, x1, mark(x2))
744.35/263.14	   U104(active(x0), x1, x2)
744.35/263.14	   U104(x0, active(x1), x2)
744.35/263.14	   U104(x0, x1, active(x2))
744.35/263.14	   plus(mark(x0), x1)
744.35/263.14	   plus(x0, mark(x1))
744.35/263.14	   plus(active(x0), x1)
744.35/263.14	   plus(x0, active(x1))
744.35/263.14	   x(mark(x0), x1)
744.35/263.14	   x(x0, mark(x1))
744.35/263.14	   x(active(x0), x1)
744.35/263.14	   x(x0, active(x1))
744.35/263.14	   U11(mark(x0), x1, x2)
744.35/263.14	   U11(x0, mark(x1), x2)
744.35/263.14	   U11(x0, x1, mark(x2))
744.35/263.14	   U11(active(x0), x1, x2)
744.35/263.14	   U11(x0, active(x1), x2)
744.35/263.14	   U11(x0, x1, active(x2))
744.35/263.14	   U12(mark(x0), x1, x2)
744.35/263.14	   U12(x0, mark(x1), x2)
744.35/263.14	   U12(x0, x1, mark(x2))
744.35/263.14	   U12(active(x0), x1, x2)
744.35/263.14	   U12(x0, active(x1), x2)
744.35/263.14	   U12(x0, x1, active(x2))
744.35/263.14	   U13(mark(x0), x1, x2)
744.35/263.14	   U13(x0, mark(x1), x2)
744.35/263.14	   U13(x0, x1, mark(x2))
744.35/263.14	   U13(active(x0), x1, x2)
744.35/263.14	   U13(x0, active(x1), x2)
744.35/263.14	   U13(x0, x1, active(x2))
744.35/263.14	   U14(mark(x0), x1, x2)
744.35/263.14	   U14(x0, mark(x1), x2)
744.35/263.14	   U14(x0, x1, mark(x2))
744.35/263.14	   U14(active(x0), x1, x2)
744.35/263.14	   U14(x0, active(x1), x2)
744.35/263.14	   U14(x0, x1, active(x2))
744.35/263.14	   U15(mark(x0), x1)
744.35/263.14	   U15(x0, mark(x1))
744.35/263.14	   U15(active(x0), x1)
744.35/263.14	   U15(x0, active(x1))
744.35/263.14	   U16(mark(x0))
744.35/263.14	   U16(active(x0))
744.35/263.14	   U21(mark(x0), x1)
744.35/263.14	   U21(x0, mark(x1))
744.35/263.14	   U21(active(x0), x1)
744.35/263.14	   U21(x0, active(x1))
744.35/263.14	   U22(mark(x0), x1)
744.35/263.14	   U22(x0, mark(x1))
744.35/263.14	   U22(active(x0), x1)
744.35/263.14	   U22(x0, active(x1))
744.35/263.14	   U23(mark(x0))
744.35/263.14	   U23(active(x0))
744.35/263.14	   U31(mark(x0), x1, x2)
744.35/263.14	   U31(x0, mark(x1), x2)
744.35/263.14	   U31(x0, x1, mark(x2))
744.35/263.14	   U31(active(x0), x1, x2)
744.35/263.14	   U31(x0, active(x1), x2)
744.35/263.14	   U31(x0, x1, active(x2))
744.35/263.14	   U32(mark(x0), x1, x2)
744.35/263.14	   U32(x0, mark(x1), x2)
744.35/263.14	   U32(x0, x1, mark(x2))
744.35/263.14	   U32(active(x0), x1, x2)
744.35/263.14	   U32(x0, active(x1), x2)
744.35/263.14	   U32(x0, x1, active(x2))
744.35/263.14	   U33(mark(x0), x1, x2)
744.35/263.14	   U33(x0, mark(x1), x2)
744.35/263.14	   U33(x0, x1, mark(x2))
744.35/263.14	   U33(active(x0), x1, x2)
744.35/263.14	   U33(x0, active(x1), x2)
744.35/263.14	   U33(x0, x1, active(x2))
744.35/263.14	   U34(mark(x0), x1, x2)
744.35/263.14	   U34(x0, mark(x1), x2)
744.35/263.14	   U34(x0, x1, mark(x2))
744.35/263.14	   U34(active(x0), x1, x2)
744.35/263.14	   U34(x0, active(x1), x2)
744.35/263.14	   U34(x0, x1, active(x2))
744.35/263.14	   U35(mark(x0), x1)
744.35/263.14	   U35(x0, mark(x1))
744.35/263.14	   U35(active(x0), x1)
744.35/263.14	   U35(x0, active(x1))
744.35/263.14	   U36(mark(x0))
744.35/263.14	   U36(active(x0))
744.35/263.14	   U41(mark(x0), x1)
744.35/263.14	   U41(x0, mark(x1))
744.35/263.14	   U41(active(x0), x1)
744.35/263.14	   U41(x0, active(x1))
744.35/263.14	   U42(mark(x0))
744.35/263.14	   U42(active(x0))
744.35/263.14	   U51(mark(x0))
744.35/263.14	   U51(active(x0))
744.35/263.14	   U61(mark(x0), x1)
744.35/263.14	   U61(x0, mark(x1))
744.35/263.14	   U61(active(x0), x1)
744.35/263.14	   U61(x0, active(x1))
744.35/263.14	   U62(mark(x0))
744.35/263.14	   U62(active(x0))
744.35/263.14	   U71(mark(x0), x1)
744.35/263.14	   U71(x0, mark(x1))
744.35/263.14	   U71(active(x0), x1)
744.35/263.14	   U71(x0, active(x1))
744.35/263.14	   U72(mark(x0), x1)
744.35/263.14	   U72(x0, mark(x1))
744.35/263.14	   U72(active(x0), x1)
744.35/263.14	   U72(x0, active(x1))
744.35/263.14	   U81(mark(x0), x1, x2)
744.35/263.14	   U81(x0, mark(x1), x2)
744.35/263.14	   U81(x0, x1, mark(x2))
744.35/263.14	   U81(active(x0), x1, x2)
744.35/263.14	   U81(x0, active(x1), x2)
744.35/263.14	   U81(x0, x1, active(x2))
744.35/263.14	   U82(mark(x0), x1, x2)
744.35/263.14	   U82(x0, mark(x1), x2)
744.35/263.14	   U82(x0, x1, mark(x2))
744.35/263.14	   U82(active(x0), x1, x2)
744.35/263.14	   U82(x0, active(x1), x2)
744.35/263.14	   U82(x0, x1, active(x2))
744.35/263.14	   U83(mark(x0), x1, x2)
744.35/263.14	   U83(x0, mark(x1), x2)
744.35/263.14	   U83(x0, x1, mark(x2))
744.35/263.14	   U83(active(x0), x1, x2)
744.35/263.14	   U83(x0, active(x1), x2)
744.35/263.14	   U83(x0, x1, active(x2))
744.35/263.14	   U84(mark(x0), x1, x2)
744.35/263.14	   U84(x0, mark(x1), x2)
744.35/263.14	   U84(x0, x1, mark(x2))
744.35/263.14	   U84(active(x0), x1, x2)
744.35/263.14	   U84(x0, active(x1), x2)
744.35/263.14	   U84(x0, x1, active(x2))
744.35/263.14	   s(mark(x0))
744.35/263.14	   s(active(x0))
744.35/263.14	   U91(mark(x0), x1)
744.35/263.14	   U91(x0, mark(x1))
744.35/263.14	   U91(active(x0), x1)
744.35/263.14	   U91(x0, active(x1))
744.35/263.14	   U92(mark(x0))
744.35/263.14	   U92(active(x0))
744.35/263.14	
744.35/263.14	We have to consider all minimal (P,Q,R)-chains.
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(359) QDPOrderProof (EQUIVALENT)
744.35/263.14	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.14	
744.35/263.14	
744.35/263.14	The following pairs can be oriented strictly and are deleted.
744.35/263.14	
744.35/263.14	   MARK(U42(X)) -> MARK(X)
744.35/263.14	The remaining pairs can at least be oriented weakly.
744.35/263.14	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.14	
744.35/263.14	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.35/263.14	POL( U11_3(x_1, ..., x_3) ) = 1
744.35/263.14	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.14	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.14	POL( U14_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.14	POL( U21_2(x_1, x_2) ) = 2x_1 + 1
744.35/263.14	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.35/263.14	POL( mark_1(x_1) ) = max{0, x_1 - 2}
744.35/263.14	POL( U102_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_2 + 2x_3 - 2}
744.35/263.14	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.35/263.14	POL( U101_3(x_1, ..., x_3) ) = max{0, x_3 - 2}
744.35/263.14	POL( tt ) = 1
744.35/263.14	POL( isNatKind_1(x_1) ) = 0
744.35/263.14	POL( U103_3(x_1, ..., x_3) ) = max{0, 2x_2 + x_3 - 2}
744.35/263.14	POL( isNat_1(x_1) ) = 0
744.35/263.14	POL( U104_3(x_1, ..., x_3) ) = max{0, 2x_2 + x_3 - 2}
744.35/263.14	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.14	POL( x_2(x_1, x_2) ) = x_1 + 2
744.35/263.14	POL( U15_2(x_1, x_2) ) = x_1 + 1
744.35/263.14	POL( U16_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.14	POL( U23_1(x_1) ) = 2x_1 + 1
744.35/263.14	POL( U31_3(x_1, ..., x_3) ) = 2x_1 + 2
744.35/263.14	POL( U32_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.35/263.14	POL( U33_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.35/263.14	POL( U34_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 + x_3 - 2}
744.35/263.14	POL( U35_2(x_1, x_2) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.14	POL( U36_1(x_1) ) = max{0, x_1 - 2}
744.35/263.14	POL( U41_2(x_1, x_2) ) = 2x_1 + 1
744.35/263.14	POL( U42_1(x_1) ) = 2x_1 + 2
744.35/263.14	POL( U61_2(x_1, x_2) ) = 2
744.35/263.14	POL( U62_1(x_1) ) = 2
744.35/263.14	POL( U71_2(x_1, x_2) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.14	POL( U72_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.14	POL( U81_3(x_1, ..., x_3) ) = max{0, 2x_1 + x_2 + x_3 - 2}
744.35/263.14	POL( U82_3(x_1, ..., x_3) ) = 2
744.35/263.14	POL( U83_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2}
744.35/263.14	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.14	POL( s_1(x_1) ) = 0
744.35/263.14	POL( U91_2(x_1, x_2) ) = 2
744.35/263.14	POL( U92_1(x_1) ) = max{0, -2}
744.35/263.14	POL( U51_1(x_1) ) = 2x_1 + 1
744.35/263.14	POL( 0 ) = 0
744.35/263.14	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.35/263.14	
744.35/263.14	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.14	none
744.35/263.14	
744.35/263.14	
744.35/263.14	----------------------------------------
744.35/263.14	
744.35/263.14	(360)
744.35/263.14	Obligation:
744.35/263.14	Q DP problem:
744.35/263.14	The TRS P consists of the following rules:
744.35/263.14	
744.35/263.14	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.14	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.14	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.14	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.14	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.14	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.14	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.14	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.14	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.14	   MARK(U23(X)) -> MARK(X)
744.35/263.14	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.14	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.14	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.14	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.14	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.14	   MARK(U51(X)) -> MARK(X)
744.35/263.14	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.14	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.14	
744.35/263.14	The TRS R consists of the following rules:
744.35/263.14	
744.35/263.14	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.14	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.14	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.14	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.14	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.14	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.14	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.14	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.14	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.14	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.14	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.14	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.14	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.14	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.14	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.14	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.14	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.14	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.14	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.14	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.14	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.14	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.14	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.14	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.14	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.14	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.14	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.14	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.14	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.14	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.14	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.14	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.14	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.14	   active(U72(tt, N)) -> mark(N)
744.35/263.14	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.14	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.14	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.14	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.14	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.14	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.14	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.14	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.14	   mark(s(X)) -> active(s(mark(X)))
744.35/263.14	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.14	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.14	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.14	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.14	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.14	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.14	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.14	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.14	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.14	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.14	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.14	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.14	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.14	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.14	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.14	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.14	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.14	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.14	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.14	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.14	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.14	   mark(isNat(X)) -> active(isNat(X))
744.35/263.14	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.14	   mark(tt) -> active(tt)
744.35/263.14	   mark(0) -> active(0)
744.35/263.14	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.14	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.14	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.14	   active(U16(tt)) -> mark(tt)
744.35/263.14	   active(U23(tt)) -> mark(tt)
744.35/263.14	   active(U36(tt)) -> mark(tt)
744.35/263.14	   active(U42(tt)) -> mark(tt)
744.35/263.14	   active(U51(tt)) -> mark(tt)
744.35/263.14	   active(U62(tt)) -> mark(tt)
744.35/263.14	   active(U92(tt)) -> mark(0)
744.35/263.14	   active(isNat(0)) -> mark(tt)
744.35/263.14	   active(isNatKind(0)) -> mark(tt)
744.35/263.14	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.14	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.14	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.14	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.15	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.15	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.15	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.15	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.15	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.15	   U16(active(X)) -> U16(X)
744.35/263.15	   U16(mark(X)) -> U16(X)
744.35/263.15	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.15	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.15	   U23(active(X)) -> U23(X)
744.35/263.15	   U23(mark(X)) -> U23(X)
744.35/263.15	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.15	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.15	   U36(active(X)) -> U36(X)
744.35/263.15	   U36(mark(X)) -> U36(X)
744.35/263.15	   U42(active(X)) -> U42(X)
744.35/263.15	   U42(mark(X)) -> U42(X)
744.35/263.15	   U62(active(X)) -> U62(X)
744.35/263.15	   U62(mark(X)) -> U62(X)
744.35/263.15	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.15	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.15	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.15	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.15	   s(active(X)) -> s(X)
744.35/263.15	   s(mark(X)) -> s(X)
744.35/263.15	   U92(active(X)) -> U92(X)
744.35/263.15	   U92(mark(X)) -> U92(X)
744.35/263.15	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.15	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.15	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.15	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.15	   U51(active(X)) -> U51(X)
744.35/263.15	   U51(mark(X)) -> U51(X)
744.35/263.15	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.15	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.15	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.15	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.15	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.15	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.15	   x(active(X1), X2) -> x(X1, X2)
744.35/263.15	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.15	
744.35/263.15	The set Q consists of the following terms:
744.35/263.15	
744.35/263.15	   active(U101(tt, x0, x1))
744.35/263.15	   active(U102(tt, x0, x1))
744.35/263.15	   active(U103(tt, x0, x1))
744.35/263.15	   active(U104(tt, x0, x1))
744.35/263.15	   active(U11(tt, x0, x1))
744.35/263.15	   active(U12(tt, x0, x1))
744.35/263.15	   active(U13(tt, x0, x1))
744.35/263.15	   active(U14(tt, x0, x1))
744.35/263.15	   active(U15(tt, x0))
744.35/263.15	   active(U16(tt))
744.35/263.15	   active(U21(tt, x0))
744.35/263.15	   active(U22(tt, x0))
744.35/263.15	   active(U23(tt))
744.35/263.15	   active(U31(tt, x0, x1))
744.35/263.15	   active(U32(tt, x0, x1))
744.35/263.15	   active(U33(tt, x0, x1))
744.35/263.15	   active(U34(tt, x0, x1))
744.35/263.15	   active(U35(tt, x0))
744.35/263.15	   active(U36(tt))
744.35/263.15	   active(U41(tt, x0))
744.35/263.15	   active(U42(tt))
744.35/263.15	   active(U51(tt))
744.35/263.15	   active(U61(tt, x0))
744.35/263.15	   active(U62(tt))
744.35/263.15	   active(U71(tt, x0))
744.35/263.15	   active(U72(tt, x0))
744.35/263.15	   active(U81(tt, x0, x1))
744.35/263.15	   active(U82(tt, x0, x1))
744.35/263.15	   active(U83(tt, x0, x1))
744.35/263.15	   active(U84(tt, x0, x1))
744.35/263.15	   active(U91(tt, x0))
744.35/263.15	   active(U92(tt))
744.35/263.15	   active(isNat(0))
744.35/263.15	   active(isNat(plus(x0, x1)))
744.35/263.15	   active(isNat(s(x0)))
744.35/263.15	   active(isNat(x(x0, x1)))
744.35/263.15	   active(isNatKind(0))
744.35/263.15	   active(isNatKind(plus(x0, x1)))
744.35/263.15	   active(isNatKind(s(x0)))
744.35/263.15	   active(isNatKind(x(x0, x1)))
744.35/263.15	   active(plus(x0, 0))
744.35/263.15	   active(plus(x0, s(x1)))
744.35/263.15	   active(x(x0, 0))
744.35/263.15	   active(x(x0, s(x1)))
744.35/263.15	   mark(U101(x0, x1, x2))
744.35/263.15	   mark(tt)
744.35/263.15	   mark(U102(x0, x1, x2))
744.35/263.15	   mark(isNatKind(x0))
744.35/263.15	   mark(U103(x0, x1, x2))
744.35/263.15	   mark(isNat(x0))
744.35/263.15	   mark(U104(x0, x1, x2))
744.35/263.15	   mark(plus(x0, x1))
744.35/263.15	   mark(x(x0, x1))
744.35/263.15	   mark(U11(x0, x1, x2))
744.35/263.15	   mark(U12(x0, x1, x2))
744.35/263.15	   mark(U13(x0, x1, x2))
744.35/263.15	   mark(U14(x0, x1, x2))
744.35/263.15	   mark(U15(x0, x1))
744.35/263.15	   mark(U16(x0))
744.35/263.15	   mark(U21(x0, x1))
744.35/263.15	   mark(U22(x0, x1))
744.35/263.15	   mark(U23(x0))
744.35/263.15	   mark(U31(x0, x1, x2))
744.35/263.15	   mark(U32(x0, x1, x2))
744.35/263.15	   mark(U33(x0, x1, x2))
744.35/263.15	   mark(U34(x0, x1, x2))
744.35/263.15	   mark(U35(x0, x1))
744.35/263.15	   mark(U36(x0))
744.35/263.15	   mark(U41(x0, x1))
744.35/263.15	   mark(U42(x0))
744.35/263.15	   mark(U51(x0))
744.35/263.15	   mark(U61(x0, x1))
744.35/263.15	   mark(U62(x0))
744.35/263.15	   mark(U71(x0, x1))
744.35/263.15	   mark(U72(x0, x1))
744.35/263.15	   mark(U81(x0, x1, x2))
744.35/263.15	   mark(U82(x0, x1, x2))
744.35/263.15	   mark(U83(x0, x1, x2))
744.35/263.15	   mark(U84(x0, x1, x2))
744.35/263.15	   mark(s(x0))
744.35/263.15	   mark(U91(x0, x1))
744.35/263.15	   mark(U92(x0))
744.35/263.15	   mark(0)
744.35/263.15	   U101(mark(x0), x1, x2)
744.35/263.15	   U101(x0, mark(x1), x2)
744.35/263.15	   U101(x0, x1, mark(x2))
744.35/263.15	   U101(active(x0), x1, x2)
744.35/263.15	   U101(x0, active(x1), x2)
744.35/263.15	   U101(x0, x1, active(x2))
744.35/263.15	   U102(mark(x0), x1, x2)
744.35/263.15	   U102(x0, mark(x1), x2)
744.35/263.15	   U102(x0, x1, mark(x2))
744.35/263.15	   U102(active(x0), x1, x2)
744.35/263.15	   U102(x0, active(x1), x2)
744.35/263.15	   U102(x0, x1, active(x2))
744.35/263.15	   isNatKind(mark(x0))
744.35/263.15	   isNatKind(active(x0))
744.35/263.15	   U103(mark(x0), x1, x2)
744.35/263.15	   U103(x0, mark(x1), x2)
744.35/263.15	   U103(x0, x1, mark(x2))
744.35/263.15	   U103(active(x0), x1, x2)
744.35/263.15	   U103(x0, active(x1), x2)
744.35/263.15	   U103(x0, x1, active(x2))
744.35/263.15	   isNat(mark(x0))
744.35/263.15	   isNat(active(x0))
744.35/263.15	   U104(mark(x0), x1, x2)
744.35/263.15	   U104(x0, mark(x1), x2)
744.35/263.15	   U104(x0, x1, mark(x2))
744.35/263.15	   U104(active(x0), x1, x2)
744.35/263.15	   U104(x0, active(x1), x2)
744.35/263.15	   U104(x0, x1, active(x2))
744.35/263.15	   plus(mark(x0), x1)
744.35/263.15	   plus(x0, mark(x1))
744.35/263.15	   plus(active(x0), x1)
744.35/263.15	   plus(x0, active(x1))
744.35/263.15	   x(mark(x0), x1)
744.35/263.15	   x(x0, mark(x1))
744.35/263.15	   x(active(x0), x1)
744.35/263.15	   x(x0, active(x1))
744.35/263.15	   U11(mark(x0), x1, x2)
744.35/263.15	   U11(x0, mark(x1), x2)
744.35/263.15	   U11(x0, x1, mark(x2))
744.35/263.15	   U11(active(x0), x1, x2)
744.35/263.15	   U11(x0, active(x1), x2)
744.35/263.15	   U11(x0, x1, active(x2))
744.35/263.15	   U12(mark(x0), x1, x2)
744.35/263.15	   U12(x0, mark(x1), x2)
744.35/263.15	   U12(x0, x1, mark(x2))
744.35/263.15	   U12(active(x0), x1, x2)
744.35/263.15	   U12(x0, active(x1), x2)
744.35/263.15	   U12(x0, x1, active(x2))
744.35/263.15	   U13(mark(x0), x1, x2)
744.35/263.15	   U13(x0, mark(x1), x2)
744.35/263.15	   U13(x0, x1, mark(x2))
744.35/263.15	   U13(active(x0), x1, x2)
744.35/263.15	   U13(x0, active(x1), x2)
744.35/263.15	   U13(x0, x1, active(x2))
744.35/263.15	   U14(mark(x0), x1, x2)
744.35/263.15	   U14(x0, mark(x1), x2)
744.35/263.15	   U14(x0, x1, mark(x2))
744.35/263.15	   U14(active(x0), x1, x2)
744.35/263.15	   U14(x0, active(x1), x2)
744.35/263.15	   U14(x0, x1, active(x2))
744.35/263.15	   U15(mark(x0), x1)
744.35/263.15	   U15(x0, mark(x1))
744.35/263.15	   U15(active(x0), x1)
744.35/263.15	   U15(x0, active(x1))
744.35/263.15	   U16(mark(x0))
744.35/263.15	   U16(active(x0))
744.35/263.15	   U21(mark(x0), x1)
744.35/263.15	   U21(x0, mark(x1))
744.35/263.15	   U21(active(x0), x1)
744.35/263.15	   U21(x0, active(x1))
744.35/263.15	   U22(mark(x0), x1)
744.35/263.15	   U22(x0, mark(x1))
744.35/263.15	   U22(active(x0), x1)
744.35/263.15	   U22(x0, active(x1))
744.35/263.15	   U23(mark(x0))
744.35/263.15	   U23(active(x0))
744.35/263.15	   U31(mark(x0), x1, x2)
744.35/263.15	   U31(x0, mark(x1), x2)
744.35/263.15	   U31(x0, x1, mark(x2))
744.35/263.15	   U31(active(x0), x1, x2)
744.35/263.15	   U31(x0, active(x1), x2)
744.35/263.15	   U31(x0, x1, active(x2))
744.35/263.15	   U32(mark(x0), x1, x2)
744.35/263.15	   U32(x0, mark(x1), x2)
744.35/263.15	   U32(x0, x1, mark(x2))
744.35/263.15	   U32(active(x0), x1, x2)
744.35/263.15	   U32(x0, active(x1), x2)
744.35/263.15	   U32(x0, x1, active(x2))
744.35/263.15	   U33(mark(x0), x1, x2)
744.35/263.15	   U33(x0, mark(x1), x2)
744.35/263.15	   U33(x0, x1, mark(x2))
744.35/263.15	   U33(active(x0), x1, x2)
744.35/263.15	   U33(x0, active(x1), x2)
744.35/263.15	   U33(x0, x1, active(x2))
744.35/263.15	   U34(mark(x0), x1, x2)
744.35/263.15	   U34(x0, mark(x1), x2)
744.35/263.15	   U34(x0, x1, mark(x2))
744.35/263.15	   U34(active(x0), x1, x2)
744.35/263.15	   U34(x0, active(x1), x2)
744.35/263.15	   U34(x0, x1, active(x2))
744.35/263.15	   U35(mark(x0), x1)
744.35/263.15	   U35(x0, mark(x1))
744.35/263.15	   U35(active(x0), x1)
744.35/263.15	   U35(x0, active(x1))
744.35/263.15	   U36(mark(x0))
744.35/263.15	   U36(active(x0))
744.35/263.15	   U41(mark(x0), x1)
744.35/263.15	   U41(x0, mark(x1))
744.35/263.15	   U41(active(x0), x1)
744.35/263.15	   U41(x0, active(x1))
744.35/263.15	   U42(mark(x0))
744.35/263.15	   U42(active(x0))
744.35/263.15	   U51(mark(x0))
744.35/263.15	   U51(active(x0))
744.35/263.15	   U61(mark(x0), x1)
744.35/263.15	   U61(x0, mark(x1))
744.35/263.15	   U61(active(x0), x1)
744.35/263.15	   U61(x0, active(x1))
744.35/263.15	   U62(mark(x0))
744.35/263.15	   U62(active(x0))
744.35/263.15	   U71(mark(x0), x1)
744.35/263.15	   U71(x0, mark(x1))
744.35/263.15	   U71(active(x0), x1)
744.35/263.15	   U71(x0, active(x1))
744.35/263.15	   U72(mark(x0), x1)
744.35/263.15	   U72(x0, mark(x1))
744.35/263.15	   U72(active(x0), x1)
744.35/263.15	   U72(x0, active(x1))
744.35/263.15	   U81(mark(x0), x1, x2)
744.35/263.15	   U81(x0, mark(x1), x2)
744.35/263.15	   U81(x0, x1, mark(x2))
744.35/263.15	   U81(active(x0), x1, x2)
744.35/263.15	   U81(x0, active(x1), x2)
744.35/263.15	   U81(x0, x1, active(x2))
744.35/263.15	   U82(mark(x0), x1, x2)
744.35/263.15	   U82(x0, mark(x1), x2)
744.35/263.15	   U82(x0, x1, mark(x2))
744.35/263.15	   U82(active(x0), x1, x2)
744.35/263.15	   U82(x0, active(x1), x2)
744.35/263.15	   U82(x0, x1, active(x2))
744.35/263.15	   U83(mark(x0), x1, x2)
744.35/263.15	   U83(x0, mark(x1), x2)
744.35/263.15	   U83(x0, x1, mark(x2))
744.35/263.15	   U83(active(x0), x1, x2)
744.35/263.15	   U83(x0, active(x1), x2)
744.35/263.15	   U83(x0, x1, active(x2))
744.35/263.15	   U84(mark(x0), x1, x2)
744.35/263.15	   U84(x0, mark(x1), x2)
744.35/263.15	   U84(x0, x1, mark(x2))
744.35/263.15	   U84(active(x0), x1, x2)
744.35/263.15	   U84(x0, active(x1), x2)
744.35/263.15	   U84(x0, x1, active(x2))
744.35/263.15	   s(mark(x0))
744.35/263.15	   s(active(x0))
744.35/263.15	   U91(mark(x0), x1)
744.35/263.15	   U91(x0, mark(x1))
744.35/263.15	   U91(active(x0), x1)
744.35/263.15	   U91(x0, active(x1))
744.35/263.15	   U92(mark(x0))
744.35/263.15	   U92(active(x0))
744.35/263.15	
744.35/263.15	We have to consider all minimal (P,Q,R)-chains.
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(361) QDPOrderProof (EQUIVALENT)
744.35/263.15	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.15	
744.35/263.15	
744.35/263.15	The following pairs can be oriented strictly and are deleted.
744.35/263.15	
744.35/263.15	   ACTIVE(isNatKind(plus(V1, V2))) -> MARK(U41(isNatKind(V1), V2))
744.35/263.15	   ACTIVE(isNatKind(s(V1))) -> MARK(U51(isNatKind(V1)))
744.35/263.15	The remaining pairs can at least be oriented weakly.
744.35/263.15	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.15	
744.35/263.15	POL( ACTIVE_1(x_1) ) = max{0, x_1 - 2}
744.35/263.15	POL( U11_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.15	POL( U12_3(x_1, ..., x_3) ) = 2
744.35/263.15	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.15	POL( U14_3(x_1, ..., x_3) ) = 2
744.35/263.15	POL( U21_2(x_1, x_2) ) = max{0, -2}
744.35/263.15	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.35/263.15	POL( mark_1(x_1) ) = max{0, 2x_1 - 2}
744.35/263.15	POL( U102_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.35/263.15	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.35/263.15	POL( U101_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + x_3 - 2}
744.35/263.15	POL( tt ) = 2
744.35/263.15	POL( isNatKind_1(x_1) ) = 2x_1 + 2
744.35/263.15	POL( U103_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.35/263.15	POL( isNat_1(x_1) ) = 0
744.35/263.15	POL( U104_3(x_1, ..., x_3) ) = 2
744.35/263.15	POL( plus_2(x_1, x_2) ) = 2x_1 + 2x_2 + 2
744.35/263.15	POL( x_2(x_1, x_2) ) = max{0, x_1 - 2}
744.35/263.15	POL( U15_2(x_1, x_2) ) = 2x_1 + 2
744.35/263.15	POL( U16_1(x_1) ) = 0
744.35/263.15	POL( U23_1(x_1) ) = 2x_1 + 2
744.35/263.15	POL( U31_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.35/263.15	POL( U32_3(x_1, ..., x_3) ) = 2x_1 + 2
744.35/263.15	POL( U33_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.15	POL( U34_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.15	POL( U35_2(x_1, x_2) ) = 2
744.35/263.15	POL( U36_1(x_1) ) = max{0, -2}
744.35/263.15	POL( U41_2(x_1, x_2) ) = x_1 + x_2 + 2
744.35/263.15	POL( U42_1(x_1) ) = 1
744.35/263.15	POL( U61_2(x_1, x_2) ) = max{0, x_2 - 2}
744.35/263.15	POL( U62_1(x_1) ) = max{0, x_1 - 2}
744.35/263.15	POL( U71_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.15	POL( U72_2(x_1, x_2) ) = max{0, -2}
744.35/263.15	POL( U81_3(x_1, ..., x_3) ) = 2
744.35/263.15	POL( U82_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + x_3 - 1}
744.35/263.15	POL( U83_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.15	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.35/263.15	POL( s_1(x_1) ) = x_1 + 2
744.35/263.15	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.35/263.15	POL( U92_1(x_1) ) = 2x_1 + 1
744.35/263.15	POL( U51_1(x_1) ) = x_1 + 2
744.35/263.15	POL( 0 ) = 0
744.35/263.15	POL( MARK_1(x_1) ) = max{0, x_1 - 2}
744.35/263.15	
744.35/263.15	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.15	
744.35/263.15	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.15	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.15	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.15	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.15	
744.35/263.15	
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(362)
744.35/263.15	Obligation:
744.35/263.15	Q DP problem:
744.35/263.15	The TRS P consists of the following rules:
744.35/263.15	
744.35/263.15	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.15	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.15	   MARK(isNatKind(X)) -> ACTIVE(isNatKind(X))
744.35/263.15	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.15	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.15	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.15	   MARK(U23(X)) -> MARK(X)
744.35/263.15	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.15	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.15	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.15	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.15	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.15	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.15	   MARK(U51(X)) -> MARK(X)
744.35/263.15	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.15	
744.35/263.15	The TRS R consists of the following rules:
744.35/263.15	
744.35/263.15	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.15	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.15	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.15	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.15	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.15	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.15	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.15	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.15	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.15	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.15	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.15	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.15	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.15	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.15	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.15	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.15	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.15	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.15	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.15	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.15	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.15	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.15	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.15	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.15	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.15	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.15	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.15	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.15	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.15	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.15	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.15	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.15	   active(U72(tt, N)) -> mark(N)
744.35/263.15	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.15	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.15	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.15	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.15	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.15	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.15	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.15	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.15	   mark(s(X)) -> active(s(mark(X)))
744.35/263.15	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.15	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.15	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.15	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.15	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.15	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.15	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.15	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.15	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.15	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.15	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.15	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.15	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.15	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.15	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.15	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.15	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.15	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.15	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.15	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.15	   mark(isNat(X)) -> active(isNat(X))
744.35/263.15	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.15	   mark(tt) -> active(tt)
744.35/263.15	   mark(0) -> active(0)
744.35/263.15	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.15	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.15	   active(U16(tt)) -> mark(tt)
744.35/263.15	   active(U23(tt)) -> mark(tt)
744.35/263.15	   active(U36(tt)) -> mark(tt)
744.35/263.15	   active(U42(tt)) -> mark(tt)
744.35/263.15	   active(U51(tt)) -> mark(tt)
744.35/263.15	   active(U62(tt)) -> mark(tt)
744.35/263.15	   active(U92(tt)) -> mark(0)
744.35/263.15	   active(isNat(0)) -> mark(tt)
744.35/263.15	   active(isNatKind(0)) -> mark(tt)
744.35/263.15	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.15	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.15	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.15	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.15	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.15	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.15	   U16(active(X)) -> U16(X)
744.35/263.15	   U16(mark(X)) -> U16(X)
744.35/263.15	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.15	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.15	   U23(active(X)) -> U23(X)
744.35/263.15	   U23(mark(X)) -> U23(X)
744.35/263.15	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.15	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.15	   U36(active(X)) -> U36(X)
744.35/263.15	   U36(mark(X)) -> U36(X)
744.35/263.15	   U42(active(X)) -> U42(X)
744.35/263.15	   U42(mark(X)) -> U42(X)
744.35/263.15	   U62(active(X)) -> U62(X)
744.35/263.15	   U62(mark(X)) -> U62(X)
744.35/263.15	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.15	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.15	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.15	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.15	   s(active(X)) -> s(X)
744.35/263.15	   s(mark(X)) -> s(X)
744.35/263.15	   U92(active(X)) -> U92(X)
744.35/263.15	   U92(mark(X)) -> U92(X)
744.35/263.15	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.15	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.15	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.15	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.15	   U51(active(X)) -> U51(X)
744.35/263.15	   U51(mark(X)) -> U51(X)
744.35/263.15	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.15	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.15	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.15	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.15	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.15	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.15	   x(active(X1), X2) -> x(X1, X2)
744.35/263.15	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.15	
744.35/263.15	The set Q consists of the following terms:
744.35/263.15	
744.35/263.15	   active(U101(tt, x0, x1))
744.35/263.15	   active(U102(tt, x0, x1))
744.35/263.15	   active(U103(tt, x0, x1))
744.35/263.15	   active(U104(tt, x0, x1))
744.35/263.15	   active(U11(tt, x0, x1))
744.35/263.15	   active(U12(tt, x0, x1))
744.35/263.15	   active(U13(tt, x0, x1))
744.35/263.15	   active(U14(tt, x0, x1))
744.35/263.15	   active(U15(tt, x0))
744.35/263.15	   active(U16(tt))
744.35/263.15	   active(U21(tt, x0))
744.35/263.15	   active(U22(tt, x0))
744.35/263.15	   active(U23(tt))
744.35/263.15	   active(U31(tt, x0, x1))
744.35/263.15	   active(U32(tt, x0, x1))
744.35/263.15	   active(U33(tt, x0, x1))
744.35/263.15	   active(U34(tt, x0, x1))
744.35/263.15	   active(U35(tt, x0))
744.35/263.15	   active(U36(tt))
744.35/263.15	   active(U41(tt, x0))
744.35/263.15	   active(U42(tt))
744.35/263.15	   active(U51(tt))
744.35/263.15	   active(U61(tt, x0))
744.35/263.15	   active(U62(tt))
744.35/263.15	   active(U71(tt, x0))
744.35/263.15	   active(U72(tt, x0))
744.35/263.15	   active(U81(tt, x0, x1))
744.35/263.15	   active(U82(tt, x0, x1))
744.35/263.15	   active(U83(tt, x0, x1))
744.35/263.15	   active(U84(tt, x0, x1))
744.35/263.15	   active(U91(tt, x0))
744.35/263.15	   active(U92(tt))
744.35/263.15	   active(isNat(0))
744.35/263.15	   active(isNat(plus(x0, x1)))
744.35/263.15	   active(isNat(s(x0)))
744.35/263.15	   active(isNat(x(x0, x1)))
744.35/263.15	   active(isNatKind(0))
744.35/263.15	   active(isNatKind(plus(x0, x1)))
744.35/263.15	   active(isNatKind(s(x0)))
744.35/263.15	   active(isNatKind(x(x0, x1)))
744.35/263.15	   active(plus(x0, 0))
744.35/263.15	   active(plus(x0, s(x1)))
744.35/263.15	   active(x(x0, 0))
744.35/263.15	   active(x(x0, s(x1)))
744.35/263.15	   mark(U101(x0, x1, x2))
744.35/263.15	   mark(tt)
744.35/263.15	   mark(U102(x0, x1, x2))
744.35/263.15	   mark(isNatKind(x0))
744.35/263.15	   mark(U103(x0, x1, x2))
744.35/263.15	   mark(isNat(x0))
744.35/263.15	   mark(U104(x0, x1, x2))
744.35/263.15	   mark(plus(x0, x1))
744.35/263.15	   mark(x(x0, x1))
744.35/263.15	   mark(U11(x0, x1, x2))
744.35/263.15	   mark(U12(x0, x1, x2))
744.35/263.15	   mark(U13(x0, x1, x2))
744.35/263.15	   mark(U14(x0, x1, x2))
744.35/263.15	   mark(U15(x0, x1))
744.35/263.15	   mark(U16(x0))
744.35/263.15	   mark(U21(x0, x1))
744.35/263.15	   mark(U22(x0, x1))
744.35/263.15	   mark(U23(x0))
744.35/263.15	   mark(U31(x0, x1, x2))
744.35/263.15	   mark(U32(x0, x1, x2))
744.35/263.15	   mark(U33(x0, x1, x2))
744.35/263.15	   mark(U34(x0, x1, x2))
744.35/263.15	   mark(U35(x0, x1))
744.35/263.15	   mark(U36(x0))
744.35/263.15	   mark(U41(x0, x1))
744.35/263.15	   mark(U42(x0))
744.35/263.15	   mark(U51(x0))
744.35/263.15	   mark(U61(x0, x1))
744.35/263.15	   mark(U62(x0))
744.35/263.15	   mark(U71(x0, x1))
744.35/263.15	   mark(U72(x0, x1))
744.35/263.15	   mark(U81(x0, x1, x2))
744.35/263.15	   mark(U82(x0, x1, x2))
744.35/263.15	   mark(U83(x0, x1, x2))
744.35/263.15	   mark(U84(x0, x1, x2))
744.35/263.15	   mark(s(x0))
744.35/263.15	   mark(U91(x0, x1))
744.35/263.15	   mark(U92(x0))
744.35/263.15	   mark(0)
744.35/263.15	   U101(mark(x0), x1, x2)
744.35/263.15	   U101(x0, mark(x1), x2)
744.35/263.15	   U101(x0, x1, mark(x2))
744.35/263.15	   U101(active(x0), x1, x2)
744.35/263.15	   U101(x0, active(x1), x2)
744.35/263.15	   U101(x0, x1, active(x2))
744.35/263.15	   U102(mark(x0), x1, x2)
744.35/263.15	   U102(x0, mark(x1), x2)
744.35/263.15	   U102(x0, x1, mark(x2))
744.35/263.15	   U102(active(x0), x1, x2)
744.35/263.15	   U102(x0, active(x1), x2)
744.35/263.15	   U102(x0, x1, active(x2))
744.35/263.15	   isNatKind(mark(x0))
744.35/263.15	   isNatKind(active(x0))
744.35/263.15	   U103(mark(x0), x1, x2)
744.35/263.15	   U103(x0, mark(x1), x2)
744.35/263.15	   U103(x0, x1, mark(x2))
744.35/263.15	   U103(active(x0), x1, x2)
744.35/263.15	   U103(x0, active(x1), x2)
744.35/263.15	   U103(x0, x1, active(x2))
744.35/263.15	   isNat(mark(x0))
744.35/263.15	   isNat(active(x0))
744.35/263.15	   U104(mark(x0), x1, x2)
744.35/263.15	   U104(x0, mark(x1), x2)
744.35/263.15	   U104(x0, x1, mark(x2))
744.35/263.15	   U104(active(x0), x1, x2)
744.35/263.15	   U104(x0, active(x1), x2)
744.35/263.15	   U104(x0, x1, active(x2))
744.35/263.15	   plus(mark(x0), x1)
744.35/263.15	   plus(x0, mark(x1))
744.35/263.15	   plus(active(x0), x1)
744.35/263.15	   plus(x0, active(x1))
744.35/263.15	   x(mark(x0), x1)
744.35/263.15	   x(x0, mark(x1))
744.35/263.15	   x(active(x0), x1)
744.35/263.15	   x(x0, active(x1))
744.35/263.15	   U11(mark(x0), x1, x2)
744.35/263.15	   U11(x0, mark(x1), x2)
744.35/263.15	   U11(x0, x1, mark(x2))
744.35/263.15	   U11(active(x0), x1, x2)
744.35/263.15	   U11(x0, active(x1), x2)
744.35/263.15	   U11(x0, x1, active(x2))
744.35/263.15	   U12(mark(x0), x1, x2)
744.35/263.15	   U12(x0, mark(x1), x2)
744.35/263.15	   U12(x0, x1, mark(x2))
744.35/263.15	   U12(active(x0), x1, x2)
744.35/263.15	   U12(x0, active(x1), x2)
744.35/263.15	   U12(x0, x1, active(x2))
744.35/263.15	   U13(mark(x0), x1, x2)
744.35/263.15	   U13(x0, mark(x1), x2)
744.35/263.15	   U13(x0, x1, mark(x2))
744.35/263.15	   U13(active(x0), x1, x2)
744.35/263.15	   U13(x0, active(x1), x2)
744.35/263.15	   U13(x0, x1, active(x2))
744.35/263.15	   U14(mark(x0), x1, x2)
744.35/263.15	   U14(x0, mark(x1), x2)
744.35/263.15	   U14(x0, x1, mark(x2))
744.35/263.15	   U14(active(x0), x1, x2)
744.35/263.15	   U14(x0, active(x1), x2)
744.35/263.15	   U14(x0, x1, active(x2))
744.35/263.15	   U15(mark(x0), x1)
744.35/263.15	   U15(x0, mark(x1))
744.35/263.15	   U15(active(x0), x1)
744.35/263.15	   U15(x0, active(x1))
744.35/263.15	   U16(mark(x0))
744.35/263.15	   U16(active(x0))
744.35/263.15	   U21(mark(x0), x1)
744.35/263.15	   U21(x0, mark(x1))
744.35/263.15	   U21(active(x0), x1)
744.35/263.15	   U21(x0, active(x1))
744.35/263.15	   U22(mark(x0), x1)
744.35/263.15	   U22(x0, mark(x1))
744.35/263.15	   U22(active(x0), x1)
744.35/263.15	   U22(x0, active(x1))
744.35/263.15	   U23(mark(x0))
744.35/263.15	   U23(active(x0))
744.35/263.15	   U31(mark(x0), x1, x2)
744.35/263.15	   U31(x0, mark(x1), x2)
744.35/263.15	   U31(x0, x1, mark(x2))
744.35/263.15	   U31(active(x0), x1, x2)
744.35/263.15	   U31(x0, active(x1), x2)
744.35/263.15	   U31(x0, x1, active(x2))
744.35/263.15	   U32(mark(x0), x1, x2)
744.35/263.15	   U32(x0, mark(x1), x2)
744.35/263.15	   U32(x0, x1, mark(x2))
744.35/263.15	   U32(active(x0), x1, x2)
744.35/263.15	   U32(x0, active(x1), x2)
744.35/263.15	   U32(x0, x1, active(x2))
744.35/263.15	   U33(mark(x0), x1, x2)
744.35/263.15	   U33(x0, mark(x1), x2)
744.35/263.15	   U33(x0, x1, mark(x2))
744.35/263.15	   U33(active(x0), x1, x2)
744.35/263.15	   U33(x0, active(x1), x2)
744.35/263.15	   U33(x0, x1, active(x2))
744.35/263.15	   U34(mark(x0), x1, x2)
744.35/263.15	   U34(x0, mark(x1), x2)
744.35/263.15	   U34(x0, x1, mark(x2))
744.35/263.15	   U34(active(x0), x1, x2)
744.35/263.15	   U34(x0, active(x1), x2)
744.35/263.15	   U34(x0, x1, active(x2))
744.35/263.15	   U35(mark(x0), x1)
744.35/263.15	   U35(x0, mark(x1))
744.35/263.15	   U35(active(x0), x1)
744.35/263.15	   U35(x0, active(x1))
744.35/263.15	   U36(mark(x0))
744.35/263.15	   U36(active(x0))
744.35/263.15	   U41(mark(x0), x1)
744.35/263.15	   U41(x0, mark(x1))
744.35/263.15	   U41(active(x0), x1)
744.35/263.15	   U41(x0, active(x1))
744.35/263.15	   U42(mark(x0))
744.35/263.15	   U42(active(x0))
744.35/263.15	   U51(mark(x0))
744.35/263.15	   U51(active(x0))
744.35/263.15	   U61(mark(x0), x1)
744.35/263.15	   U61(x0, mark(x1))
744.35/263.15	   U61(active(x0), x1)
744.35/263.15	   U61(x0, active(x1))
744.35/263.15	   U62(mark(x0))
744.35/263.15	   U62(active(x0))
744.35/263.15	   U71(mark(x0), x1)
744.35/263.15	   U71(x0, mark(x1))
744.35/263.15	   U71(active(x0), x1)
744.35/263.15	   U71(x0, active(x1))
744.35/263.15	   U72(mark(x0), x1)
744.35/263.15	   U72(x0, mark(x1))
744.35/263.15	   U72(active(x0), x1)
744.35/263.15	   U72(x0, active(x1))
744.35/263.15	   U81(mark(x0), x1, x2)
744.35/263.15	   U81(x0, mark(x1), x2)
744.35/263.15	   U81(x0, x1, mark(x2))
744.35/263.15	   U81(active(x0), x1, x2)
744.35/263.15	   U81(x0, active(x1), x2)
744.35/263.15	   U81(x0, x1, active(x2))
744.35/263.15	   U82(mark(x0), x1, x2)
744.35/263.15	   U82(x0, mark(x1), x2)
744.35/263.15	   U82(x0, x1, mark(x2))
744.35/263.15	   U82(active(x0), x1, x2)
744.35/263.15	   U82(x0, active(x1), x2)
744.35/263.15	   U82(x0, x1, active(x2))
744.35/263.15	   U83(mark(x0), x1, x2)
744.35/263.15	   U83(x0, mark(x1), x2)
744.35/263.15	   U83(x0, x1, mark(x2))
744.35/263.15	   U83(active(x0), x1, x2)
744.35/263.15	   U83(x0, active(x1), x2)
744.35/263.15	   U83(x0, x1, active(x2))
744.35/263.15	   U84(mark(x0), x1, x2)
744.35/263.15	   U84(x0, mark(x1), x2)
744.35/263.15	   U84(x0, x1, mark(x2))
744.35/263.15	   U84(active(x0), x1, x2)
744.35/263.15	   U84(x0, active(x1), x2)
744.35/263.15	   U84(x0, x1, active(x2))
744.35/263.15	   s(mark(x0))
744.35/263.15	   s(active(x0))
744.35/263.15	   U91(mark(x0), x1)
744.35/263.15	   U91(x0, mark(x1))
744.35/263.15	   U91(active(x0), x1)
744.35/263.15	   U91(x0, active(x1))
744.35/263.15	   U92(mark(x0))
744.35/263.15	   U92(active(x0))
744.35/263.15	
744.35/263.15	We have to consider all minimal (P,Q,R)-chains.
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(363) DependencyGraphProof (EQUIVALENT)
744.35/263.15	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(364)
744.35/263.15	Obligation:
744.35/263.15	Q DP problem:
744.35/263.15	The TRS P consists of the following rules:
744.35/263.15	
744.35/263.15	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.15	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.15	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.15	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.15	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.15	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.15	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.15	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.15	   MARK(U23(X)) -> MARK(X)
744.35/263.15	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.15	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.15	   MARK(U51(X)) -> MARK(X)
744.35/263.15	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.15	
744.35/263.15	The TRS R consists of the following rules:
744.35/263.15	
744.35/263.15	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.15	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.15	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.15	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.15	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.15	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.15	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.15	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.15	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.15	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.15	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.15	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.15	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.15	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.15	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.15	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.15	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.15	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.15	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.15	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.15	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.15	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.15	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.15	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.15	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.15	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.15	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.15	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.15	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.15	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.15	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.15	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.15	   active(U72(tt, N)) -> mark(N)
744.35/263.15	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.15	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.15	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.15	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.15	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.15	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.15	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.15	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.15	   mark(s(X)) -> active(s(mark(X)))
744.35/263.15	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.15	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.15	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.15	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.15	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.15	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.15	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.15	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.15	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.15	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.15	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.15	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.15	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.15	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.15	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.15	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.15	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.15	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.15	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.15	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.15	   mark(isNat(X)) -> active(isNat(X))
744.35/263.15	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.15	   mark(tt) -> active(tt)
744.35/263.15	   mark(0) -> active(0)
744.35/263.15	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.15	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.15	   active(U16(tt)) -> mark(tt)
744.35/263.15	   active(U23(tt)) -> mark(tt)
744.35/263.15	   active(U36(tt)) -> mark(tt)
744.35/263.15	   active(U42(tt)) -> mark(tt)
744.35/263.15	   active(U51(tt)) -> mark(tt)
744.35/263.15	   active(U62(tt)) -> mark(tt)
744.35/263.15	   active(U92(tt)) -> mark(0)
744.35/263.15	   active(isNat(0)) -> mark(tt)
744.35/263.15	   active(isNatKind(0)) -> mark(tt)
744.35/263.15	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.15	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.15	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.15	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.15	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.35/263.15	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.35/263.15	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.35/263.15	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.35/263.15	   U15(X1, mark(X2)) -> U15(X1, X2)
744.35/263.15	   U15(mark(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(active(X1), X2) -> U15(X1, X2)
744.35/263.15	   U15(X1, active(X2)) -> U15(X1, X2)
744.35/263.15	   U16(active(X)) -> U16(X)
744.35/263.15	   U16(mark(X)) -> U16(X)
744.35/263.15	   U22(X1, mark(X2)) -> U22(X1, X2)
744.35/263.15	   U22(mark(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(active(X1), X2) -> U22(X1, X2)
744.35/263.15	   U22(X1, active(X2)) -> U22(X1, X2)
744.35/263.15	   U23(active(X)) -> U23(X)
744.35/263.15	   U23(mark(X)) -> U23(X)
744.35/263.15	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.35/263.15	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.35/263.15	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.35/263.15	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.35/263.15	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.35/263.15	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.35/263.15	   U35(X1, mark(X2)) -> U35(X1, X2)
744.35/263.15	   U35(mark(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(active(X1), X2) -> U35(X1, X2)
744.35/263.15	   U35(X1, active(X2)) -> U35(X1, X2)
744.35/263.15	   U36(active(X)) -> U36(X)
744.35/263.15	   U36(mark(X)) -> U36(X)
744.35/263.15	   U42(active(X)) -> U42(X)
744.35/263.15	   U42(mark(X)) -> U42(X)
744.35/263.15	   U62(active(X)) -> U62(X)
744.35/263.15	   U62(mark(X)) -> U62(X)
744.35/263.15	   U72(X1, mark(X2)) -> U72(X1, X2)
744.35/263.15	   U72(mark(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(active(X1), X2) -> U72(X1, X2)
744.35/263.15	   U72(X1, active(X2)) -> U72(X1, X2)
744.35/263.15	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.35/263.15	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.35/263.15	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.35/263.15	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.35/263.15	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.35/263.15	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.35/263.15	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.35/263.15	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.35/263.15	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.35/263.15	   s(active(X)) -> s(X)
744.35/263.15	   s(mark(X)) -> s(X)
744.35/263.15	   U92(active(X)) -> U92(X)
744.35/263.15	   U92(mark(X)) -> U92(X)
744.35/263.15	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.35/263.15	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.35/263.15	   U21(X1, mark(X2)) -> U21(X1, X2)
744.35/263.15	   U21(mark(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(active(X1), X2) -> U21(X1, X2)
744.35/263.15	   U21(X1, active(X2)) -> U21(X1, X2)
744.35/263.15	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.35/263.15	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.35/263.15	   U41(X1, mark(X2)) -> U41(X1, X2)
744.35/263.15	   U41(mark(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(active(X1), X2) -> U41(X1, X2)
744.35/263.15	   U41(X1, active(X2)) -> U41(X1, X2)
744.35/263.15	   U51(active(X)) -> U51(X)
744.35/263.15	   U51(mark(X)) -> U51(X)
744.35/263.15	   U71(X1, mark(X2)) -> U71(X1, X2)
744.35/263.15	   U71(mark(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(active(X1), X2) -> U71(X1, X2)
744.35/263.15	   U71(X1, active(X2)) -> U71(X1, X2)
744.35/263.15	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.35/263.15	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.35/263.15	   U91(X1, mark(X2)) -> U91(X1, X2)
744.35/263.15	   U91(mark(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(active(X1), X2) -> U91(X1, X2)
744.35/263.15	   U91(X1, active(X2)) -> U91(X1, X2)
744.35/263.15	   x(X1, mark(X2)) -> x(X1, X2)
744.35/263.15	   x(mark(X1), X2) -> x(X1, X2)
744.35/263.15	   x(active(X1), X2) -> x(X1, X2)
744.35/263.15	   x(X1, active(X2)) -> x(X1, X2)
744.35/263.15	
744.35/263.15	The set Q consists of the following terms:
744.35/263.15	
744.35/263.15	   active(U101(tt, x0, x1))
744.35/263.15	   active(U102(tt, x0, x1))
744.35/263.15	   active(U103(tt, x0, x1))
744.35/263.15	   active(U104(tt, x0, x1))
744.35/263.15	   active(U11(tt, x0, x1))
744.35/263.15	   active(U12(tt, x0, x1))
744.35/263.15	   active(U13(tt, x0, x1))
744.35/263.15	   active(U14(tt, x0, x1))
744.35/263.15	   active(U15(tt, x0))
744.35/263.15	   active(U16(tt))
744.35/263.15	   active(U21(tt, x0))
744.35/263.15	   active(U22(tt, x0))
744.35/263.15	   active(U23(tt))
744.35/263.15	   active(U31(tt, x0, x1))
744.35/263.15	   active(U32(tt, x0, x1))
744.35/263.15	   active(U33(tt, x0, x1))
744.35/263.15	   active(U34(tt, x0, x1))
744.35/263.15	   active(U35(tt, x0))
744.35/263.15	   active(U36(tt))
744.35/263.15	   active(U41(tt, x0))
744.35/263.15	   active(U42(tt))
744.35/263.15	   active(U51(tt))
744.35/263.15	   active(U61(tt, x0))
744.35/263.15	   active(U62(tt))
744.35/263.15	   active(U71(tt, x0))
744.35/263.15	   active(U72(tt, x0))
744.35/263.15	   active(U81(tt, x0, x1))
744.35/263.15	   active(U82(tt, x0, x1))
744.35/263.15	   active(U83(tt, x0, x1))
744.35/263.15	   active(U84(tt, x0, x1))
744.35/263.15	   active(U91(tt, x0))
744.35/263.15	   active(U92(tt))
744.35/263.15	   active(isNat(0))
744.35/263.15	   active(isNat(plus(x0, x1)))
744.35/263.15	   active(isNat(s(x0)))
744.35/263.15	   active(isNat(x(x0, x1)))
744.35/263.15	   active(isNatKind(0))
744.35/263.15	   active(isNatKind(plus(x0, x1)))
744.35/263.15	   active(isNatKind(s(x0)))
744.35/263.15	   active(isNatKind(x(x0, x1)))
744.35/263.15	   active(plus(x0, 0))
744.35/263.15	   active(plus(x0, s(x1)))
744.35/263.15	   active(x(x0, 0))
744.35/263.15	   active(x(x0, s(x1)))
744.35/263.15	   mark(U101(x0, x1, x2))
744.35/263.15	   mark(tt)
744.35/263.15	   mark(U102(x0, x1, x2))
744.35/263.15	   mark(isNatKind(x0))
744.35/263.15	   mark(U103(x0, x1, x2))
744.35/263.15	   mark(isNat(x0))
744.35/263.15	   mark(U104(x0, x1, x2))
744.35/263.15	   mark(plus(x0, x1))
744.35/263.15	   mark(x(x0, x1))
744.35/263.15	   mark(U11(x0, x1, x2))
744.35/263.15	   mark(U12(x0, x1, x2))
744.35/263.15	   mark(U13(x0, x1, x2))
744.35/263.15	   mark(U14(x0, x1, x2))
744.35/263.15	   mark(U15(x0, x1))
744.35/263.15	   mark(U16(x0))
744.35/263.15	   mark(U21(x0, x1))
744.35/263.15	   mark(U22(x0, x1))
744.35/263.15	   mark(U23(x0))
744.35/263.15	   mark(U31(x0, x1, x2))
744.35/263.15	   mark(U32(x0, x1, x2))
744.35/263.15	   mark(U33(x0, x1, x2))
744.35/263.15	   mark(U34(x0, x1, x2))
744.35/263.15	   mark(U35(x0, x1))
744.35/263.15	   mark(U36(x0))
744.35/263.15	   mark(U41(x0, x1))
744.35/263.15	   mark(U42(x0))
744.35/263.15	   mark(U51(x0))
744.35/263.15	   mark(U61(x0, x1))
744.35/263.15	   mark(U62(x0))
744.35/263.15	   mark(U71(x0, x1))
744.35/263.15	   mark(U72(x0, x1))
744.35/263.15	   mark(U81(x0, x1, x2))
744.35/263.15	   mark(U82(x0, x1, x2))
744.35/263.15	   mark(U83(x0, x1, x2))
744.35/263.15	   mark(U84(x0, x1, x2))
744.35/263.15	   mark(s(x0))
744.35/263.15	   mark(U91(x0, x1))
744.35/263.15	   mark(U92(x0))
744.35/263.15	   mark(0)
744.35/263.15	   U101(mark(x0), x1, x2)
744.35/263.15	   U101(x0, mark(x1), x2)
744.35/263.15	   U101(x0, x1, mark(x2))
744.35/263.15	   U101(active(x0), x1, x2)
744.35/263.15	   U101(x0, active(x1), x2)
744.35/263.15	   U101(x0, x1, active(x2))
744.35/263.15	   U102(mark(x0), x1, x2)
744.35/263.15	   U102(x0, mark(x1), x2)
744.35/263.15	   U102(x0, x1, mark(x2))
744.35/263.15	   U102(active(x0), x1, x2)
744.35/263.15	   U102(x0, active(x1), x2)
744.35/263.15	   U102(x0, x1, active(x2))
744.35/263.15	   isNatKind(mark(x0))
744.35/263.15	   isNatKind(active(x0))
744.35/263.15	   U103(mark(x0), x1, x2)
744.35/263.15	   U103(x0, mark(x1), x2)
744.35/263.15	   U103(x0, x1, mark(x2))
744.35/263.15	   U103(active(x0), x1, x2)
744.35/263.15	   U103(x0, active(x1), x2)
744.35/263.15	   U103(x0, x1, active(x2))
744.35/263.15	   isNat(mark(x0))
744.35/263.15	   isNat(active(x0))
744.35/263.15	   U104(mark(x0), x1, x2)
744.35/263.15	   U104(x0, mark(x1), x2)
744.35/263.15	   U104(x0, x1, mark(x2))
744.35/263.15	   U104(active(x0), x1, x2)
744.35/263.15	   U104(x0, active(x1), x2)
744.35/263.15	   U104(x0, x1, active(x2))
744.35/263.15	   plus(mark(x0), x1)
744.35/263.15	   plus(x0, mark(x1))
744.35/263.15	   plus(active(x0), x1)
744.35/263.15	   plus(x0, active(x1))
744.35/263.15	   x(mark(x0), x1)
744.35/263.15	   x(x0, mark(x1))
744.35/263.15	   x(active(x0), x1)
744.35/263.15	   x(x0, active(x1))
744.35/263.15	   U11(mark(x0), x1, x2)
744.35/263.15	   U11(x0, mark(x1), x2)
744.35/263.15	   U11(x0, x1, mark(x2))
744.35/263.15	   U11(active(x0), x1, x2)
744.35/263.15	   U11(x0, active(x1), x2)
744.35/263.15	   U11(x0, x1, active(x2))
744.35/263.15	   U12(mark(x0), x1, x2)
744.35/263.15	   U12(x0, mark(x1), x2)
744.35/263.15	   U12(x0, x1, mark(x2))
744.35/263.15	   U12(active(x0), x1, x2)
744.35/263.15	   U12(x0, active(x1), x2)
744.35/263.15	   U12(x0, x1, active(x2))
744.35/263.15	   U13(mark(x0), x1, x2)
744.35/263.15	   U13(x0, mark(x1), x2)
744.35/263.15	   U13(x0, x1, mark(x2))
744.35/263.15	   U13(active(x0), x1, x2)
744.35/263.15	   U13(x0, active(x1), x2)
744.35/263.15	   U13(x0, x1, active(x2))
744.35/263.15	   U14(mark(x0), x1, x2)
744.35/263.15	   U14(x0, mark(x1), x2)
744.35/263.15	   U14(x0, x1, mark(x2))
744.35/263.15	   U14(active(x0), x1, x2)
744.35/263.15	   U14(x0, active(x1), x2)
744.35/263.15	   U14(x0, x1, active(x2))
744.35/263.15	   U15(mark(x0), x1)
744.35/263.15	   U15(x0, mark(x1))
744.35/263.15	   U15(active(x0), x1)
744.35/263.15	   U15(x0, active(x1))
744.35/263.15	   U16(mark(x0))
744.35/263.15	   U16(active(x0))
744.35/263.15	   U21(mark(x0), x1)
744.35/263.15	   U21(x0, mark(x1))
744.35/263.15	   U21(active(x0), x1)
744.35/263.15	   U21(x0, active(x1))
744.35/263.15	   U22(mark(x0), x1)
744.35/263.15	   U22(x0, mark(x1))
744.35/263.15	   U22(active(x0), x1)
744.35/263.15	   U22(x0, active(x1))
744.35/263.15	   U23(mark(x0))
744.35/263.15	   U23(active(x0))
744.35/263.15	   U31(mark(x0), x1, x2)
744.35/263.15	   U31(x0, mark(x1), x2)
744.35/263.15	   U31(x0, x1, mark(x2))
744.35/263.15	   U31(active(x0), x1, x2)
744.35/263.15	   U31(x0, active(x1), x2)
744.35/263.15	   U31(x0, x1, active(x2))
744.35/263.15	   U32(mark(x0), x1, x2)
744.35/263.15	   U32(x0, mark(x1), x2)
744.35/263.15	   U32(x0, x1, mark(x2))
744.35/263.15	   U32(active(x0), x1, x2)
744.35/263.15	   U32(x0, active(x1), x2)
744.35/263.15	   U32(x0, x1, active(x2))
744.35/263.15	   U33(mark(x0), x1, x2)
744.35/263.15	   U33(x0, mark(x1), x2)
744.35/263.15	   U33(x0, x1, mark(x2))
744.35/263.15	   U33(active(x0), x1, x2)
744.35/263.15	   U33(x0, active(x1), x2)
744.35/263.15	   U33(x0, x1, active(x2))
744.35/263.15	   U34(mark(x0), x1, x2)
744.35/263.15	   U34(x0, mark(x1), x2)
744.35/263.15	   U34(x0, x1, mark(x2))
744.35/263.15	   U34(active(x0), x1, x2)
744.35/263.15	   U34(x0, active(x1), x2)
744.35/263.15	   U34(x0, x1, active(x2))
744.35/263.15	   U35(mark(x0), x1)
744.35/263.15	   U35(x0, mark(x1))
744.35/263.15	   U35(active(x0), x1)
744.35/263.15	   U35(x0, active(x1))
744.35/263.15	   U36(mark(x0))
744.35/263.15	   U36(active(x0))
744.35/263.15	   U41(mark(x0), x1)
744.35/263.15	   U41(x0, mark(x1))
744.35/263.15	   U41(active(x0), x1)
744.35/263.15	   U41(x0, active(x1))
744.35/263.15	   U42(mark(x0))
744.35/263.15	   U42(active(x0))
744.35/263.15	   U51(mark(x0))
744.35/263.15	   U51(active(x0))
744.35/263.15	   U61(mark(x0), x1)
744.35/263.15	   U61(x0, mark(x1))
744.35/263.15	   U61(active(x0), x1)
744.35/263.15	   U61(x0, active(x1))
744.35/263.15	   U62(mark(x0))
744.35/263.15	   U62(active(x0))
744.35/263.15	   U71(mark(x0), x1)
744.35/263.15	   U71(x0, mark(x1))
744.35/263.15	   U71(active(x0), x1)
744.35/263.15	   U71(x0, active(x1))
744.35/263.15	   U72(mark(x0), x1)
744.35/263.15	   U72(x0, mark(x1))
744.35/263.15	   U72(active(x0), x1)
744.35/263.15	   U72(x0, active(x1))
744.35/263.15	   U81(mark(x0), x1, x2)
744.35/263.15	   U81(x0, mark(x1), x2)
744.35/263.15	   U81(x0, x1, mark(x2))
744.35/263.15	   U81(active(x0), x1, x2)
744.35/263.15	   U81(x0, active(x1), x2)
744.35/263.15	   U81(x0, x1, active(x2))
744.35/263.15	   U82(mark(x0), x1, x2)
744.35/263.15	   U82(x0, mark(x1), x2)
744.35/263.15	   U82(x0, x1, mark(x2))
744.35/263.15	   U82(active(x0), x1, x2)
744.35/263.15	   U82(x0, active(x1), x2)
744.35/263.15	   U82(x0, x1, active(x2))
744.35/263.15	   U83(mark(x0), x1, x2)
744.35/263.15	   U83(x0, mark(x1), x2)
744.35/263.15	   U83(x0, x1, mark(x2))
744.35/263.15	   U83(active(x0), x1, x2)
744.35/263.15	   U83(x0, active(x1), x2)
744.35/263.15	   U83(x0, x1, active(x2))
744.35/263.15	   U84(mark(x0), x1, x2)
744.35/263.15	   U84(x0, mark(x1), x2)
744.35/263.15	   U84(x0, x1, mark(x2))
744.35/263.15	   U84(active(x0), x1, x2)
744.35/263.15	   U84(x0, active(x1), x2)
744.35/263.15	   U84(x0, x1, active(x2))
744.35/263.15	   s(mark(x0))
744.35/263.15	   s(active(x0))
744.35/263.15	   U91(mark(x0), x1)
744.35/263.15	   U91(x0, mark(x1))
744.35/263.15	   U91(active(x0), x1)
744.35/263.15	   U91(x0, active(x1))
744.35/263.15	   U92(mark(x0))
744.35/263.15	   U92(active(x0))
744.35/263.15	
744.35/263.15	We have to consider all minimal (P,Q,R)-chains.
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(365) QDPOrderProof (EQUIVALENT)
744.35/263.15	We use the reduction pair processor [LPAR04,JAR06].
744.35/263.15	
744.35/263.15	
744.35/263.15	The following pairs can be oriented strictly and are deleted.
744.35/263.15	
744.35/263.15	   MARK(U51(X)) -> MARK(X)
744.35/263.15	The remaining pairs can at least be oriented weakly.
744.35/263.15	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.35/263.15	
744.35/263.15	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.35/263.15	POL( U11_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.15	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.15	POL( U13_3(x_1, ..., x_3) ) = 1
744.35/263.15	POL( U14_3(x_1, ..., x_3) ) = max{0, -2}
744.35/263.15	POL( U21_2(x_1, x_2) ) = max{0, -2}
744.35/263.15	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.35/263.15	POL( mark_1(x_1) ) = max{0, -2}
744.35/263.15	POL( U102_3(x_1, ..., x_3) ) = 2x_2 + 2
744.35/263.15	POL( active_1(x_1) ) = max{0, x_1 - 2}
744.35/263.15	POL( U101_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.35/263.15	POL( tt ) = 1
744.35/263.15	POL( isNatKind_1(x_1) ) = 0
744.35/263.15	POL( U103_3(x_1, ..., x_3) ) = 2x_1 + x_2 + 2
744.35/263.15	POL( isNat_1(x_1) ) = 0
744.35/263.15	POL( U104_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.15	POL( plus_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.35/263.15	POL( x_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.35/263.15	POL( U15_2(x_1, x_2) ) = x_1 + 1
744.35/263.15	POL( U16_1(x_1) ) = 0
744.35/263.15	POL( U23_1(x_1) ) = 2x_1 + 1
744.35/263.15	POL( U31_3(x_1, ..., x_3) ) = max{0, 2x_2 + 2x_3 - 2}
744.35/263.15	POL( U32_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.15	POL( U33_3(x_1, ..., x_3) ) = 2
744.35/263.15	POL( U34_3(x_1, ..., x_3) ) = max{0, x_1 - 2}
744.35/263.15	POL( U35_2(x_1, x_2) ) = max{0, x_1 + 2x_2 - 2}
744.35/263.15	POL( U36_1(x_1) ) = 0
744.35/263.15	POL( U41_2(x_1, x_2) ) = x_1 + x_2 + 1
744.35/263.15	POL( U42_1(x_1) ) = 2
744.35/263.15	POL( U61_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.35/263.15	POL( U62_1(x_1) ) = 2
744.35/263.15	POL( U71_2(x_1, x_2) ) = 2
744.35/263.15	POL( U72_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.15	POL( U81_3(x_1, ..., x_3) ) = x_1 + 2
744.35/263.15	POL( U82_3(x_1, ..., x_3) ) = max{0, x_1 + 2x_2 + x_3 - 2}
744.35/263.15	POL( U83_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + 2x_3 - 2}
744.35/263.15	POL( U84_3(x_1, ..., x_3) ) = 2x_3 + 2
744.35/263.15	POL( s_1(x_1) ) = 2
744.35/263.15	POL( U91_2(x_1, x_2) ) = max{0, 2x_2 - 2}
744.35/263.15	POL( U92_1(x_1) ) = max{0, -2}
744.35/263.15	POL( U51_1(x_1) ) = x_1 + 2
744.35/263.15	POL( 0 ) = 0
744.35/263.15	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.35/263.15	
744.35/263.15	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.35/263.15	none
744.35/263.15	
744.35/263.15	
744.35/263.15	----------------------------------------
744.35/263.15	
744.35/263.15	(366)
744.35/263.15	Obligation:
744.35/263.15	Q DP problem:
744.35/263.15	The TRS P consists of the following rules:
744.35/263.15	
744.35/263.15	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.35/263.15	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.35/263.15	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.35/263.15	   MARK(U15(X1, X2)) -> MARK(X1)
744.35/263.15	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.35/263.15	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.35/263.15	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.35/263.15	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.35/263.15	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.35/263.15	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.35/263.15	   MARK(U23(X)) -> MARK(X)
744.35/263.15	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.35/263.15	   MARK(U41(X1, X2)) -> MARK(X1)
744.35/263.15	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.35/263.15	
744.35/263.15	The TRS R consists of the following rules:
744.35/263.15	
744.35/263.15	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.35/263.15	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.35/263.15	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.35/263.15	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.35/263.15	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.35/263.15	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.35/263.15	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.35/263.15	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.35/263.15	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.35/263.15	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.35/263.15	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.35/263.15	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.35/263.15	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.35/263.15	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.35/263.15	   mark(U16(X)) -> active(U16(mark(X)))
744.35/263.15	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.35/263.15	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.35/263.15	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.35/263.15	   mark(U23(X)) -> active(U23(mark(X)))
744.35/263.15	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.35/263.15	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.35/263.15	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.35/263.15	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.35/263.15	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.35/263.15	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.35/263.15	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.35/263.15	   mark(U36(X)) -> active(U36(mark(X)))
744.35/263.15	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.35/263.15	   mark(U42(X)) -> active(U42(mark(X)))
744.35/263.15	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.35/263.15	   mark(U62(X)) -> active(U62(mark(X)))
744.35/263.15	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.35/263.15	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.35/263.15	   active(U72(tt, N)) -> mark(N)
744.35/263.15	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.35/263.15	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.35/263.15	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.35/263.15	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.35/263.15	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.35/263.15	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.35/263.15	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.35/263.15	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.35/263.15	   mark(s(X)) -> active(s(mark(X)))
744.35/263.15	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.35/263.15	   mark(U92(X)) -> active(U92(mark(X)))
744.35/263.15	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.35/263.15	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.35/263.15	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.35/263.15	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.35/263.15	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.35/263.15	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.35/263.15	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.35/263.15	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.35/263.15	   mark(U51(X)) -> active(U51(mark(X)))
744.35/263.15	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.35/263.15	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.35/263.15	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.35/263.15	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.35/263.15	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.35/263.15	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.35/263.15	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.35/263.15	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.35/263.15	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.35/263.15	   mark(isNatKind(X)) -> active(isNatKind(X))
744.35/263.15	   mark(isNat(X)) -> active(isNat(X))
744.35/263.15	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.35/263.15	   mark(tt) -> active(tt)
744.35/263.15	   mark(0) -> active(0)
744.35/263.15	   U61(X1, mark(X2)) -> U61(X1, X2)
744.35/263.15	   U61(mark(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(active(X1), X2) -> U61(X1, X2)
744.35/263.15	   U61(X1, active(X2)) -> U61(X1, X2)
744.35/263.15	   active(U16(tt)) -> mark(tt)
744.35/263.15	   active(U23(tt)) -> mark(tt)
744.35/263.15	   active(U36(tt)) -> mark(tt)
744.35/263.15	   active(U42(tt)) -> mark(tt)
744.35/263.15	   active(U51(tt)) -> mark(tt)
744.35/263.15	   active(U62(tt)) -> mark(tt)
744.35/263.15	   active(U92(tt)) -> mark(0)
744.35/263.15	   active(isNat(0)) -> mark(tt)
744.35/263.15	   active(isNatKind(0)) -> mark(tt)
744.35/263.15	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.35/263.15	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.35/263.15	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.35/263.15	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.35/263.15	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.35/263.15	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.35/263.15	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.35/263.15	   plus(X1, mark(X2)) -> plus(X1, X2)
744.35/263.15	   plus(mark(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(active(X1), X2) -> plus(X1, X2)
744.35/263.15	   plus(X1, active(X2)) -> plus(X1, X2)
744.35/263.15	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.35/263.15	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.35/263.15	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.41/263.15	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.41/263.15	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.15	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.41/263.15	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.15	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.41/263.15	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.41/263.15	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.41/263.15	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.15	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.41/263.15	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.15	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.41/263.15	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.41/263.15	   U15(X1, mark(X2)) -> U15(X1, X2)
744.41/263.15	   U15(mark(X1), X2) -> U15(X1, X2)
744.41/263.15	   U15(active(X1), X2) -> U15(X1, X2)
744.41/263.15	   U15(X1, active(X2)) -> U15(X1, X2)
744.41/263.15	   U16(active(X)) -> U16(X)
744.41/263.15	   U16(mark(X)) -> U16(X)
744.41/263.15	   U22(X1, mark(X2)) -> U22(X1, X2)
744.41/263.15	   U22(mark(X1), X2) -> U22(X1, X2)
744.41/263.15	   U22(active(X1), X2) -> U22(X1, X2)
744.41/263.15	   U22(X1, active(X2)) -> U22(X1, X2)
744.41/263.15	   U23(active(X)) -> U23(X)
744.41/263.15	   U23(mark(X)) -> U23(X)
744.41/263.15	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.41/263.15	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.15	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.41/263.15	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.15	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.41/263.15	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.41/263.15	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.41/263.15	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.15	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.41/263.15	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.15	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.41/263.15	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.41/263.15	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.41/263.15	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.15	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.41/263.15	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.15	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.41/263.15	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.41/263.15	   U35(X1, mark(X2)) -> U35(X1, X2)
744.41/263.15	   U35(mark(X1), X2) -> U35(X1, X2)
744.41/263.15	   U35(active(X1), X2) -> U35(X1, X2)
744.41/263.15	   U35(X1, active(X2)) -> U35(X1, X2)
744.41/263.15	   U36(active(X)) -> U36(X)
744.41/263.15	   U36(mark(X)) -> U36(X)
744.41/263.15	   U42(active(X)) -> U42(X)
744.41/263.15	   U42(mark(X)) -> U42(X)
744.41/263.15	   U62(active(X)) -> U62(X)
744.41/263.15	   U62(mark(X)) -> U62(X)
744.41/263.15	   U72(X1, mark(X2)) -> U72(X1, X2)
744.41/263.15	   U72(mark(X1), X2) -> U72(X1, X2)
744.41/263.15	   U72(active(X1), X2) -> U72(X1, X2)
744.41/263.15	   U72(X1, active(X2)) -> U72(X1, X2)
744.41/263.15	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.41/263.15	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.15	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.41/263.15	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.15	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.41/263.15	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.41/263.15	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.41/263.15	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.15	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.41/263.15	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.15	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.41/263.15	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.41/263.15	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.41/263.15	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.15	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.41/263.15	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.15	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.41/263.15	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.41/263.15	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.41/263.15	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.15	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.41/263.15	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.15	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.41/263.15	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.41/263.15	   s(active(X)) -> s(X)
744.41/263.15	   s(mark(X)) -> s(X)
744.41/263.15	   U92(active(X)) -> U92(X)
744.41/263.15	   U92(mark(X)) -> U92(X)
744.41/263.15	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.41/263.15	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.15	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.41/263.15	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.15	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.41/263.15	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.41/263.15	   U21(X1, mark(X2)) -> U21(X1, X2)
744.41/263.15	   U21(mark(X1), X2) -> U21(X1, X2)
744.41/263.15	   U21(active(X1), X2) -> U21(X1, X2)
744.41/263.15	   U21(X1, active(X2)) -> U21(X1, X2)
744.41/263.15	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.41/263.15	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.15	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.41/263.15	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.15	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.41/263.15	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.41/263.15	   U41(X1, mark(X2)) -> U41(X1, X2)
744.41/263.15	   U41(mark(X1), X2) -> U41(X1, X2)
744.41/263.15	   U41(active(X1), X2) -> U41(X1, X2)
744.41/263.15	   U41(X1, active(X2)) -> U41(X1, X2)
744.41/263.15	   U51(active(X)) -> U51(X)
744.41/263.15	   U51(mark(X)) -> U51(X)
744.41/263.15	   U71(X1, mark(X2)) -> U71(X1, X2)
744.41/263.15	   U71(mark(X1), X2) -> U71(X1, X2)
744.41/263.15	   U71(active(X1), X2) -> U71(X1, X2)
744.41/263.15	   U71(X1, active(X2)) -> U71(X1, X2)
744.41/263.15	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.41/263.15	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.15	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.41/263.15	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.15	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.41/263.15	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.41/263.15	   U91(X1, mark(X2)) -> U91(X1, X2)
744.41/263.15	   U91(mark(X1), X2) -> U91(X1, X2)
744.41/263.15	   U91(active(X1), X2) -> U91(X1, X2)
744.41/263.15	   U91(X1, active(X2)) -> U91(X1, X2)
744.41/263.15	   x(X1, mark(X2)) -> x(X1, X2)
744.41/263.15	   x(mark(X1), X2) -> x(X1, X2)
744.41/263.15	   x(active(X1), X2) -> x(X1, X2)
744.41/263.15	   x(X1, active(X2)) -> x(X1, X2)
744.41/263.15	
744.41/263.15	The set Q consists of the following terms:
744.41/263.15	
744.41/263.15	   active(U101(tt, x0, x1))
744.41/263.15	   active(U102(tt, x0, x1))
744.41/263.15	   active(U103(tt, x0, x1))
744.41/263.15	   active(U104(tt, x0, x1))
744.41/263.15	   active(U11(tt, x0, x1))
744.41/263.15	   active(U12(tt, x0, x1))
744.41/263.15	   active(U13(tt, x0, x1))
744.41/263.15	   active(U14(tt, x0, x1))
744.41/263.15	   active(U15(tt, x0))
744.41/263.15	   active(U16(tt))
744.41/263.15	   active(U21(tt, x0))
744.41/263.15	   active(U22(tt, x0))
744.41/263.15	   active(U23(tt))
744.41/263.15	   active(U31(tt, x0, x1))
744.41/263.15	   active(U32(tt, x0, x1))
744.41/263.15	   active(U33(tt, x0, x1))
744.41/263.15	   active(U34(tt, x0, x1))
744.41/263.15	   active(U35(tt, x0))
744.41/263.15	   active(U36(tt))
744.41/263.15	   active(U41(tt, x0))
744.41/263.15	   active(U42(tt))
744.41/263.15	   active(U51(tt))
744.41/263.15	   active(U61(tt, x0))
744.41/263.15	   active(U62(tt))
744.41/263.15	   active(U71(tt, x0))
744.41/263.15	   active(U72(tt, x0))
744.41/263.15	   active(U81(tt, x0, x1))
744.41/263.15	   active(U82(tt, x0, x1))
744.41/263.15	   active(U83(tt, x0, x1))
744.41/263.15	   active(U84(tt, x0, x1))
744.41/263.15	   active(U91(tt, x0))
744.41/263.15	   active(U92(tt))
744.41/263.15	   active(isNat(0))
744.41/263.15	   active(isNat(plus(x0, x1)))
744.41/263.15	   active(isNat(s(x0)))
744.41/263.15	   active(isNat(x(x0, x1)))
744.41/263.15	   active(isNatKind(0))
744.41/263.15	   active(isNatKind(plus(x0, x1)))
744.41/263.15	   active(isNatKind(s(x0)))
744.41/263.15	   active(isNatKind(x(x0, x1)))
744.41/263.15	   active(plus(x0, 0))
744.41/263.15	   active(plus(x0, s(x1)))
744.41/263.15	   active(x(x0, 0))
744.41/263.15	   active(x(x0, s(x1)))
744.41/263.15	   mark(U101(x0, x1, x2))
744.41/263.15	   mark(tt)
744.41/263.15	   mark(U102(x0, x1, x2))
744.41/263.15	   mark(isNatKind(x0))
744.41/263.15	   mark(U103(x0, x1, x2))
744.41/263.15	   mark(isNat(x0))
744.41/263.15	   mark(U104(x0, x1, x2))
744.41/263.15	   mark(plus(x0, x1))
744.41/263.15	   mark(x(x0, x1))
744.41/263.15	   mark(U11(x0, x1, x2))
744.41/263.15	   mark(U12(x0, x1, x2))
744.41/263.15	   mark(U13(x0, x1, x2))
744.41/263.15	   mark(U14(x0, x1, x2))
744.41/263.15	   mark(U15(x0, x1))
744.41/263.15	   mark(U16(x0))
744.41/263.15	   mark(U21(x0, x1))
744.41/263.15	   mark(U22(x0, x1))
744.41/263.15	   mark(U23(x0))
744.41/263.15	   mark(U31(x0, x1, x2))
744.41/263.15	   mark(U32(x0, x1, x2))
744.41/263.15	   mark(U33(x0, x1, x2))
744.41/263.15	   mark(U34(x0, x1, x2))
744.41/263.15	   mark(U35(x0, x1))
744.41/263.15	   mark(U36(x0))
744.41/263.15	   mark(U41(x0, x1))
744.41/263.15	   mark(U42(x0))
744.41/263.15	   mark(U51(x0))
744.41/263.15	   mark(U61(x0, x1))
744.41/263.15	   mark(U62(x0))
744.41/263.15	   mark(U71(x0, x1))
744.41/263.15	   mark(U72(x0, x1))
744.41/263.15	   mark(U81(x0, x1, x2))
744.41/263.15	   mark(U82(x0, x1, x2))
744.41/263.15	   mark(U83(x0, x1, x2))
744.41/263.15	   mark(U84(x0, x1, x2))
744.41/263.15	   mark(s(x0))
744.41/263.15	   mark(U91(x0, x1))
744.41/263.15	   mark(U92(x0))
744.41/263.15	   mark(0)
744.41/263.15	   U101(mark(x0), x1, x2)
744.41/263.15	   U101(x0, mark(x1), x2)
744.41/263.15	   U101(x0, x1, mark(x2))
744.41/263.15	   U101(active(x0), x1, x2)
744.41/263.15	   U101(x0, active(x1), x2)
744.41/263.15	   U101(x0, x1, active(x2))
744.41/263.15	   U102(mark(x0), x1, x2)
744.41/263.15	   U102(x0, mark(x1), x2)
744.41/263.16	   U102(x0, x1, mark(x2))
744.41/263.16	   U102(active(x0), x1, x2)
744.41/263.16	   U102(x0, active(x1), x2)
744.41/263.16	   U102(x0, x1, active(x2))
744.41/263.16	   isNatKind(mark(x0))
744.41/263.16	   isNatKind(active(x0))
744.41/263.16	   U103(mark(x0), x1, x2)
744.41/263.16	   U103(x0, mark(x1), x2)
744.41/263.16	   U103(x0, x1, mark(x2))
744.41/263.16	   U103(active(x0), x1, x2)
744.41/263.16	   U103(x0, active(x1), x2)
744.41/263.16	   U103(x0, x1, active(x2))
744.41/263.16	   isNat(mark(x0))
744.41/263.16	   isNat(active(x0))
744.41/263.16	   U104(mark(x0), x1, x2)
744.41/263.16	   U104(x0, mark(x1), x2)
744.41/263.16	   U104(x0, x1, mark(x2))
744.41/263.16	   U104(active(x0), x1, x2)
744.41/263.16	   U104(x0, active(x1), x2)
744.41/263.16	   U104(x0, x1, active(x2))
744.41/263.16	   plus(mark(x0), x1)
744.41/263.16	   plus(x0, mark(x1))
744.41/263.16	   plus(active(x0), x1)
744.41/263.16	   plus(x0, active(x1))
744.41/263.16	   x(mark(x0), x1)
744.41/263.16	   x(x0, mark(x1))
744.41/263.16	   x(active(x0), x1)
744.41/263.16	   x(x0, active(x1))
744.41/263.16	   U11(mark(x0), x1, x2)
744.41/263.16	   U11(x0, mark(x1), x2)
744.41/263.16	   U11(x0, x1, mark(x2))
744.41/263.16	   U11(active(x0), x1, x2)
744.41/263.16	   U11(x0, active(x1), x2)
744.41/263.16	   U11(x0, x1, active(x2))
744.41/263.16	   U12(mark(x0), x1, x2)
744.41/263.16	   U12(x0, mark(x1), x2)
744.41/263.16	   U12(x0, x1, mark(x2))
744.41/263.16	   U12(active(x0), x1, x2)
744.41/263.16	   U12(x0, active(x1), x2)
744.41/263.16	   U12(x0, x1, active(x2))
744.41/263.16	   U13(mark(x0), x1, x2)
744.41/263.16	   U13(x0, mark(x1), x2)
744.41/263.16	   U13(x0, x1, mark(x2))
744.41/263.16	   U13(active(x0), x1, x2)
744.41/263.16	   U13(x0, active(x1), x2)
744.41/263.16	   U13(x0, x1, active(x2))
744.41/263.16	   U14(mark(x0), x1, x2)
744.41/263.16	   U14(x0, mark(x1), x2)
744.41/263.16	   U14(x0, x1, mark(x2))
744.41/263.16	   U14(active(x0), x1, x2)
744.41/263.16	   U14(x0, active(x1), x2)
744.41/263.16	   U14(x0, x1, active(x2))
744.41/263.16	   U15(mark(x0), x1)
744.41/263.16	   U15(x0, mark(x1))
744.41/263.16	   U15(active(x0), x1)
744.41/263.16	   U15(x0, active(x1))
744.41/263.16	   U16(mark(x0))
744.41/263.16	   U16(active(x0))
744.41/263.16	   U21(mark(x0), x1)
744.41/263.16	   U21(x0, mark(x1))
744.41/263.16	   U21(active(x0), x1)
744.41/263.16	   U21(x0, active(x1))
744.41/263.16	   U22(mark(x0), x1)
744.41/263.16	   U22(x0, mark(x1))
744.41/263.16	   U22(active(x0), x1)
744.41/263.16	   U22(x0, active(x1))
744.41/263.16	   U23(mark(x0))
744.41/263.16	   U23(active(x0))
744.41/263.16	   U31(mark(x0), x1, x2)
744.41/263.16	   U31(x0, mark(x1), x2)
744.41/263.16	   U31(x0, x1, mark(x2))
744.41/263.16	   U31(active(x0), x1, x2)
744.41/263.16	   U31(x0, active(x1), x2)
744.41/263.16	   U31(x0, x1, active(x2))
744.41/263.16	   U32(mark(x0), x1, x2)
744.41/263.16	   U32(x0, mark(x1), x2)
744.41/263.16	   U32(x0, x1, mark(x2))
744.41/263.16	   U32(active(x0), x1, x2)
744.41/263.16	   U32(x0, active(x1), x2)
744.41/263.16	   U32(x0, x1, active(x2))
744.41/263.16	   U33(mark(x0), x1, x2)
744.41/263.16	   U33(x0, mark(x1), x2)
744.41/263.16	   U33(x0, x1, mark(x2))
744.41/263.16	   U33(active(x0), x1, x2)
744.41/263.16	   U33(x0, active(x1), x2)
744.41/263.16	   U33(x0, x1, active(x2))
744.41/263.16	   U34(mark(x0), x1, x2)
744.41/263.16	   U34(x0, mark(x1), x2)
744.41/263.16	   U34(x0, x1, mark(x2))
744.41/263.16	   U34(active(x0), x1, x2)
744.41/263.16	   U34(x0, active(x1), x2)
744.41/263.16	   U34(x0, x1, active(x2))
744.41/263.16	   U35(mark(x0), x1)
744.41/263.16	   U35(x0, mark(x1))
744.41/263.16	   U35(active(x0), x1)
744.41/263.16	   U35(x0, active(x1))
744.41/263.16	   U36(mark(x0))
744.41/263.16	   U36(active(x0))
744.41/263.16	   U41(mark(x0), x1)
744.41/263.16	   U41(x0, mark(x1))
744.41/263.16	   U41(active(x0), x1)
744.41/263.16	   U41(x0, active(x1))
744.41/263.16	   U42(mark(x0))
744.41/263.16	   U42(active(x0))
744.41/263.16	   U51(mark(x0))
744.41/263.16	   U51(active(x0))
744.41/263.16	   U61(mark(x0), x1)
744.41/263.16	   U61(x0, mark(x1))
744.41/263.16	   U61(active(x0), x1)
744.41/263.16	   U61(x0, active(x1))
744.41/263.16	   U62(mark(x0))
744.41/263.16	   U62(active(x0))
744.41/263.16	   U71(mark(x0), x1)
744.41/263.16	   U71(x0, mark(x1))
744.41/263.16	   U71(active(x0), x1)
744.41/263.16	   U71(x0, active(x1))
744.41/263.16	   U72(mark(x0), x1)
744.41/263.16	   U72(x0, mark(x1))
744.41/263.16	   U72(active(x0), x1)
744.41/263.16	   U72(x0, active(x1))
744.41/263.16	   U81(mark(x0), x1, x2)
744.41/263.16	   U81(x0, mark(x1), x2)
744.41/263.16	   U81(x0, x1, mark(x2))
744.41/263.16	   U81(active(x0), x1, x2)
744.41/263.16	   U81(x0, active(x1), x2)
744.41/263.16	   U81(x0, x1, active(x2))
744.41/263.16	   U82(mark(x0), x1, x2)
744.41/263.16	   U82(x0, mark(x1), x2)
744.41/263.16	   U82(x0, x1, mark(x2))
744.41/263.16	   U82(active(x0), x1, x2)
744.41/263.16	   U82(x0, active(x1), x2)
744.41/263.16	   U82(x0, x1, active(x2))
744.41/263.16	   U83(mark(x0), x1, x2)
744.41/263.16	   U83(x0, mark(x1), x2)
744.41/263.16	   U83(x0, x1, mark(x2))
744.41/263.16	   U83(active(x0), x1, x2)
744.41/263.16	   U83(x0, active(x1), x2)
744.41/263.16	   U83(x0, x1, active(x2))
744.41/263.16	   U84(mark(x0), x1, x2)
744.41/263.16	   U84(x0, mark(x1), x2)
744.41/263.16	   U84(x0, x1, mark(x2))
744.41/263.16	   U84(active(x0), x1, x2)
744.41/263.16	   U84(x0, active(x1), x2)
744.41/263.16	   U84(x0, x1, active(x2))
744.41/263.16	   s(mark(x0))
744.41/263.16	   s(active(x0))
744.41/263.16	   U91(mark(x0), x1)
744.41/263.16	   U91(x0, mark(x1))
744.41/263.16	   U91(active(x0), x1)
744.41/263.16	   U91(x0, active(x1))
744.41/263.16	   U92(mark(x0))
744.41/263.16	   U92(active(x0))
744.41/263.16	
744.41/263.16	We have to consider all minimal (P,Q,R)-chains.
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(367) QDPOrderProof (EQUIVALENT)
744.41/263.16	We use the reduction pair processor [LPAR04,JAR06].
744.41/263.16	
744.41/263.16	
744.41/263.16	The following pairs can be oriented strictly and are deleted.
744.41/263.16	
744.41/263.16	   MARK(U41(X1, X2)) -> MARK(X1)
744.41/263.16	The remaining pairs can at least be oriented weakly.
744.41/263.16	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.41/263.16	
744.41/263.16	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.41/263.16	POL( U11_3(x_1, ..., x_3) ) = 0
744.41/263.16	POL( U12_3(x_1, ..., x_3) ) = 0
744.41/263.16	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.41/263.16	POL( U14_3(x_1, ..., x_3) ) = 0
744.41/263.16	POL( U21_2(x_1, x_2) ) = max{0, -2}
744.41/263.16	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.41/263.16	POL( mark_1(x_1) ) = 2
744.41/263.16	POL( U102_3(x_1, ..., x_3) ) = 2x_1 + 2
744.41/263.16	POL( active_1(x_1) ) = x_1 + 2
744.41/263.16	POL( U101_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 2}
744.41/263.16	POL( tt ) = 0
744.41/263.16	POL( isNatKind_1(x_1) ) = 0
744.41/263.16	POL( U103_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.41/263.16	POL( isNat_1(x_1) ) = 0
744.41/263.16	POL( U104_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.41/263.16	POL( plus_2(x_1, x_2) ) = max{0, x_1 - 2}
744.41/263.16	POL( x_2(x_1, x_2) ) = 2x_1 + 2
744.41/263.16	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.41/263.16	POL( U16_1(x_1) ) = max{0, 2x_1 - 2}
744.41/263.16	POL( U23_1(x_1) ) = 2x_1 + 1
744.41/263.16	POL( U31_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.41/263.16	POL( U32_3(x_1, ..., x_3) ) = 2x_3 + 2
744.41/263.16	POL( U33_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.41/263.16	POL( U34_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.41/263.16	POL( U35_2(x_1, x_2) ) = max{0, x_1 - 1}
744.41/263.16	POL( U36_1(x_1) ) = max{0, 2x_1 - 2}
744.41/263.16	POL( U41_2(x_1, x_2) ) = 2x_1 + 2
744.41/263.16	POL( U42_1(x_1) ) = 2
744.41/263.16	POL( U61_2(x_1, x_2) ) = max{0, x_2 - 2}
744.41/263.16	POL( U62_1(x_1) ) = 0
744.41/263.16	POL( U71_2(x_1, x_2) ) = max{0, x_2 - 2}
744.41/263.16	POL( U72_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.41/263.16	POL( U81_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.41/263.16	POL( U82_3(x_1, ..., x_3) ) = 2
744.41/263.16	POL( U83_3(x_1, ..., x_3) ) = 2x_1 + 2
744.41/263.16	POL( U84_3(x_1, ..., x_3) ) = 2x_1 + 2x_3 + 2
744.41/263.16	POL( s_1(x_1) ) = max{0, x_1 - 2}
744.41/263.16	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.41/263.16	POL( U92_1(x_1) ) = 2
744.41/263.16	POL( U51_1(x_1) ) = 1
744.41/263.16	POL( 0 ) = 0
744.41/263.16	POL( MARK_1(x_1) ) = max{0, 2x_1 - 2}
744.41/263.16	
744.41/263.16	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.41/263.16	none
744.41/263.16	
744.41/263.16	
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(368)
744.41/263.16	Obligation:
744.41/263.16	Q DP problem:
744.41/263.16	The TRS P consists of the following rules:
744.41/263.16	
744.41/263.16	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.41/263.16	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.41/263.16	   MARK(U15(X1, X2)) -> MARK(X1)
744.41/263.16	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.41/263.16	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.41/263.16	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.41/263.16	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.41/263.16	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.41/263.16	   MARK(U23(X)) -> MARK(X)
744.41/263.16	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.41/263.16	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.41/263.16	
744.41/263.16	The TRS R consists of the following rules:
744.41/263.16	
744.41/263.16	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.41/263.16	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.41/263.16	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.41/263.16	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.41/263.16	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.41/263.16	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.41/263.16	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.41/263.16	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.41/263.16	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.41/263.16	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.41/263.16	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.41/263.16	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.41/263.16	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.41/263.16	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.41/263.16	   mark(U16(X)) -> active(U16(mark(X)))
744.41/263.16	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.41/263.16	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.41/263.16	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.41/263.16	   mark(U23(X)) -> active(U23(mark(X)))
744.41/263.16	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.41/263.16	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.41/263.16	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.41/263.16	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.41/263.16	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.41/263.16	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.41/263.16	   mark(U36(X)) -> active(U36(mark(X)))
744.41/263.16	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.41/263.16	   mark(U42(X)) -> active(U42(mark(X)))
744.41/263.16	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.41/263.16	   mark(U62(X)) -> active(U62(mark(X)))
744.41/263.16	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.41/263.16	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.41/263.16	   active(U72(tt, N)) -> mark(N)
744.41/263.16	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.41/263.16	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.41/263.16	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.41/263.16	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.41/263.16	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.41/263.16	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.41/263.16	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.41/263.16	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.41/263.16	   mark(s(X)) -> active(s(mark(X)))
744.41/263.16	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.41/263.16	   mark(U92(X)) -> active(U92(mark(X)))
744.41/263.16	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.41/263.16	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.41/263.16	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.41/263.16	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.41/263.16	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.41/263.16	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.41/263.16	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.41/263.16	   mark(U51(X)) -> active(U51(mark(X)))
744.41/263.16	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.41/263.16	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.41/263.16	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.41/263.16	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.41/263.16	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.41/263.16	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.41/263.16	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.41/263.16	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.41/263.16	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.41/263.16	   mark(isNatKind(X)) -> active(isNatKind(X))
744.41/263.16	   mark(isNat(X)) -> active(isNat(X))
744.41/263.16	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.41/263.16	   mark(tt) -> active(tt)
744.41/263.16	   mark(0) -> active(0)
744.41/263.16	   U61(X1, mark(X2)) -> U61(X1, X2)
744.41/263.16	   U61(mark(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(active(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(X1, active(X2)) -> U61(X1, X2)
744.41/263.16	   active(U16(tt)) -> mark(tt)
744.41/263.16	   active(U23(tt)) -> mark(tt)
744.41/263.16	   active(U36(tt)) -> mark(tt)
744.41/263.16	   active(U42(tt)) -> mark(tt)
744.41/263.16	   active(U51(tt)) -> mark(tt)
744.41/263.16	   active(U62(tt)) -> mark(tt)
744.41/263.16	   active(U92(tt)) -> mark(0)
744.41/263.16	   active(isNat(0)) -> mark(tt)
744.41/263.16	   active(isNatKind(0)) -> mark(tt)
744.41/263.16	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.41/263.16	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.41/263.16	   plus(X1, mark(X2)) -> plus(X1, X2)
744.41/263.16	   plus(mark(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(active(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(X1, active(X2)) -> plus(X1, X2)
744.41/263.16	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U15(X1, mark(X2)) -> U15(X1, X2)
744.41/263.16	   U15(mark(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(active(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(X1, active(X2)) -> U15(X1, X2)
744.41/263.16	   U16(active(X)) -> U16(X)
744.41/263.16	   U16(mark(X)) -> U16(X)
744.41/263.16	   U22(X1, mark(X2)) -> U22(X1, X2)
744.41/263.16	   U22(mark(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(active(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(X1, active(X2)) -> U22(X1, X2)
744.41/263.16	   U23(active(X)) -> U23(X)
744.41/263.16	   U23(mark(X)) -> U23(X)
744.41/263.16	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U35(X1, mark(X2)) -> U35(X1, X2)
744.41/263.16	   U35(mark(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(active(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(X1, active(X2)) -> U35(X1, X2)
744.41/263.16	   U36(active(X)) -> U36(X)
744.41/263.16	   U36(mark(X)) -> U36(X)
744.41/263.16	   U42(active(X)) -> U42(X)
744.41/263.16	   U42(mark(X)) -> U42(X)
744.41/263.16	   U62(active(X)) -> U62(X)
744.41/263.16	   U62(mark(X)) -> U62(X)
744.41/263.16	   U72(X1, mark(X2)) -> U72(X1, X2)
744.41/263.16	   U72(mark(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(active(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(X1, active(X2)) -> U72(X1, X2)
744.41/263.16	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.41/263.16	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.41/263.16	   s(active(X)) -> s(X)
744.41/263.16	   s(mark(X)) -> s(X)
744.41/263.16	   U92(active(X)) -> U92(X)
744.41/263.16	   U92(mark(X)) -> U92(X)
744.41/263.16	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U21(X1, mark(X2)) -> U21(X1, X2)
744.41/263.16	   U21(mark(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(active(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(X1, active(X2)) -> U21(X1, X2)
744.41/263.16	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.41/263.16	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.41/263.16	   U41(X1, mark(X2)) -> U41(X1, X2)
744.41/263.16	   U41(mark(X1), X2) -> U41(X1, X2)
744.41/263.16	   U41(active(X1), X2) -> U41(X1, X2)
744.41/263.16	   U41(X1, active(X2)) -> U41(X1, X2)
744.41/263.16	   U51(active(X)) -> U51(X)
744.41/263.16	   U51(mark(X)) -> U51(X)
744.41/263.16	   U71(X1, mark(X2)) -> U71(X1, X2)
744.41/263.16	   U71(mark(X1), X2) -> U71(X1, X2)
744.41/263.16	   U71(active(X1), X2) -> U71(X1, X2)
744.41/263.16	   U71(X1, active(X2)) -> U71(X1, X2)
744.41/263.16	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.41/263.16	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.41/263.16	   U91(X1, mark(X2)) -> U91(X1, X2)
744.41/263.16	   U91(mark(X1), X2) -> U91(X1, X2)
744.41/263.16	   U91(active(X1), X2) -> U91(X1, X2)
744.41/263.16	   U91(X1, active(X2)) -> U91(X1, X2)
744.41/263.16	   x(X1, mark(X2)) -> x(X1, X2)
744.41/263.16	   x(mark(X1), X2) -> x(X1, X2)
744.41/263.16	   x(active(X1), X2) -> x(X1, X2)
744.41/263.16	   x(X1, active(X2)) -> x(X1, X2)
744.41/263.16	
744.41/263.16	The set Q consists of the following terms:
744.41/263.16	
744.41/263.16	   active(U101(tt, x0, x1))
744.41/263.16	   active(U102(tt, x0, x1))
744.41/263.16	   active(U103(tt, x0, x1))
744.41/263.16	   active(U104(tt, x0, x1))
744.41/263.16	   active(U11(tt, x0, x1))
744.41/263.16	   active(U12(tt, x0, x1))
744.41/263.16	   active(U13(tt, x0, x1))
744.41/263.16	   active(U14(tt, x0, x1))
744.41/263.16	   active(U15(tt, x0))
744.41/263.16	   active(U16(tt))
744.41/263.16	   active(U21(tt, x0))
744.41/263.16	   active(U22(tt, x0))
744.41/263.16	   active(U23(tt))
744.41/263.16	   active(U31(tt, x0, x1))
744.41/263.16	   active(U32(tt, x0, x1))
744.41/263.16	   active(U33(tt, x0, x1))
744.41/263.16	   active(U34(tt, x0, x1))
744.41/263.16	   active(U35(tt, x0))
744.41/263.16	   active(U36(tt))
744.41/263.16	   active(U41(tt, x0))
744.41/263.16	   active(U42(tt))
744.41/263.16	   active(U51(tt))
744.41/263.16	   active(U61(tt, x0))
744.41/263.16	   active(U62(tt))
744.41/263.16	   active(U71(tt, x0))
744.41/263.16	   active(U72(tt, x0))
744.41/263.16	   active(U81(tt, x0, x1))
744.41/263.16	   active(U82(tt, x0, x1))
744.41/263.16	   active(U83(tt, x0, x1))
744.41/263.16	   active(U84(tt, x0, x1))
744.41/263.16	   active(U91(tt, x0))
744.41/263.16	   active(U92(tt))
744.41/263.16	   active(isNat(0))
744.41/263.16	   active(isNat(plus(x0, x1)))
744.41/263.16	   active(isNat(s(x0)))
744.41/263.16	   active(isNat(x(x0, x1)))
744.41/263.16	   active(isNatKind(0))
744.41/263.16	   active(isNatKind(plus(x0, x1)))
744.41/263.16	   active(isNatKind(s(x0)))
744.41/263.16	   active(isNatKind(x(x0, x1)))
744.41/263.16	   active(plus(x0, 0))
744.41/263.16	   active(plus(x0, s(x1)))
744.41/263.16	   active(x(x0, 0))
744.41/263.16	   active(x(x0, s(x1)))
744.41/263.16	   mark(U101(x0, x1, x2))
744.41/263.16	   mark(tt)
744.41/263.16	   mark(U102(x0, x1, x2))
744.41/263.16	   mark(isNatKind(x0))
744.41/263.16	   mark(U103(x0, x1, x2))
744.41/263.16	   mark(isNat(x0))
744.41/263.16	   mark(U104(x0, x1, x2))
744.41/263.16	   mark(plus(x0, x1))
744.41/263.16	   mark(x(x0, x1))
744.41/263.16	   mark(U11(x0, x1, x2))
744.41/263.16	   mark(U12(x0, x1, x2))
744.41/263.16	   mark(U13(x0, x1, x2))
744.41/263.16	   mark(U14(x0, x1, x2))
744.41/263.16	   mark(U15(x0, x1))
744.41/263.16	   mark(U16(x0))
744.41/263.16	   mark(U21(x0, x1))
744.41/263.16	   mark(U22(x0, x1))
744.41/263.16	   mark(U23(x0))
744.41/263.16	   mark(U31(x0, x1, x2))
744.41/263.16	   mark(U32(x0, x1, x2))
744.41/263.16	   mark(U33(x0, x1, x2))
744.41/263.16	   mark(U34(x0, x1, x2))
744.41/263.16	   mark(U35(x0, x1))
744.41/263.16	   mark(U36(x0))
744.41/263.16	   mark(U41(x0, x1))
744.41/263.16	   mark(U42(x0))
744.41/263.16	   mark(U51(x0))
744.41/263.16	   mark(U61(x0, x1))
744.41/263.16	   mark(U62(x0))
744.41/263.16	   mark(U71(x0, x1))
744.41/263.16	   mark(U72(x0, x1))
744.41/263.16	   mark(U81(x0, x1, x2))
744.41/263.16	   mark(U82(x0, x1, x2))
744.41/263.16	   mark(U83(x0, x1, x2))
744.41/263.16	   mark(U84(x0, x1, x2))
744.41/263.16	   mark(s(x0))
744.41/263.16	   mark(U91(x0, x1))
744.41/263.16	   mark(U92(x0))
744.41/263.16	   mark(0)
744.41/263.16	   U101(mark(x0), x1, x2)
744.41/263.16	   U101(x0, mark(x1), x2)
744.41/263.16	   U101(x0, x1, mark(x2))
744.41/263.16	   U101(active(x0), x1, x2)
744.41/263.16	   U101(x0, active(x1), x2)
744.41/263.16	   U101(x0, x1, active(x2))
744.41/263.16	   U102(mark(x0), x1, x2)
744.41/263.16	   U102(x0, mark(x1), x2)
744.41/263.16	   U102(x0, x1, mark(x2))
744.41/263.16	   U102(active(x0), x1, x2)
744.41/263.16	   U102(x0, active(x1), x2)
744.41/263.16	   U102(x0, x1, active(x2))
744.41/263.16	   isNatKind(mark(x0))
744.41/263.16	   isNatKind(active(x0))
744.41/263.16	   U103(mark(x0), x1, x2)
744.41/263.16	   U103(x0, mark(x1), x2)
744.41/263.16	   U103(x0, x1, mark(x2))
744.41/263.16	   U103(active(x0), x1, x2)
744.41/263.16	   U103(x0, active(x1), x2)
744.41/263.16	   U103(x0, x1, active(x2))
744.41/263.16	   isNat(mark(x0))
744.41/263.16	   isNat(active(x0))
744.41/263.16	   U104(mark(x0), x1, x2)
744.41/263.16	   U104(x0, mark(x1), x2)
744.41/263.16	   U104(x0, x1, mark(x2))
744.41/263.16	   U104(active(x0), x1, x2)
744.41/263.16	   U104(x0, active(x1), x2)
744.41/263.16	   U104(x0, x1, active(x2))
744.41/263.16	   plus(mark(x0), x1)
744.41/263.16	   plus(x0, mark(x1))
744.41/263.16	   plus(active(x0), x1)
744.41/263.16	   plus(x0, active(x1))
744.41/263.16	   x(mark(x0), x1)
744.41/263.16	   x(x0, mark(x1))
744.41/263.16	   x(active(x0), x1)
744.41/263.16	   x(x0, active(x1))
744.41/263.16	   U11(mark(x0), x1, x2)
744.41/263.16	   U11(x0, mark(x1), x2)
744.41/263.16	   U11(x0, x1, mark(x2))
744.41/263.16	   U11(active(x0), x1, x2)
744.41/263.16	   U11(x0, active(x1), x2)
744.41/263.16	   U11(x0, x1, active(x2))
744.41/263.16	   U12(mark(x0), x1, x2)
744.41/263.16	   U12(x0, mark(x1), x2)
744.41/263.16	   U12(x0, x1, mark(x2))
744.41/263.16	   U12(active(x0), x1, x2)
744.41/263.16	   U12(x0, active(x1), x2)
744.41/263.16	   U12(x0, x1, active(x2))
744.41/263.16	   U13(mark(x0), x1, x2)
744.41/263.16	   U13(x0, mark(x1), x2)
744.41/263.16	   U13(x0, x1, mark(x2))
744.41/263.16	   U13(active(x0), x1, x2)
744.41/263.16	   U13(x0, active(x1), x2)
744.41/263.16	   U13(x0, x1, active(x2))
744.41/263.16	   U14(mark(x0), x1, x2)
744.41/263.16	   U14(x0, mark(x1), x2)
744.41/263.16	   U14(x0, x1, mark(x2))
744.41/263.16	   U14(active(x0), x1, x2)
744.41/263.16	   U14(x0, active(x1), x2)
744.41/263.16	   U14(x0, x1, active(x2))
744.41/263.16	   U15(mark(x0), x1)
744.41/263.16	   U15(x0, mark(x1))
744.41/263.16	   U15(active(x0), x1)
744.41/263.16	   U15(x0, active(x1))
744.41/263.16	   U16(mark(x0))
744.41/263.16	   U16(active(x0))
744.41/263.16	   U21(mark(x0), x1)
744.41/263.16	   U21(x0, mark(x1))
744.41/263.16	   U21(active(x0), x1)
744.41/263.16	   U21(x0, active(x1))
744.41/263.16	   U22(mark(x0), x1)
744.41/263.16	   U22(x0, mark(x1))
744.41/263.16	   U22(active(x0), x1)
744.41/263.16	   U22(x0, active(x1))
744.41/263.16	   U23(mark(x0))
744.41/263.16	   U23(active(x0))
744.41/263.16	   U31(mark(x0), x1, x2)
744.41/263.16	   U31(x0, mark(x1), x2)
744.41/263.16	   U31(x0, x1, mark(x2))
744.41/263.16	   U31(active(x0), x1, x2)
744.41/263.16	   U31(x0, active(x1), x2)
744.41/263.16	   U31(x0, x1, active(x2))
744.41/263.16	   U32(mark(x0), x1, x2)
744.41/263.16	   U32(x0, mark(x1), x2)
744.41/263.16	   U32(x0, x1, mark(x2))
744.41/263.16	   U32(active(x0), x1, x2)
744.41/263.16	   U32(x0, active(x1), x2)
744.41/263.16	   U32(x0, x1, active(x2))
744.41/263.16	   U33(mark(x0), x1, x2)
744.41/263.16	   U33(x0, mark(x1), x2)
744.41/263.16	   U33(x0, x1, mark(x2))
744.41/263.16	   U33(active(x0), x1, x2)
744.41/263.16	   U33(x0, active(x1), x2)
744.41/263.16	   U33(x0, x1, active(x2))
744.41/263.16	   U34(mark(x0), x1, x2)
744.41/263.16	   U34(x0, mark(x1), x2)
744.41/263.16	   U34(x0, x1, mark(x2))
744.41/263.16	   U34(active(x0), x1, x2)
744.41/263.16	   U34(x0, active(x1), x2)
744.41/263.16	   U34(x0, x1, active(x2))
744.41/263.16	   U35(mark(x0), x1)
744.41/263.16	   U35(x0, mark(x1))
744.41/263.16	   U35(active(x0), x1)
744.41/263.16	   U35(x0, active(x1))
744.41/263.16	   U36(mark(x0))
744.41/263.16	   U36(active(x0))
744.41/263.16	   U41(mark(x0), x1)
744.41/263.16	   U41(x0, mark(x1))
744.41/263.16	   U41(active(x0), x1)
744.41/263.16	   U41(x0, active(x1))
744.41/263.16	   U42(mark(x0))
744.41/263.16	   U42(active(x0))
744.41/263.16	   U51(mark(x0))
744.41/263.16	   U51(active(x0))
744.41/263.16	   U61(mark(x0), x1)
744.41/263.16	   U61(x0, mark(x1))
744.41/263.16	   U61(active(x0), x1)
744.41/263.16	   U61(x0, active(x1))
744.41/263.16	   U62(mark(x0))
744.41/263.16	   U62(active(x0))
744.41/263.16	   U71(mark(x0), x1)
744.41/263.16	   U71(x0, mark(x1))
744.41/263.16	   U71(active(x0), x1)
744.41/263.16	   U71(x0, active(x1))
744.41/263.16	   U72(mark(x0), x1)
744.41/263.16	   U72(x0, mark(x1))
744.41/263.16	   U72(active(x0), x1)
744.41/263.16	   U72(x0, active(x1))
744.41/263.16	   U81(mark(x0), x1, x2)
744.41/263.16	   U81(x0, mark(x1), x2)
744.41/263.16	   U81(x0, x1, mark(x2))
744.41/263.16	   U81(active(x0), x1, x2)
744.41/263.16	   U81(x0, active(x1), x2)
744.41/263.16	   U81(x0, x1, active(x2))
744.41/263.16	   U82(mark(x0), x1, x2)
744.41/263.16	   U82(x0, mark(x1), x2)
744.41/263.16	   U82(x0, x1, mark(x2))
744.41/263.16	   U82(active(x0), x1, x2)
744.41/263.16	   U82(x0, active(x1), x2)
744.41/263.16	   U82(x0, x1, active(x2))
744.41/263.16	   U83(mark(x0), x1, x2)
744.41/263.16	   U83(x0, mark(x1), x2)
744.41/263.16	   U83(x0, x1, mark(x2))
744.41/263.16	   U83(active(x0), x1, x2)
744.41/263.16	   U83(x0, active(x1), x2)
744.41/263.16	   U83(x0, x1, active(x2))
744.41/263.16	   U84(mark(x0), x1, x2)
744.41/263.16	   U84(x0, mark(x1), x2)
744.41/263.16	   U84(x0, x1, mark(x2))
744.41/263.16	   U84(active(x0), x1, x2)
744.41/263.16	   U84(x0, active(x1), x2)
744.41/263.16	   U84(x0, x1, active(x2))
744.41/263.16	   s(mark(x0))
744.41/263.16	   s(active(x0))
744.41/263.16	   U91(mark(x0), x1)
744.41/263.16	   U91(x0, mark(x1))
744.41/263.16	   U91(active(x0), x1)
744.41/263.16	   U91(x0, active(x1))
744.41/263.16	   U92(mark(x0))
744.41/263.16	   U92(active(x0))
744.41/263.16	
744.41/263.16	We have to consider all minimal (P,Q,R)-chains.
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(369) QDPOrderProof (EQUIVALENT)
744.41/263.16	We use the reduction pair processor [LPAR04,JAR06].
744.41/263.16	
744.41/263.16	
744.41/263.16	The following pairs can be oriented strictly and are deleted.
744.41/263.16	
744.41/263.16	   ACTIVE(isNat(plus(V1, V2))) -> MARK(U11(isNatKind(V1), V1, V2))
744.41/263.16	   ACTIVE(isNat(s(V1))) -> MARK(U21(isNatKind(V1), V1))
744.41/263.16	The remaining pairs can at least be oriented weakly.
744.41/263.16	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.41/263.16	
744.41/263.16	POL( ACTIVE_1(x_1) ) = max{0, x_1 - 1}
744.41/263.16	POL( U11_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.41/263.16	POL( U12_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.41/263.16	POL( U13_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.41/263.16	POL( U14_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.41/263.16	POL( U21_2(x_1, x_2) ) = 2x_2 + 2
744.41/263.16	POL( U22_2(x_1, x_2) ) = 2x_2 + 2
744.41/263.16	POL( mark_1(x_1) ) = 2x_1
744.41/263.16	POL( U102_3(x_1, ..., x_3) ) = x_1 + 2
744.41/263.16	POL( active_1(x_1) ) = x_1
744.41/263.16	POL( U101_3(x_1, ..., x_3) ) = max{0, x_3 - 2}
744.41/263.16	POL( tt ) = 2
744.41/263.16	POL( isNatKind_1(x_1) ) = 1
744.41/263.16	POL( U103_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.41/263.16	POL( isNat_1(x_1) ) = 2x_1 + 1
744.41/263.16	POL( U104_3(x_1, ..., x_3) ) = 2x_2 + 2x_3 + 2
744.41/263.16	POL( plus_2(x_1, x_2) ) = 2x_1 + x_2 + 1
744.41/263.16	POL( x_2(x_1, x_2) ) = max{0, 2x_1 - 1}
744.41/263.16	POL( U15_2(x_1, x_2) ) = x_1 + 2x_2 + 1
744.41/263.16	POL( U16_1(x_1) ) = max{0, -2}
744.41/263.16	POL( U23_1(x_1) ) = x_1 + 1
744.41/263.16	POL( U31_3(x_1, ..., x_3) ) = x_1 + 2x_3 + 2
744.41/263.16	POL( U32_3(x_1, ..., x_3) ) = x_1 + 2x_2 + 2
744.41/263.16	POL( U33_3(x_1, ..., x_3) ) = 2x_1 + x_2 + 2x_3 + 2
744.41/263.16	POL( U34_3(x_1, ..., x_3) ) = max{0, 2x_1 + 2x_2 + x_3 - 2}
744.41/263.16	POL( U35_2(x_1, x_2) ) = max{0, x_1 - 2}
744.41/263.16	POL( U36_1(x_1) ) = 0
744.41/263.16	POL( U41_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.41/263.16	POL( U42_1(x_1) ) = 2x_1 + 1
744.41/263.16	POL( U61_2(x_1, x_2) ) = max{0, 2x_1 - 2}
744.41/263.16	POL( U62_1(x_1) ) = 2
744.41/263.16	POL( U71_2(x_1, x_2) ) = max{0, x_2 - 2}
744.41/263.16	POL( U72_2(x_1, x_2) ) = max{0, x_2 - 2}
744.41/263.16	POL( U81_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.41/263.16	POL( U82_3(x_1, ..., x_3) ) = x_1 + x_2
744.41/263.16	POL( U83_3(x_1, ..., x_3) ) = 2x_1 + x_2 + 1
744.41/263.16	POL( U84_3(x_1, ..., x_3) ) = max{0, x_2 + x_3 - 2}
744.41/263.16	POL( s_1(x_1) ) = x_1 + 1
744.41/263.16	POL( U91_2(x_1, x_2) ) = x_1 + 2
744.41/263.16	POL( U92_1(x_1) ) = max{0, x_1 - 2}
744.41/263.16	POL( U51_1(x_1) ) = max{0, x_1 - 2}
744.41/263.16	POL( 0 ) = 0
744.41/263.16	POL( MARK_1(x_1) ) = max{0, x_1 - 1}
744.41/263.16	
744.41/263.16	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.41/263.16	
744.41/263.16	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U22(X1, mark(X2)) -> U22(X1, X2)
744.41/263.16	   U22(mark(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(active(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(X1, active(X2)) -> U22(X1, X2)
744.41/263.16	   U21(X1, mark(X2)) -> U21(X1, X2)
744.41/263.16	   U21(mark(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(active(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(X1, active(X2)) -> U21(X1, X2)
744.41/263.16	
744.41/263.16	
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(370)
744.41/263.16	Obligation:
744.41/263.16	Q DP problem:
744.41/263.16	The TRS P consists of the following rules:
744.41/263.16	
744.41/263.16	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.41/263.16	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.41/263.16	   MARK(U15(X1, X2)) -> MARK(X1)
744.41/263.16	   MARK(isNat(X)) -> ACTIVE(isNat(X))
744.41/263.16	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.41/263.16	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.41/263.16	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.41/263.16	   MARK(U23(X)) -> MARK(X)
744.41/263.16	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.41/263.16	
744.41/263.16	The TRS R consists of the following rules:
744.41/263.16	
744.41/263.16	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.41/263.16	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.41/263.16	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.41/263.16	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.41/263.16	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.41/263.16	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.41/263.16	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.41/263.16	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.41/263.16	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.41/263.16	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.41/263.16	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.41/263.16	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.41/263.16	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.41/263.16	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.41/263.16	   mark(U16(X)) -> active(U16(mark(X)))
744.41/263.16	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.41/263.16	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.41/263.16	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.41/263.16	   mark(U23(X)) -> active(U23(mark(X)))
744.41/263.16	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.41/263.16	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.41/263.16	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.41/263.16	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.41/263.16	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.41/263.16	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.41/263.16	   mark(U36(X)) -> active(U36(mark(X)))
744.41/263.16	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.41/263.16	   mark(U42(X)) -> active(U42(mark(X)))
744.41/263.16	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.41/263.16	   mark(U62(X)) -> active(U62(mark(X)))
744.41/263.16	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.41/263.16	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.41/263.16	   active(U72(tt, N)) -> mark(N)
744.41/263.16	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.41/263.16	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.41/263.16	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.41/263.16	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.41/263.16	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.41/263.16	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.41/263.16	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.41/263.16	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.41/263.16	   mark(s(X)) -> active(s(mark(X)))
744.41/263.16	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.41/263.16	   mark(U92(X)) -> active(U92(mark(X)))
744.41/263.16	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.41/263.16	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.41/263.16	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.41/263.16	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.41/263.16	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.41/263.16	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.41/263.16	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.41/263.16	   mark(U51(X)) -> active(U51(mark(X)))
744.41/263.16	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.41/263.16	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.41/263.16	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.41/263.16	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.41/263.16	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.41/263.16	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.41/263.16	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.41/263.16	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.41/263.16	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.41/263.16	   mark(isNatKind(X)) -> active(isNatKind(X))
744.41/263.16	   mark(isNat(X)) -> active(isNat(X))
744.41/263.16	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.41/263.16	   mark(tt) -> active(tt)
744.41/263.16	   mark(0) -> active(0)
744.41/263.16	   U61(X1, mark(X2)) -> U61(X1, X2)
744.41/263.16	   U61(mark(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(active(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(X1, active(X2)) -> U61(X1, X2)
744.41/263.16	   active(U16(tt)) -> mark(tt)
744.41/263.16	   active(U23(tt)) -> mark(tt)
744.41/263.16	   active(U36(tt)) -> mark(tt)
744.41/263.16	   active(U42(tt)) -> mark(tt)
744.41/263.16	   active(U51(tt)) -> mark(tt)
744.41/263.16	   active(U62(tt)) -> mark(tt)
744.41/263.16	   active(U92(tt)) -> mark(0)
744.41/263.16	   active(isNat(0)) -> mark(tt)
744.41/263.16	   active(isNatKind(0)) -> mark(tt)
744.41/263.16	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.41/263.16	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.41/263.16	   plus(X1, mark(X2)) -> plus(X1, X2)
744.41/263.16	   plus(mark(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(active(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(X1, active(X2)) -> plus(X1, X2)
744.41/263.16	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U15(X1, mark(X2)) -> U15(X1, X2)
744.41/263.16	   U15(mark(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(active(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(X1, active(X2)) -> U15(X1, X2)
744.41/263.16	   U16(active(X)) -> U16(X)
744.41/263.16	   U16(mark(X)) -> U16(X)
744.41/263.16	   U22(X1, mark(X2)) -> U22(X1, X2)
744.41/263.16	   U22(mark(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(active(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(X1, active(X2)) -> U22(X1, X2)
744.41/263.16	   U23(active(X)) -> U23(X)
744.41/263.16	   U23(mark(X)) -> U23(X)
744.41/263.16	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U35(X1, mark(X2)) -> U35(X1, X2)
744.41/263.16	   U35(mark(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(active(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(X1, active(X2)) -> U35(X1, X2)
744.41/263.16	   U36(active(X)) -> U36(X)
744.41/263.16	   U36(mark(X)) -> U36(X)
744.41/263.16	   U42(active(X)) -> U42(X)
744.41/263.16	   U42(mark(X)) -> U42(X)
744.41/263.16	   U62(active(X)) -> U62(X)
744.41/263.16	   U62(mark(X)) -> U62(X)
744.41/263.16	   U72(X1, mark(X2)) -> U72(X1, X2)
744.41/263.16	   U72(mark(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(active(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(X1, active(X2)) -> U72(X1, X2)
744.41/263.16	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.41/263.16	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.41/263.16	   s(active(X)) -> s(X)
744.41/263.16	   s(mark(X)) -> s(X)
744.41/263.16	   U92(active(X)) -> U92(X)
744.41/263.16	   U92(mark(X)) -> U92(X)
744.41/263.16	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.41/263.16	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.41/263.16	   U21(X1, mark(X2)) -> U21(X1, X2)
744.41/263.16	   U21(mark(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(active(X1), X2) -> U21(X1, X2)
744.41/263.16	   U21(X1, active(X2)) -> U21(X1, X2)
744.41/263.16	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.41/263.16	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.41/263.16	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.41/263.16	   U41(X1, mark(X2)) -> U41(X1, X2)
744.41/263.16	   U41(mark(X1), X2) -> U41(X1, X2)
744.41/263.16	   U41(active(X1), X2) -> U41(X1, X2)
744.41/263.16	   U41(X1, active(X2)) -> U41(X1, X2)
744.41/263.16	   U51(active(X)) -> U51(X)
744.41/263.16	   U51(mark(X)) -> U51(X)
744.41/263.16	   U71(X1, mark(X2)) -> U71(X1, X2)
744.41/263.16	   U71(mark(X1), X2) -> U71(X1, X2)
744.41/263.16	   U71(active(X1), X2) -> U71(X1, X2)
744.41/263.16	   U71(X1, active(X2)) -> U71(X1, X2)
744.41/263.16	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.41/263.16	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.41/263.16	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.41/263.16	   U91(X1, mark(X2)) -> U91(X1, X2)
744.41/263.16	   U91(mark(X1), X2) -> U91(X1, X2)
744.41/263.16	   U91(active(X1), X2) -> U91(X1, X2)
744.41/263.16	   U91(X1, active(X2)) -> U91(X1, X2)
744.41/263.16	   x(X1, mark(X2)) -> x(X1, X2)
744.41/263.16	   x(mark(X1), X2) -> x(X1, X2)
744.41/263.16	   x(active(X1), X2) -> x(X1, X2)
744.41/263.16	   x(X1, active(X2)) -> x(X1, X2)
744.41/263.16	
744.41/263.16	The set Q consists of the following terms:
744.41/263.16	
744.41/263.16	   active(U101(tt, x0, x1))
744.41/263.16	   active(U102(tt, x0, x1))
744.41/263.16	   active(U103(tt, x0, x1))
744.41/263.16	   active(U104(tt, x0, x1))
744.41/263.16	   active(U11(tt, x0, x1))
744.41/263.16	   active(U12(tt, x0, x1))
744.41/263.16	   active(U13(tt, x0, x1))
744.41/263.16	   active(U14(tt, x0, x1))
744.41/263.16	   active(U15(tt, x0))
744.41/263.16	   active(U16(tt))
744.41/263.16	   active(U21(tt, x0))
744.41/263.16	   active(U22(tt, x0))
744.41/263.16	   active(U23(tt))
744.41/263.16	   active(U31(tt, x0, x1))
744.41/263.16	   active(U32(tt, x0, x1))
744.41/263.16	   active(U33(tt, x0, x1))
744.41/263.16	   active(U34(tt, x0, x1))
744.41/263.16	   active(U35(tt, x0))
744.41/263.16	   active(U36(tt))
744.41/263.16	   active(U41(tt, x0))
744.41/263.16	   active(U42(tt))
744.41/263.16	   active(U51(tt))
744.41/263.16	   active(U61(tt, x0))
744.41/263.16	   active(U62(tt))
744.41/263.16	   active(U71(tt, x0))
744.41/263.16	   active(U72(tt, x0))
744.41/263.16	   active(U81(tt, x0, x1))
744.41/263.16	   active(U82(tt, x0, x1))
744.41/263.16	   active(U83(tt, x0, x1))
744.41/263.16	   active(U84(tt, x0, x1))
744.41/263.16	   active(U91(tt, x0))
744.41/263.16	   active(U92(tt))
744.41/263.16	   active(isNat(0))
744.41/263.16	   active(isNat(plus(x0, x1)))
744.41/263.16	   active(isNat(s(x0)))
744.41/263.16	   active(isNat(x(x0, x1)))
744.41/263.16	   active(isNatKind(0))
744.41/263.16	   active(isNatKind(plus(x0, x1)))
744.41/263.16	   active(isNatKind(s(x0)))
744.41/263.16	   active(isNatKind(x(x0, x1)))
744.41/263.16	   active(plus(x0, 0))
744.41/263.16	   active(plus(x0, s(x1)))
744.41/263.16	   active(x(x0, 0))
744.41/263.16	   active(x(x0, s(x1)))
744.41/263.16	   mark(U101(x0, x1, x2))
744.41/263.16	   mark(tt)
744.41/263.16	   mark(U102(x0, x1, x2))
744.41/263.16	   mark(isNatKind(x0))
744.41/263.16	   mark(U103(x0, x1, x2))
744.41/263.16	   mark(isNat(x0))
744.41/263.16	   mark(U104(x0, x1, x2))
744.41/263.16	   mark(plus(x0, x1))
744.41/263.16	   mark(x(x0, x1))
744.41/263.16	   mark(U11(x0, x1, x2))
744.41/263.16	   mark(U12(x0, x1, x2))
744.41/263.16	   mark(U13(x0, x1, x2))
744.41/263.16	   mark(U14(x0, x1, x2))
744.41/263.16	   mark(U15(x0, x1))
744.41/263.16	   mark(U16(x0))
744.41/263.16	   mark(U21(x0, x1))
744.41/263.16	   mark(U22(x0, x1))
744.41/263.16	   mark(U23(x0))
744.41/263.16	   mark(U31(x0, x1, x2))
744.41/263.16	   mark(U32(x0, x1, x2))
744.41/263.16	   mark(U33(x0, x1, x2))
744.41/263.16	   mark(U34(x0, x1, x2))
744.41/263.16	   mark(U35(x0, x1))
744.41/263.16	   mark(U36(x0))
744.41/263.16	   mark(U41(x0, x1))
744.41/263.16	   mark(U42(x0))
744.41/263.16	   mark(U51(x0))
744.41/263.16	   mark(U61(x0, x1))
744.41/263.16	   mark(U62(x0))
744.41/263.16	   mark(U71(x0, x1))
744.41/263.16	   mark(U72(x0, x1))
744.41/263.16	   mark(U81(x0, x1, x2))
744.41/263.16	   mark(U82(x0, x1, x2))
744.41/263.16	   mark(U83(x0, x1, x2))
744.41/263.16	   mark(U84(x0, x1, x2))
744.41/263.16	   mark(s(x0))
744.41/263.16	   mark(U91(x0, x1))
744.41/263.16	   mark(U92(x0))
744.41/263.16	   mark(0)
744.41/263.16	   U101(mark(x0), x1, x2)
744.41/263.16	   U101(x0, mark(x1), x2)
744.41/263.16	   U101(x0, x1, mark(x2))
744.41/263.16	   U101(active(x0), x1, x2)
744.41/263.16	   U101(x0, active(x1), x2)
744.41/263.16	   U101(x0, x1, active(x2))
744.41/263.16	   U102(mark(x0), x1, x2)
744.41/263.16	   U102(x0, mark(x1), x2)
744.41/263.16	   U102(x0, x1, mark(x2))
744.41/263.16	   U102(active(x0), x1, x2)
744.41/263.16	   U102(x0, active(x1), x2)
744.41/263.16	   U102(x0, x1, active(x2))
744.41/263.16	   isNatKind(mark(x0))
744.41/263.16	   isNatKind(active(x0))
744.41/263.16	   U103(mark(x0), x1, x2)
744.41/263.16	   U103(x0, mark(x1), x2)
744.41/263.16	   U103(x0, x1, mark(x2))
744.41/263.16	   U103(active(x0), x1, x2)
744.41/263.16	   U103(x0, active(x1), x2)
744.41/263.16	   U103(x0, x1, active(x2))
744.41/263.16	   isNat(mark(x0))
744.41/263.16	   isNat(active(x0))
744.41/263.16	   U104(mark(x0), x1, x2)
744.41/263.16	   U104(x0, mark(x1), x2)
744.41/263.16	   U104(x0, x1, mark(x2))
744.41/263.16	   U104(active(x0), x1, x2)
744.41/263.16	   U104(x0, active(x1), x2)
744.41/263.16	   U104(x0, x1, active(x2))
744.41/263.16	   plus(mark(x0), x1)
744.41/263.16	   plus(x0, mark(x1))
744.41/263.16	   plus(active(x0), x1)
744.41/263.16	   plus(x0, active(x1))
744.41/263.16	   x(mark(x0), x1)
744.41/263.16	   x(x0, mark(x1))
744.41/263.16	   x(active(x0), x1)
744.41/263.16	   x(x0, active(x1))
744.41/263.16	   U11(mark(x0), x1, x2)
744.41/263.16	   U11(x0, mark(x1), x2)
744.41/263.16	   U11(x0, x1, mark(x2))
744.41/263.16	   U11(active(x0), x1, x2)
744.41/263.16	   U11(x0, active(x1), x2)
744.41/263.16	   U11(x0, x1, active(x2))
744.41/263.16	   U12(mark(x0), x1, x2)
744.41/263.16	   U12(x0, mark(x1), x2)
744.41/263.16	   U12(x0, x1, mark(x2))
744.41/263.16	   U12(active(x0), x1, x2)
744.41/263.16	   U12(x0, active(x1), x2)
744.41/263.16	   U12(x0, x1, active(x2))
744.41/263.16	   U13(mark(x0), x1, x2)
744.41/263.16	   U13(x0, mark(x1), x2)
744.41/263.16	   U13(x0, x1, mark(x2))
744.41/263.16	   U13(active(x0), x1, x2)
744.41/263.16	   U13(x0, active(x1), x2)
744.41/263.16	   U13(x0, x1, active(x2))
744.41/263.16	   U14(mark(x0), x1, x2)
744.41/263.16	   U14(x0, mark(x1), x2)
744.41/263.16	   U14(x0, x1, mark(x2))
744.41/263.16	   U14(active(x0), x1, x2)
744.41/263.16	   U14(x0, active(x1), x2)
744.41/263.16	   U14(x0, x1, active(x2))
744.41/263.16	   U15(mark(x0), x1)
744.41/263.16	   U15(x0, mark(x1))
744.41/263.16	   U15(active(x0), x1)
744.41/263.16	   U15(x0, active(x1))
744.41/263.16	   U16(mark(x0))
744.41/263.16	   U16(active(x0))
744.41/263.16	   U21(mark(x0), x1)
744.41/263.16	   U21(x0, mark(x1))
744.41/263.16	   U21(active(x0), x1)
744.41/263.16	   U21(x0, active(x1))
744.41/263.16	   U22(mark(x0), x1)
744.41/263.16	   U22(x0, mark(x1))
744.41/263.16	   U22(active(x0), x1)
744.41/263.16	   U22(x0, active(x1))
744.41/263.16	   U23(mark(x0))
744.41/263.16	   U23(active(x0))
744.41/263.16	   U31(mark(x0), x1, x2)
744.41/263.16	   U31(x0, mark(x1), x2)
744.41/263.16	   U31(x0, x1, mark(x2))
744.41/263.16	   U31(active(x0), x1, x2)
744.41/263.16	   U31(x0, active(x1), x2)
744.41/263.16	   U31(x0, x1, active(x2))
744.41/263.16	   U32(mark(x0), x1, x2)
744.41/263.16	   U32(x0, mark(x1), x2)
744.41/263.16	   U32(x0, x1, mark(x2))
744.41/263.16	   U32(active(x0), x1, x2)
744.41/263.16	   U32(x0, active(x1), x2)
744.41/263.16	   U32(x0, x1, active(x2))
744.41/263.16	   U33(mark(x0), x1, x2)
744.41/263.16	   U33(x0, mark(x1), x2)
744.41/263.16	   U33(x0, x1, mark(x2))
744.41/263.16	   U33(active(x0), x1, x2)
744.41/263.16	   U33(x0, active(x1), x2)
744.41/263.16	   U33(x0, x1, active(x2))
744.41/263.16	   U34(mark(x0), x1, x2)
744.41/263.16	   U34(x0, mark(x1), x2)
744.41/263.16	   U34(x0, x1, mark(x2))
744.41/263.16	   U34(active(x0), x1, x2)
744.41/263.16	   U34(x0, active(x1), x2)
744.41/263.16	   U34(x0, x1, active(x2))
744.41/263.16	   U35(mark(x0), x1)
744.41/263.16	   U35(x0, mark(x1))
744.41/263.16	   U35(active(x0), x1)
744.41/263.16	   U35(x0, active(x1))
744.41/263.16	   U36(mark(x0))
744.41/263.16	   U36(active(x0))
744.41/263.16	   U41(mark(x0), x1)
744.41/263.16	   U41(x0, mark(x1))
744.41/263.16	   U41(active(x0), x1)
744.41/263.16	   U41(x0, active(x1))
744.41/263.16	   U42(mark(x0))
744.41/263.16	   U42(active(x0))
744.41/263.16	   U51(mark(x0))
744.41/263.16	   U51(active(x0))
744.41/263.16	   U61(mark(x0), x1)
744.41/263.16	   U61(x0, mark(x1))
744.41/263.16	   U61(active(x0), x1)
744.41/263.16	   U61(x0, active(x1))
744.41/263.16	   U62(mark(x0))
744.41/263.16	   U62(active(x0))
744.41/263.16	   U71(mark(x0), x1)
744.41/263.16	   U71(x0, mark(x1))
744.41/263.16	   U71(active(x0), x1)
744.41/263.16	   U71(x0, active(x1))
744.41/263.16	   U72(mark(x0), x1)
744.41/263.16	   U72(x0, mark(x1))
744.41/263.16	   U72(active(x0), x1)
744.41/263.16	   U72(x0, active(x1))
744.41/263.16	   U81(mark(x0), x1, x2)
744.41/263.16	   U81(x0, mark(x1), x2)
744.41/263.16	   U81(x0, x1, mark(x2))
744.41/263.16	   U81(active(x0), x1, x2)
744.41/263.16	   U81(x0, active(x1), x2)
744.41/263.16	   U81(x0, x1, active(x2))
744.41/263.16	   U82(mark(x0), x1, x2)
744.41/263.16	   U82(x0, mark(x1), x2)
744.41/263.16	   U82(x0, x1, mark(x2))
744.41/263.16	   U82(active(x0), x1, x2)
744.41/263.16	   U82(x0, active(x1), x2)
744.41/263.16	   U82(x0, x1, active(x2))
744.41/263.16	   U83(mark(x0), x1, x2)
744.41/263.16	   U83(x0, mark(x1), x2)
744.41/263.16	   U83(x0, x1, mark(x2))
744.41/263.16	   U83(active(x0), x1, x2)
744.41/263.16	   U83(x0, active(x1), x2)
744.41/263.16	   U83(x0, x1, active(x2))
744.41/263.16	   U84(mark(x0), x1, x2)
744.41/263.16	   U84(x0, mark(x1), x2)
744.41/263.16	   U84(x0, x1, mark(x2))
744.41/263.16	   U84(active(x0), x1, x2)
744.41/263.16	   U84(x0, active(x1), x2)
744.41/263.16	   U84(x0, x1, active(x2))
744.41/263.16	   s(mark(x0))
744.41/263.16	   s(active(x0))
744.41/263.16	   U91(mark(x0), x1)
744.41/263.16	   U91(x0, mark(x1))
744.41/263.16	   U91(active(x0), x1)
744.41/263.16	   U91(x0, active(x1))
744.41/263.16	   U92(mark(x0))
744.41/263.16	   U92(active(x0))
744.41/263.16	
744.41/263.16	We have to consider all minimal (P,Q,R)-chains.
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(371) DependencyGraphProof (EQUIVALENT)
744.41/263.16	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
744.41/263.16	----------------------------------------
744.41/263.16	
744.41/263.16	(372)
744.41/263.16	Obligation:
744.41/263.16	Q DP problem:
744.41/263.16	The TRS P consists of the following rules:
744.41/263.16	
744.41/263.16	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.41/263.16	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.41/263.16	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.41/263.16	   MARK(U15(X1, X2)) -> MARK(X1)
744.41/263.16	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.41/263.16	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.41/263.16	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.41/263.16	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.41/263.16	   MARK(U23(X)) -> MARK(X)
744.41/263.16	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.41/263.16	
744.41/263.16	The TRS R consists of the following rules:
744.41/263.16	
744.41/263.16	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.41/263.16	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.41/263.16	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.41/263.16	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.41/263.16	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.41/263.16	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.41/263.16	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.41/263.16	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.41/263.16	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.41/263.16	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.41/263.16	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.41/263.16	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.41/263.16	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.41/263.16	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.41/263.16	   mark(U16(X)) -> active(U16(mark(X)))
744.41/263.16	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.41/263.16	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.41/263.16	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.41/263.16	   mark(U23(X)) -> active(U23(mark(X)))
744.41/263.16	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.41/263.16	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.41/263.16	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.41/263.16	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.41/263.16	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.41/263.16	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.41/263.16	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.41/263.16	   mark(U36(X)) -> active(U36(mark(X)))
744.41/263.16	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.41/263.16	   mark(U42(X)) -> active(U42(mark(X)))
744.41/263.16	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.41/263.16	   mark(U62(X)) -> active(U62(mark(X)))
744.41/263.16	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.41/263.16	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.41/263.16	   active(U72(tt, N)) -> mark(N)
744.41/263.16	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.41/263.16	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.41/263.16	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.41/263.16	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.41/263.16	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.41/263.16	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.41/263.16	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.41/263.16	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.41/263.16	   mark(s(X)) -> active(s(mark(X)))
744.41/263.16	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.41/263.16	   mark(U92(X)) -> active(U92(mark(X)))
744.41/263.16	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.41/263.16	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.41/263.16	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.41/263.16	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.41/263.16	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.41/263.16	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.41/263.16	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.41/263.16	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.41/263.16	   mark(U51(X)) -> active(U51(mark(X)))
744.41/263.16	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.41/263.16	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.41/263.16	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.41/263.16	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.41/263.16	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.41/263.16	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.41/263.16	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.41/263.16	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.41/263.16	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.41/263.16	   mark(isNatKind(X)) -> active(isNatKind(X))
744.41/263.16	   mark(isNat(X)) -> active(isNat(X))
744.41/263.16	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.41/263.16	   mark(tt) -> active(tt)
744.41/263.16	   mark(0) -> active(0)
744.41/263.16	   U61(X1, mark(X2)) -> U61(X1, X2)
744.41/263.16	   U61(mark(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(active(X1), X2) -> U61(X1, X2)
744.41/263.16	   U61(X1, active(X2)) -> U61(X1, X2)
744.41/263.16	   active(U16(tt)) -> mark(tt)
744.41/263.16	   active(U23(tt)) -> mark(tt)
744.41/263.16	   active(U36(tt)) -> mark(tt)
744.41/263.16	   active(U42(tt)) -> mark(tt)
744.41/263.16	   active(U51(tt)) -> mark(tt)
744.41/263.16	   active(U62(tt)) -> mark(tt)
744.41/263.16	   active(U92(tt)) -> mark(0)
744.41/263.16	   active(isNat(0)) -> mark(tt)
744.41/263.16	   active(isNatKind(0)) -> mark(tt)
744.41/263.16	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.41/263.16	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.41/263.16	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.41/263.16	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.41/263.16	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.41/263.16	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.41/263.16	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.41/263.16	   plus(X1, mark(X2)) -> plus(X1, X2)
744.41/263.16	   plus(mark(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(active(X1), X2) -> plus(X1, X2)
744.41/263.16	   plus(X1, active(X2)) -> plus(X1, X2)
744.41/263.16	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.41/263.16	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.41/263.16	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.41/263.16	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.41/263.16	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.41/263.16	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.41/263.16	   U15(X1, mark(X2)) -> U15(X1, X2)
744.41/263.16	   U15(mark(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(active(X1), X2) -> U15(X1, X2)
744.41/263.16	   U15(X1, active(X2)) -> U15(X1, X2)
744.41/263.16	   U16(active(X)) -> U16(X)
744.41/263.16	   U16(mark(X)) -> U16(X)
744.41/263.16	   U22(X1, mark(X2)) -> U22(X1, X2)
744.41/263.16	   U22(mark(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(active(X1), X2) -> U22(X1, X2)
744.41/263.16	   U22(X1, active(X2)) -> U22(X1, X2)
744.41/263.16	   U23(active(X)) -> U23(X)
744.41/263.16	   U23(mark(X)) -> U23(X)
744.41/263.16	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.41/263.16	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.41/263.16	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.41/263.16	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.41/263.16	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.41/263.16	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.41/263.16	   U35(X1, mark(X2)) -> U35(X1, X2)
744.41/263.16	   U35(mark(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(active(X1), X2) -> U35(X1, X2)
744.41/263.16	   U35(X1, active(X2)) -> U35(X1, X2)
744.41/263.16	   U36(active(X)) -> U36(X)
744.41/263.16	   U36(mark(X)) -> U36(X)
744.41/263.16	   U42(active(X)) -> U42(X)
744.41/263.16	   U42(mark(X)) -> U42(X)
744.41/263.16	   U62(active(X)) -> U62(X)
744.41/263.16	   U62(mark(X)) -> U62(X)
744.41/263.16	   U72(X1, mark(X2)) -> U72(X1, X2)
744.41/263.16	   U72(mark(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(active(X1), X2) -> U72(X1, X2)
744.41/263.16	   U72(X1, active(X2)) -> U72(X1, X2)
744.41/263.16	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.41/263.16	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.41/263.16	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.41/263.16	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.41/263.16	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.41/263.16	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.41/263.16	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.41/263.16	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.41/263.16	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.41/263.16	   s(active(X)) -> s(X)
744.41/263.16	   s(mark(X)) -> s(X)
744.41/263.16	   U92(active(X)) -> U92(X)
744.41/263.16	   U92(mark(X)) -> U92(X)
744.41/263.16	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.42/263.16	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.16	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.42/263.16	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.16	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.42/263.16	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.42/263.16	   U21(X1, mark(X2)) -> U21(X1, X2)
744.42/263.16	   U21(mark(X1), X2) -> U21(X1, X2)
744.42/263.16	   U21(active(X1), X2) -> U21(X1, X2)
744.42/263.16	   U21(X1, active(X2)) -> U21(X1, X2)
744.42/263.16	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.42/263.16	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.16	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.42/263.16	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.16	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.42/263.16	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.42/263.16	   U41(X1, mark(X2)) -> U41(X1, X2)
744.42/263.16	   U41(mark(X1), X2) -> U41(X1, X2)
744.42/263.16	   U41(active(X1), X2) -> U41(X1, X2)
744.42/263.16	   U41(X1, active(X2)) -> U41(X1, X2)
744.42/263.16	   U51(active(X)) -> U51(X)
744.42/263.16	   U51(mark(X)) -> U51(X)
744.42/263.16	   U71(X1, mark(X2)) -> U71(X1, X2)
744.42/263.16	   U71(mark(X1), X2) -> U71(X1, X2)
744.42/263.16	   U71(active(X1), X2) -> U71(X1, X2)
744.42/263.16	   U71(X1, active(X2)) -> U71(X1, X2)
744.42/263.16	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.42/263.16	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.16	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.42/263.16	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.16	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.42/263.16	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.42/263.16	   U91(X1, mark(X2)) -> U91(X1, X2)
744.42/263.16	   U91(mark(X1), X2) -> U91(X1, X2)
744.42/263.16	   U91(active(X1), X2) -> U91(X1, X2)
744.42/263.16	   U91(X1, active(X2)) -> U91(X1, X2)
744.42/263.16	   x(X1, mark(X2)) -> x(X1, X2)
744.42/263.16	   x(mark(X1), X2) -> x(X1, X2)
744.42/263.16	   x(active(X1), X2) -> x(X1, X2)
744.42/263.16	   x(X1, active(X2)) -> x(X1, X2)
744.42/263.16	
744.42/263.16	The set Q consists of the following terms:
744.42/263.16	
744.42/263.16	   active(U101(tt, x0, x1))
744.42/263.16	   active(U102(tt, x0, x1))
744.42/263.16	   active(U103(tt, x0, x1))
744.42/263.16	   active(U104(tt, x0, x1))
744.42/263.16	   active(U11(tt, x0, x1))
744.42/263.16	   active(U12(tt, x0, x1))
744.42/263.16	   active(U13(tt, x0, x1))
744.42/263.16	   active(U14(tt, x0, x1))
744.42/263.16	   active(U15(tt, x0))
744.42/263.16	   active(U16(tt))
744.42/263.16	   active(U21(tt, x0))
744.42/263.16	   active(U22(tt, x0))
744.42/263.16	   active(U23(tt))
744.42/263.16	   active(U31(tt, x0, x1))
744.42/263.16	   active(U32(tt, x0, x1))
744.42/263.16	   active(U33(tt, x0, x1))
744.42/263.16	   active(U34(tt, x0, x1))
744.42/263.16	   active(U35(tt, x0))
744.42/263.16	   active(U36(tt))
744.42/263.16	   active(U41(tt, x0))
744.42/263.16	   active(U42(tt))
744.42/263.16	   active(U51(tt))
744.42/263.16	   active(U61(tt, x0))
744.42/263.16	   active(U62(tt))
744.42/263.16	   active(U71(tt, x0))
744.42/263.16	   active(U72(tt, x0))
744.42/263.16	   active(U81(tt, x0, x1))
744.42/263.16	   active(U82(tt, x0, x1))
744.42/263.16	   active(U83(tt, x0, x1))
744.42/263.16	   active(U84(tt, x0, x1))
744.42/263.16	   active(U91(tt, x0))
744.42/263.16	   active(U92(tt))
744.42/263.16	   active(isNat(0))
744.42/263.16	   active(isNat(plus(x0, x1)))
744.42/263.16	   active(isNat(s(x0)))
744.42/263.16	   active(isNat(x(x0, x1)))
744.42/263.16	   active(isNatKind(0))
744.42/263.16	   active(isNatKind(plus(x0, x1)))
744.42/263.16	   active(isNatKind(s(x0)))
744.42/263.16	   active(isNatKind(x(x0, x1)))
744.42/263.16	   active(plus(x0, 0))
744.42/263.16	   active(plus(x0, s(x1)))
744.42/263.16	   active(x(x0, 0))
744.42/263.16	   active(x(x0, s(x1)))
744.42/263.16	   mark(U101(x0, x1, x2))
744.42/263.16	   mark(tt)
744.42/263.16	   mark(U102(x0, x1, x2))
744.42/263.16	   mark(isNatKind(x0))
744.42/263.16	   mark(U103(x0, x1, x2))
744.42/263.16	   mark(isNat(x0))
744.42/263.16	   mark(U104(x0, x1, x2))
744.42/263.16	   mark(plus(x0, x1))
744.42/263.16	   mark(x(x0, x1))
744.42/263.16	   mark(U11(x0, x1, x2))
744.42/263.16	   mark(U12(x0, x1, x2))
744.42/263.16	   mark(U13(x0, x1, x2))
744.42/263.16	   mark(U14(x0, x1, x2))
744.42/263.16	   mark(U15(x0, x1))
744.42/263.16	   mark(U16(x0))
744.42/263.16	   mark(U21(x0, x1))
744.42/263.16	   mark(U22(x0, x1))
744.42/263.16	   mark(U23(x0))
744.42/263.16	   mark(U31(x0, x1, x2))
744.42/263.16	   mark(U32(x0, x1, x2))
744.42/263.16	   mark(U33(x0, x1, x2))
744.42/263.16	   mark(U34(x0, x1, x2))
744.42/263.16	   mark(U35(x0, x1))
744.42/263.16	   mark(U36(x0))
744.42/263.16	   mark(U41(x0, x1))
744.42/263.16	   mark(U42(x0))
744.42/263.16	   mark(U51(x0))
744.42/263.16	   mark(U61(x0, x1))
744.42/263.16	   mark(U62(x0))
744.42/263.16	   mark(U71(x0, x1))
744.42/263.16	   mark(U72(x0, x1))
744.42/263.16	   mark(U81(x0, x1, x2))
744.42/263.16	   mark(U82(x0, x1, x2))
744.42/263.16	   mark(U83(x0, x1, x2))
744.42/263.16	   mark(U84(x0, x1, x2))
744.42/263.16	   mark(s(x0))
744.42/263.16	   mark(U91(x0, x1))
744.42/263.16	   mark(U92(x0))
744.42/263.16	   mark(0)
744.42/263.16	   U101(mark(x0), x1, x2)
744.42/263.16	   U101(x0, mark(x1), x2)
744.42/263.16	   U101(x0, x1, mark(x2))
744.42/263.16	   U101(active(x0), x1, x2)
744.42/263.16	   U101(x0, active(x1), x2)
744.42/263.16	   U101(x0, x1, active(x2))
744.42/263.16	   U102(mark(x0), x1, x2)
744.42/263.16	   U102(x0, mark(x1), x2)
744.42/263.16	   U102(x0, x1, mark(x2))
744.42/263.16	   U102(active(x0), x1, x2)
744.42/263.16	   U102(x0, active(x1), x2)
744.42/263.16	   U102(x0, x1, active(x2))
744.42/263.16	   isNatKind(mark(x0))
744.42/263.16	   isNatKind(active(x0))
744.42/263.16	   U103(mark(x0), x1, x2)
744.42/263.16	   U103(x0, mark(x1), x2)
744.42/263.16	   U103(x0, x1, mark(x2))
744.42/263.16	   U103(active(x0), x1, x2)
744.42/263.16	   U103(x0, active(x1), x2)
744.42/263.16	   U103(x0, x1, active(x2))
744.42/263.16	   isNat(mark(x0))
744.42/263.16	   isNat(active(x0))
744.42/263.16	   U104(mark(x0), x1, x2)
744.42/263.16	   U104(x0, mark(x1), x2)
744.42/263.16	   U104(x0, x1, mark(x2))
744.42/263.16	   U104(active(x0), x1, x2)
744.42/263.16	   U104(x0, active(x1), x2)
744.42/263.16	   U104(x0, x1, active(x2))
744.42/263.16	   plus(mark(x0), x1)
744.42/263.16	   plus(x0, mark(x1))
744.42/263.16	   plus(active(x0), x1)
744.42/263.16	   plus(x0, active(x1))
744.42/263.16	   x(mark(x0), x1)
744.42/263.16	   x(x0, mark(x1))
744.42/263.16	   x(active(x0), x1)
744.42/263.16	   x(x0, active(x1))
744.42/263.16	   U11(mark(x0), x1, x2)
744.42/263.16	   U11(x0, mark(x1), x2)
744.42/263.16	   U11(x0, x1, mark(x2))
744.42/263.16	   U11(active(x0), x1, x2)
744.42/263.16	   U11(x0, active(x1), x2)
744.42/263.16	   U11(x0, x1, active(x2))
744.42/263.16	   U12(mark(x0), x1, x2)
744.42/263.16	   U12(x0, mark(x1), x2)
744.42/263.16	   U12(x0, x1, mark(x2))
744.42/263.16	   U12(active(x0), x1, x2)
744.42/263.16	   U12(x0, active(x1), x2)
744.42/263.16	   U12(x0, x1, active(x2))
744.42/263.16	   U13(mark(x0), x1, x2)
744.42/263.16	   U13(x0, mark(x1), x2)
744.42/263.16	   U13(x0, x1, mark(x2))
744.42/263.16	   U13(active(x0), x1, x2)
744.42/263.16	   U13(x0, active(x1), x2)
744.42/263.16	   U13(x0, x1, active(x2))
744.42/263.16	   U14(mark(x0), x1, x2)
744.42/263.16	   U14(x0, mark(x1), x2)
744.42/263.16	   U14(x0, x1, mark(x2))
744.42/263.16	   U14(active(x0), x1, x2)
744.42/263.16	   U14(x0, active(x1), x2)
744.42/263.16	   U14(x0, x1, active(x2))
744.42/263.16	   U15(mark(x0), x1)
744.42/263.16	   U15(x0, mark(x1))
744.42/263.16	   U15(active(x0), x1)
744.42/263.16	   U15(x0, active(x1))
744.42/263.16	   U16(mark(x0))
744.42/263.16	   U16(active(x0))
744.42/263.16	   U21(mark(x0), x1)
744.42/263.16	   U21(x0, mark(x1))
744.42/263.16	   U21(active(x0), x1)
744.42/263.16	   U21(x0, active(x1))
744.42/263.16	   U22(mark(x0), x1)
744.42/263.16	   U22(x0, mark(x1))
744.42/263.16	   U22(active(x0), x1)
744.42/263.16	   U22(x0, active(x1))
744.42/263.16	   U23(mark(x0))
744.42/263.16	   U23(active(x0))
744.42/263.16	   U31(mark(x0), x1, x2)
744.42/263.16	   U31(x0, mark(x1), x2)
744.42/263.16	   U31(x0, x1, mark(x2))
744.42/263.16	   U31(active(x0), x1, x2)
744.42/263.16	   U31(x0, active(x1), x2)
744.42/263.16	   U31(x0, x1, active(x2))
744.42/263.16	   U32(mark(x0), x1, x2)
744.42/263.16	   U32(x0, mark(x1), x2)
744.42/263.16	   U32(x0, x1, mark(x2))
744.42/263.16	   U32(active(x0), x1, x2)
744.42/263.16	   U32(x0, active(x1), x2)
744.42/263.16	   U32(x0, x1, active(x2))
744.42/263.16	   U33(mark(x0), x1, x2)
744.42/263.16	   U33(x0, mark(x1), x2)
744.42/263.16	   U33(x0, x1, mark(x2))
744.42/263.16	   U33(active(x0), x1, x2)
744.42/263.16	   U33(x0, active(x1), x2)
744.42/263.16	   U33(x0, x1, active(x2))
744.42/263.16	   U34(mark(x0), x1, x2)
744.42/263.16	   U34(x0, mark(x1), x2)
744.42/263.16	   U34(x0, x1, mark(x2))
744.42/263.16	   U34(active(x0), x1, x2)
744.42/263.16	   U34(x0, active(x1), x2)
744.42/263.16	   U34(x0, x1, active(x2))
744.42/263.16	   U35(mark(x0), x1)
744.42/263.16	   U35(x0, mark(x1))
744.42/263.16	   U35(active(x0), x1)
744.42/263.16	   U35(x0, active(x1))
744.42/263.16	   U36(mark(x0))
744.42/263.16	   U36(active(x0))
744.42/263.16	   U41(mark(x0), x1)
744.42/263.16	   U41(x0, mark(x1))
744.42/263.16	   U41(active(x0), x1)
744.42/263.16	   U41(x0, active(x1))
744.42/263.16	   U42(mark(x0))
744.42/263.16	   U42(active(x0))
744.42/263.16	   U51(mark(x0))
744.42/263.16	   U51(active(x0))
744.42/263.16	   U61(mark(x0), x1)
744.42/263.16	   U61(x0, mark(x1))
744.42/263.16	   U61(active(x0), x1)
744.42/263.16	   U61(x0, active(x1))
744.42/263.16	   U62(mark(x0))
744.42/263.16	   U62(active(x0))
744.42/263.16	   U71(mark(x0), x1)
744.42/263.16	   U71(x0, mark(x1))
744.42/263.16	   U71(active(x0), x1)
744.42/263.16	   U71(x0, active(x1))
744.42/263.16	   U72(mark(x0), x1)
744.42/263.16	   U72(x0, mark(x1))
744.42/263.16	   U72(active(x0), x1)
744.42/263.16	   U72(x0, active(x1))
744.42/263.16	   U81(mark(x0), x1, x2)
744.42/263.16	   U81(x0, mark(x1), x2)
744.42/263.16	   U81(x0, x1, mark(x2))
744.42/263.16	   U81(active(x0), x1, x2)
744.42/263.16	   U81(x0, active(x1), x2)
744.42/263.16	   U81(x0, x1, active(x2))
744.42/263.16	   U82(mark(x0), x1, x2)
744.42/263.16	   U82(x0, mark(x1), x2)
744.42/263.16	   U82(x0, x1, mark(x2))
744.42/263.16	   U82(active(x0), x1, x2)
744.42/263.16	   U82(x0, active(x1), x2)
744.42/263.16	   U82(x0, x1, active(x2))
744.42/263.16	   U83(mark(x0), x1, x2)
744.42/263.16	   U83(x0, mark(x1), x2)
744.42/263.16	   U83(x0, x1, mark(x2))
744.42/263.16	   U83(active(x0), x1, x2)
744.42/263.16	   U83(x0, active(x1), x2)
744.42/263.16	   U83(x0, x1, active(x2))
744.42/263.16	   U84(mark(x0), x1, x2)
744.42/263.16	   U84(x0, mark(x1), x2)
744.42/263.16	   U84(x0, x1, mark(x2))
744.42/263.16	   U84(active(x0), x1, x2)
744.42/263.16	   U84(x0, active(x1), x2)
744.42/263.16	   U84(x0, x1, active(x2))
744.42/263.16	   s(mark(x0))
744.42/263.16	   s(active(x0))
744.42/263.16	   U91(mark(x0), x1)
744.42/263.16	   U91(x0, mark(x1))
744.42/263.16	   U91(active(x0), x1)
744.42/263.16	   U91(x0, active(x1))
744.42/263.16	   U92(mark(x0))
744.42/263.16	   U92(active(x0))
744.42/263.16	
744.42/263.16	We have to consider all minimal (P,Q,R)-chains.
744.42/263.16	----------------------------------------
744.42/263.16	
744.42/263.16	(373) QDPOrderProof (EQUIVALENT)
744.42/263.16	We use the reduction pair processor [LPAR04,JAR06].
744.42/263.16	
744.42/263.16	
744.42/263.16	The following pairs can be oriented strictly and are deleted.
744.42/263.16	
744.42/263.16	   MARK(U11(X1, X2, X3)) -> ACTIVE(U11(mark(X1), X2, X3))
744.42/263.16	   MARK(U21(X1, X2)) -> ACTIVE(U21(mark(X1), X2))
744.42/263.16	The remaining pairs can at least be oriented weakly.
744.42/263.16	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
744.42/263.16	
744.42/263.16	POL( ACTIVE_1(x_1) ) = max{0, -2}
744.42/263.16	POL( U11_3(x_1, ..., x_3) ) = x_2 + 2x_3 + 2
744.42/263.16	POL( U12_3(x_1, ..., x_3) ) = max{0, -2}
744.42/263.16	POL( U13_3(x_1, ..., x_3) ) = max{0, -2}
744.42/263.16	POL( U14_3(x_1, ..., x_3) ) = max{0, -2}
744.42/263.16	POL( U21_2(x_1, x_2) ) = x_2 + 2
744.42/263.16	POL( U22_2(x_1, x_2) ) = max{0, -2}
744.42/263.16	POL( mark_1(x_1) ) = 0
744.42/263.16	POL( U102_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.42/263.16	POL( active_1(x_1) ) = 2
744.42/263.16	POL( U101_3(x_1, ..., x_3) ) = max{0, x_1 + x_3 - 2}
744.42/263.16	POL( tt ) = 0
744.42/263.16	POL( isNatKind_1(x_1) ) = 0
744.42/263.16	POL( U103_3(x_1, ..., x_3) ) = x_1 + 2x_3 + 2
744.42/263.16	POL( isNat_1(x_1) ) = 0
744.42/263.16	POL( U104_3(x_1, ..., x_3) ) = max{0, x_2 - 2}
744.42/263.16	POL( plus_2(x_1, x_2) ) = 2
744.42/263.16	POL( x_2(x_1, x_2) ) = 2
744.42/263.16	POL( U15_2(x_1, x_2) ) = 2x_1 + 1
744.42/263.16	POL( U16_1(x_1) ) = max{0, -2}
744.42/263.16	POL( U23_1(x_1) ) = 2x_1 + 1
744.42/263.16	POL( U31_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.42/263.16	POL( U32_3(x_1, ..., x_3) ) = max{0, 2x_2 + x_3 - 1}
744.42/263.16	POL( U33_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2}
744.42/263.16	POL( U34_3(x_1, ..., x_3) ) = max{0, x_1 + x_2 + x_3 - 2}
744.42/263.16	POL( U35_2(x_1, x_2) ) = x_1 + x_2 + 2
744.42/263.16	POL( U36_1(x_1) ) = max{0, -2}
744.42/263.16	POL( U41_2(x_1, x_2) ) = max{0, 2x_1 + x_2 - 2}
744.42/263.16	POL( U42_1(x_1) ) = 2
744.42/263.16	POL( U61_2(x_1, x_2) ) = 2
744.42/263.16	POL( U62_1(x_1) ) = 2
744.42/263.16	POL( U71_2(x_1, x_2) ) = x_1
744.42/263.16	POL( U72_2(x_1, x_2) ) = x_1 + 2
744.42/263.16	POL( U81_3(x_1, ..., x_3) ) = 2x_2 + 2
744.42/263.16	POL( U82_3(x_1, ..., x_3) ) = 2
744.42/263.16	POL( U83_3(x_1, ..., x_3) ) = max{0, x_1 - 2}
744.42/263.16	POL( U84_3(x_1, ..., x_3) ) = max{0, 2x_2 - 2}
744.42/263.16	POL( s_1(x_1) ) = 1
744.42/263.16	POL( U91_2(x_1, x_2) ) = max{0, 2x_1 + 2x_2 - 2}
744.42/263.16	POL( U92_1(x_1) ) = 1
744.42/263.16	POL( U51_1(x_1) ) = max{0, -2}
744.42/263.16	POL( 0 ) = 0
744.42/263.16	POL( MARK_1(x_1) ) = max{0, 2x_1 - 2}
744.42/263.16	
744.42/263.16	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.42/263.16	none
744.42/263.16	
744.42/263.16	
744.42/263.16	----------------------------------------
744.42/263.16	
744.42/263.16	(374)
744.42/263.16	Obligation:
744.42/263.16	Q DP problem:
744.42/263.16	The TRS P consists of the following rules:
744.42/263.16	
744.42/263.16	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.42/263.16	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.42/263.16	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.42/263.16	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.42/263.16	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.42/263.16	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.42/263.16	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.42/263.16	   MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.16	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.42/263.16	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.42/263.16	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.42/263.16	   MARK(U23(X)) -> MARK(X)
744.42/263.16	
744.42/263.16	The TRS R consists of the following rules:
744.42/263.16	
744.42/263.16	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.42/263.16	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.42/263.16	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.42/263.16	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.42/263.16	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.42/263.16	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.42/263.16	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.42/263.16	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.42/263.16	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.42/263.16	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.42/263.16	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.42/263.16	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.42/263.16	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.42/263.16	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.42/263.16	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.42/263.16	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.42/263.16	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.42/263.16	   mark(U16(X)) -> active(U16(mark(X)))
744.42/263.16	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.42/263.16	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.42/263.16	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.42/263.16	   mark(U23(X)) -> active(U23(mark(X)))
744.42/263.16	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.42/263.16	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.42/263.16	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.42/263.16	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.42/263.16	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.42/263.16	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.42/263.16	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.42/263.16	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.42/263.16	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.42/263.16	   mark(U36(X)) -> active(U36(mark(X)))
744.42/263.16	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.42/263.16	   mark(U42(X)) -> active(U42(mark(X)))
744.42/263.16	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.42/263.16	   mark(U62(X)) -> active(U62(mark(X)))
744.42/263.16	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.42/263.16	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.42/263.16	   active(U72(tt, N)) -> mark(N)
744.42/263.16	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.42/263.16	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.42/263.16	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.42/263.16	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.42/263.16	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.42/263.16	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.42/263.16	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.42/263.16	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.42/263.16	   mark(s(X)) -> active(s(mark(X)))
744.42/263.16	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.42/263.16	   mark(U92(X)) -> active(U92(mark(X)))
744.42/263.16	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.42/263.16	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.42/263.16	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.42/263.16	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.42/263.16	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.42/263.16	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.42/263.16	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.42/263.16	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.42/263.16	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.42/263.16	   mark(U51(X)) -> active(U51(mark(X)))
744.42/263.16	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.42/263.16	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.42/263.16	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.42/263.16	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.42/263.16	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.42/263.16	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.42/263.16	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.42/263.16	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.42/263.16	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.42/263.16	   mark(isNatKind(X)) -> active(isNatKind(X))
744.42/263.16	   mark(isNat(X)) -> active(isNat(X))
744.42/263.16	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.42/263.16	   mark(tt) -> active(tt)
744.42/263.16	   mark(0) -> active(0)
744.42/263.16	   U61(X1, mark(X2)) -> U61(X1, X2)
744.42/263.16	   U61(mark(X1), X2) -> U61(X1, X2)
744.42/263.16	   U61(active(X1), X2) -> U61(X1, X2)
744.42/263.16	   U61(X1, active(X2)) -> U61(X1, X2)
744.42/263.16	   active(U16(tt)) -> mark(tt)
744.42/263.16	   active(U23(tt)) -> mark(tt)
744.42/263.16	   active(U36(tt)) -> mark(tt)
744.42/263.16	   active(U42(tt)) -> mark(tt)
744.42/263.16	   active(U51(tt)) -> mark(tt)
744.42/263.16	   active(U62(tt)) -> mark(tt)
744.42/263.16	   active(U92(tt)) -> mark(0)
744.42/263.16	   active(isNat(0)) -> mark(tt)
744.42/263.16	   active(isNatKind(0)) -> mark(tt)
744.42/263.16	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.42/263.16	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.16	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.42/263.16	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.16	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.42/263.16	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.42/263.16	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.42/263.16	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.16	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.42/263.16	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.16	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.42/263.16	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.42/263.16	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.42/263.16	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.16	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.42/263.16	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.42/263.17	   plus(X1, mark(X2)) -> plus(X1, X2)
744.42/263.17	   plus(mark(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(active(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(X1, active(X2)) -> plus(X1, X2)
744.42/263.17	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U15(X1, mark(X2)) -> U15(X1, X2)
744.42/263.17	   U15(mark(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(active(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(X1, active(X2)) -> U15(X1, X2)
744.42/263.17	   U16(active(X)) -> U16(X)
744.42/263.17	   U16(mark(X)) -> U16(X)
744.42/263.17	   U22(X1, mark(X2)) -> U22(X1, X2)
744.42/263.17	   U22(mark(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(active(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(X1, active(X2)) -> U22(X1, X2)
744.42/263.17	   U23(active(X)) -> U23(X)
744.42/263.17	   U23(mark(X)) -> U23(X)
744.42/263.17	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U35(X1, mark(X2)) -> U35(X1, X2)
744.42/263.17	   U35(mark(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(active(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(X1, active(X2)) -> U35(X1, X2)
744.42/263.17	   U36(active(X)) -> U36(X)
744.42/263.17	   U36(mark(X)) -> U36(X)
744.42/263.17	   U42(active(X)) -> U42(X)
744.42/263.17	   U42(mark(X)) -> U42(X)
744.42/263.17	   U62(active(X)) -> U62(X)
744.42/263.17	   U62(mark(X)) -> U62(X)
744.42/263.17	   U72(X1, mark(X2)) -> U72(X1, X2)
744.42/263.17	   U72(mark(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(active(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(X1, active(X2)) -> U72(X1, X2)
744.42/263.17	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.42/263.17	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.42/263.17	   s(active(X)) -> s(X)
744.42/263.17	   s(mark(X)) -> s(X)
744.42/263.17	   U92(active(X)) -> U92(X)
744.42/263.17	   U92(mark(X)) -> U92(X)
744.42/263.17	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U21(X1, mark(X2)) -> U21(X1, X2)
744.42/263.17	   U21(mark(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(active(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(X1, active(X2)) -> U21(X1, X2)
744.42/263.17	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U41(X1, mark(X2)) -> U41(X1, X2)
744.42/263.17	   U41(mark(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(active(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(X1, active(X2)) -> U41(X1, X2)
744.42/263.17	   U51(active(X)) -> U51(X)
744.42/263.17	   U51(mark(X)) -> U51(X)
744.42/263.17	   U71(X1, mark(X2)) -> U71(X1, X2)
744.42/263.17	   U71(mark(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(active(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(X1, active(X2)) -> U71(X1, X2)
744.42/263.17	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U91(X1, mark(X2)) -> U91(X1, X2)
744.42/263.17	   U91(mark(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(active(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(X1, active(X2)) -> U91(X1, X2)
744.42/263.17	   x(X1, mark(X2)) -> x(X1, X2)
744.42/263.17	   x(mark(X1), X2) -> x(X1, X2)
744.42/263.17	   x(active(X1), X2) -> x(X1, X2)
744.42/263.17	   x(X1, active(X2)) -> x(X1, X2)
744.42/263.17	
744.42/263.17	The set Q consists of the following terms:
744.42/263.17	
744.42/263.17	   active(U101(tt, x0, x1))
744.42/263.17	   active(U102(tt, x0, x1))
744.42/263.17	   active(U103(tt, x0, x1))
744.42/263.17	   active(U104(tt, x0, x1))
744.42/263.17	   active(U11(tt, x0, x1))
744.42/263.17	   active(U12(tt, x0, x1))
744.42/263.17	   active(U13(tt, x0, x1))
744.42/263.17	   active(U14(tt, x0, x1))
744.42/263.17	   active(U15(tt, x0))
744.42/263.17	   active(U16(tt))
744.42/263.17	   active(U21(tt, x0))
744.42/263.17	   active(U22(tt, x0))
744.42/263.17	   active(U23(tt))
744.42/263.17	   active(U31(tt, x0, x1))
744.42/263.17	   active(U32(tt, x0, x1))
744.42/263.17	   active(U33(tt, x0, x1))
744.42/263.17	   active(U34(tt, x0, x1))
744.42/263.17	   active(U35(tt, x0))
744.42/263.17	   active(U36(tt))
744.42/263.17	   active(U41(tt, x0))
744.42/263.17	   active(U42(tt))
744.42/263.17	   active(U51(tt))
744.42/263.17	   active(U61(tt, x0))
744.42/263.17	   active(U62(tt))
744.42/263.17	   active(U71(tt, x0))
744.42/263.17	   active(U72(tt, x0))
744.42/263.17	   active(U81(tt, x0, x1))
744.42/263.17	   active(U82(tt, x0, x1))
744.42/263.17	   active(U83(tt, x0, x1))
744.42/263.17	   active(U84(tt, x0, x1))
744.42/263.17	   active(U91(tt, x0))
744.42/263.17	   active(U92(tt))
744.42/263.17	   active(isNat(0))
744.42/263.17	   active(isNat(plus(x0, x1)))
744.42/263.17	   active(isNat(s(x0)))
744.42/263.17	   active(isNat(x(x0, x1)))
744.42/263.17	   active(isNatKind(0))
744.42/263.17	   active(isNatKind(plus(x0, x1)))
744.42/263.17	   active(isNatKind(s(x0)))
744.42/263.17	   active(isNatKind(x(x0, x1)))
744.42/263.17	   active(plus(x0, 0))
744.42/263.17	   active(plus(x0, s(x1)))
744.42/263.17	   active(x(x0, 0))
744.42/263.17	   active(x(x0, s(x1)))
744.42/263.17	   mark(U101(x0, x1, x2))
744.42/263.17	   mark(tt)
744.42/263.17	   mark(U102(x0, x1, x2))
744.42/263.17	   mark(isNatKind(x0))
744.42/263.17	   mark(U103(x0, x1, x2))
744.42/263.17	   mark(isNat(x0))
744.42/263.17	   mark(U104(x0, x1, x2))
744.42/263.17	   mark(plus(x0, x1))
744.42/263.17	   mark(x(x0, x1))
744.42/263.17	   mark(U11(x0, x1, x2))
744.42/263.17	   mark(U12(x0, x1, x2))
744.42/263.17	   mark(U13(x0, x1, x2))
744.42/263.17	   mark(U14(x0, x1, x2))
744.42/263.17	   mark(U15(x0, x1))
744.42/263.17	   mark(U16(x0))
744.42/263.17	   mark(U21(x0, x1))
744.42/263.17	   mark(U22(x0, x1))
744.42/263.17	   mark(U23(x0))
744.42/263.17	   mark(U31(x0, x1, x2))
744.42/263.17	   mark(U32(x0, x1, x2))
744.42/263.17	   mark(U33(x0, x1, x2))
744.42/263.17	   mark(U34(x0, x1, x2))
744.42/263.17	   mark(U35(x0, x1))
744.42/263.17	   mark(U36(x0))
744.42/263.17	   mark(U41(x0, x1))
744.42/263.17	   mark(U42(x0))
744.42/263.17	   mark(U51(x0))
744.42/263.17	   mark(U61(x0, x1))
744.42/263.17	   mark(U62(x0))
744.42/263.17	   mark(U71(x0, x1))
744.42/263.17	   mark(U72(x0, x1))
744.42/263.17	   mark(U81(x0, x1, x2))
744.42/263.17	   mark(U82(x0, x1, x2))
744.42/263.17	   mark(U83(x0, x1, x2))
744.42/263.17	   mark(U84(x0, x1, x2))
744.42/263.17	   mark(s(x0))
744.42/263.17	   mark(U91(x0, x1))
744.42/263.17	   mark(U92(x0))
744.42/263.17	   mark(0)
744.42/263.17	   U101(mark(x0), x1, x2)
744.42/263.17	   U101(x0, mark(x1), x2)
744.42/263.17	   U101(x0, x1, mark(x2))
744.42/263.17	   U101(active(x0), x1, x2)
744.42/263.17	   U101(x0, active(x1), x2)
744.42/263.17	   U101(x0, x1, active(x2))
744.42/263.17	   U102(mark(x0), x1, x2)
744.42/263.17	   U102(x0, mark(x1), x2)
744.42/263.17	   U102(x0, x1, mark(x2))
744.42/263.17	   U102(active(x0), x1, x2)
744.42/263.17	   U102(x0, active(x1), x2)
744.42/263.17	   U102(x0, x1, active(x2))
744.42/263.17	   isNatKind(mark(x0))
744.42/263.17	   isNatKind(active(x0))
744.42/263.17	   U103(mark(x0), x1, x2)
744.42/263.17	   U103(x0, mark(x1), x2)
744.42/263.17	   U103(x0, x1, mark(x2))
744.42/263.17	   U103(active(x0), x1, x2)
744.42/263.17	   U103(x0, active(x1), x2)
744.42/263.17	   U103(x0, x1, active(x2))
744.42/263.17	   isNat(mark(x0))
744.42/263.17	   isNat(active(x0))
744.42/263.17	   U104(mark(x0), x1, x2)
744.42/263.17	   U104(x0, mark(x1), x2)
744.42/263.17	   U104(x0, x1, mark(x2))
744.42/263.17	   U104(active(x0), x1, x2)
744.42/263.17	   U104(x0, active(x1), x2)
744.42/263.17	   U104(x0, x1, active(x2))
744.42/263.17	   plus(mark(x0), x1)
744.42/263.17	   plus(x0, mark(x1))
744.42/263.17	   plus(active(x0), x1)
744.42/263.17	   plus(x0, active(x1))
744.42/263.17	   x(mark(x0), x1)
744.42/263.17	   x(x0, mark(x1))
744.42/263.17	   x(active(x0), x1)
744.42/263.17	   x(x0, active(x1))
744.42/263.17	   U11(mark(x0), x1, x2)
744.42/263.17	   U11(x0, mark(x1), x2)
744.42/263.17	   U11(x0, x1, mark(x2))
744.42/263.17	   U11(active(x0), x1, x2)
744.42/263.17	   U11(x0, active(x1), x2)
744.42/263.17	   U11(x0, x1, active(x2))
744.42/263.17	   U12(mark(x0), x1, x2)
744.42/263.17	   U12(x0, mark(x1), x2)
744.42/263.17	   U12(x0, x1, mark(x2))
744.42/263.17	   U12(active(x0), x1, x2)
744.42/263.17	   U12(x0, active(x1), x2)
744.42/263.17	   U12(x0, x1, active(x2))
744.42/263.17	   U13(mark(x0), x1, x2)
744.42/263.17	   U13(x0, mark(x1), x2)
744.42/263.17	   U13(x0, x1, mark(x2))
744.42/263.17	   U13(active(x0), x1, x2)
744.42/263.17	   U13(x0, active(x1), x2)
744.42/263.17	   U13(x0, x1, active(x2))
744.42/263.17	   U14(mark(x0), x1, x2)
744.42/263.17	   U14(x0, mark(x1), x2)
744.42/263.17	   U14(x0, x1, mark(x2))
744.42/263.17	   U14(active(x0), x1, x2)
744.42/263.17	   U14(x0, active(x1), x2)
744.42/263.17	   U14(x0, x1, active(x2))
744.42/263.17	   U15(mark(x0), x1)
744.42/263.17	   U15(x0, mark(x1))
744.42/263.17	   U15(active(x0), x1)
744.42/263.17	   U15(x0, active(x1))
744.42/263.17	   U16(mark(x0))
744.42/263.17	   U16(active(x0))
744.42/263.17	   U21(mark(x0), x1)
744.42/263.17	   U21(x0, mark(x1))
744.42/263.17	   U21(active(x0), x1)
744.42/263.17	   U21(x0, active(x1))
744.42/263.17	   U22(mark(x0), x1)
744.42/263.17	   U22(x0, mark(x1))
744.42/263.17	   U22(active(x0), x1)
744.42/263.17	   U22(x0, active(x1))
744.42/263.17	   U23(mark(x0))
744.42/263.17	   U23(active(x0))
744.42/263.17	   U31(mark(x0), x1, x2)
744.42/263.17	   U31(x0, mark(x1), x2)
744.42/263.17	   U31(x0, x1, mark(x2))
744.42/263.17	   U31(active(x0), x1, x2)
744.42/263.17	   U31(x0, active(x1), x2)
744.42/263.17	   U31(x0, x1, active(x2))
744.42/263.17	   U32(mark(x0), x1, x2)
744.42/263.17	   U32(x0, mark(x1), x2)
744.42/263.17	   U32(x0, x1, mark(x2))
744.42/263.17	   U32(active(x0), x1, x2)
744.42/263.17	   U32(x0, active(x1), x2)
744.42/263.17	   U32(x0, x1, active(x2))
744.42/263.17	   U33(mark(x0), x1, x2)
744.42/263.17	   U33(x0, mark(x1), x2)
744.42/263.17	   U33(x0, x1, mark(x2))
744.42/263.17	   U33(active(x0), x1, x2)
744.42/263.17	   U33(x0, active(x1), x2)
744.42/263.17	   U33(x0, x1, active(x2))
744.42/263.17	   U34(mark(x0), x1, x2)
744.42/263.17	   U34(x0, mark(x1), x2)
744.42/263.17	   U34(x0, x1, mark(x2))
744.42/263.17	   U34(active(x0), x1, x2)
744.42/263.17	   U34(x0, active(x1), x2)
744.42/263.17	   U34(x0, x1, active(x2))
744.42/263.17	   U35(mark(x0), x1)
744.42/263.17	   U35(x0, mark(x1))
744.42/263.17	   U35(active(x0), x1)
744.42/263.17	   U35(x0, active(x1))
744.42/263.17	   U36(mark(x0))
744.42/263.17	   U36(active(x0))
744.42/263.17	   U41(mark(x0), x1)
744.42/263.17	   U41(x0, mark(x1))
744.42/263.17	   U41(active(x0), x1)
744.42/263.17	   U41(x0, active(x1))
744.42/263.17	   U42(mark(x0))
744.42/263.17	   U42(active(x0))
744.42/263.17	   U51(mark(x0))
744.42/263.17	   U51(active(x0))
744.42/263.17	   U61(mark(x0), x1)
744.42/263.17	   U61(x0, mark(x1))
744.42/263.17	   U61(active(x0), x1)
744.42/263.17	   U61(x0, active(x1))
744.42/263.17	   U62(mark(x0))
744.42/263.17	   U62(active(x0))
744.42/263.17	   U71(mark(x0), x1)
744.42/263.17	   U71(x0, mark(x1))
744.42/263.17	   U71(active(x0), x1)
744.42/263.17	   U71(x0, active(x1))
744.42/263.17	   U72(mark(x0), x1)
744.42/263.17	   U72(x0, mark(x1))
744.42/263.17	   U72(active(x0), x1)
744.42/263.17	   U72(x0, active(x1))
744.42/263.17	   U81(mark(x0), x1, x2)
744.42/263.17	   U81(x0, mark(x1), x2)
744.42/263.17	   U81(x0, x1, mark(x2))
744.42/263.17	   U81(active(x0), x1, x2)
744.42/263.17	   U81(x0, active(x1), x2)
744.42/263.17	   U81(x0, x1, active(x2))
744.42/263.17	   U82(mark(x0), x1, x2)
744.42/263.17	   U82(x0, mark(x1), x2)
744.42/263.17	   U82(x0, x1, mark(x2))
744.42/263.17	   U82(active(x0), x1, x2)
744.42/263.17	   U82(x0, active(x1), x2)
744.42/263.17	   U82(x0, x1, active(x2))
744.42/263.17	   U83(mark(x0), x1, x2)
744.42/263.17	   U83(x0, mark(x1), x2)
744.42/263.17	   U83(x0, x1, mark(x2))
744.42/263.17	   U83(active(x0), x1, x2)
744.42/263.17	   U83(x0, active(x1), x2)
744.42/263.17	   U83(x0, x1, active(x2))
744.42/263.17	   U84(mark(x0), x1, x2)
744.42/263.17	   U84(x0, mark(x1), x2)
744.42/263.17	   U84(x0, x1, mark(x2))
744.42/263.17	   U84(active(x0), x1, x2)
744.42/263.17	   U84(x0, active(x1), x2)
744.42/263.17	   U84(x0, x1, active(x2))
744.42/263.17	   s(mark(x0))
744.42/263.17	   s(active(x0))
744.42/263.17	   U91(mark(x0), x1)
744.42/263.17	   U91(x0, mark(x1))
744.42/263.17	   U91(active(x0), x1)
744.42/263.17	   U91(x0, active(x1))
744.42/263.17	   U92(mark(x0))
744.42/263.17	   U92(active(x0))
744.42/263.17	
744.42/263.17	We have to consider all minimal (P,Q,R)-chains.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(375) QDPOrderProof (EQUIVALENT)
744.42/263.17	We use the reduction pair processor [LPAR04,JAR06].
744.42/263.17	
744.42/263.17	
744.42/263.17	The following pairs can be oriented strictly and are deleted.
744.42/263.17	
744.42/263.17	   ACTIVE(U11(tt, V1, V2)) -> MARK(U12(isNatKind(V1), V1, V2))
744.42/263.17	   ACTIVE(U12(tt, V1, V2)) -> MARK(U13(isNatKind(V2), V1, V2))
744.42/263.17	   ACTIVE(U13(tt, V1, V2)) -> MARK(U14(isNatKind(V2), V1, V2))
744.42/263.17	   ACTIVE(U14(tt, V1, V2)) -> MARK(U15(isNat(V1), V2))
744.42/263.17	   ACTIVE(U21(tt, V1)) -> MARK(U22(isNatKind(V1), V1))
744.42/263.17	   ACTIVE(U22(tt, V1)) -> MARK(U23(isNat(V1)))
744.42/263.17	The remaining pairs can at least be oriented weakly.
744.42/263.17	Used ordering:  Combined order from the following AFS and order.
744.42/263.17	MARK(x1)  =  x1
744.42/263.17	
744.42/263.17	U12(x1, x2, x3)  =  U12
744.42/263.17	
744.42/263.17	ACTIVE(x1)  =  x1
744.42/263.17	
744.42/263.17	U11(x1, x2, x3)  =  U11
744.42/263.17	
744.42/263.17	U13(x1, x2, x3)  =  U13
744.42/263.17	
744.42/263.17	U14(x1, x2, x3)  =  U14
744.42/263.17	
744.42/263.17	U15(x1, x2)  =  x1
744.42/263.17	
744.42/263.17	isNat(x1)  =  isNat
744.42/263.17	
744.42/263.17	U21(x1, x2)  =  U21
744.42/263.17	
744.42/263.17	U22(x1, x2)  =  U22
744.42/263.17	
744.42/263.17	U23(x1)  =  x1
744.42/263.17	
744.42/263.17	mark(x1)  =  x1
744.42/263.17	
744.42/263.17	active(x1)  =  x1
744.42/263.17	
744.42/263.17	
744.42/263.17	Knuth-Bendix order [KBO] with precedence:trivial
744.42/263.17	
744.42/263.17	and weight map:
744.42/263.17	
744.42/263.17	   isNat=1
744.42/263.17	   U12=4
744.42/263.17	   U22=2
744.42/263.17	   U14=2
744.42/263.17	   U13=3
744.42/263.17	   U21=3
744.42/263.17	   U11=5
744.42/263.17	
744.42/263.17	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
744.42/263.17	
744.42/263.17	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U22(X1, mark(X2)) -> U22(X1, X2)
744.42/263.17	   U22(mark(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(active(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(X1, active(X2)) -> U22(X1, X2)
744.42/263.17	
744.42/263.17	
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(376)
744.42/263.17	Obligation:
744.42/263.17	Q DP problem:
744.42/263.17	The TRS P consists of the following rules:
744.42/263.17	
744.42/263.17	   MARK(U12(X1, X2, X3)) -> ACTIVE(U12(mark(X1), X2, X3))
744.42/263.17	   MARK(U13(X1, X2, X3)) -> ACTIVE(U13(mark(X1), X2, X3))
744.42/263.17	   MARK(U14(X1, X2, X3)) -> ACTIVE(U14(mark(X1), X2, X3))
744.42/263.17	   MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.17	   MARK(U22(X1, X2)) -> ACTIVE(U22(mark(X1), X2))
744.42/263.17	   MARK(U23(X)) -> MARK(X)
744.42/263.17	
744.42/263.17	The TRS R consists of the following rules:
744.42/263.17	
744.42/263.17	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.42/263.17	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.42/263.17	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.42/263.17	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.42/263.17	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.42/263.17	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.42/263.17	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.42/263.17	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.42/263.17	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.42/263.17	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.42/263.17	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.42/263.17	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.42/263.17	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.42/263.17	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.42/263.17	   mark(U16(X)) -> active(U16(mark(X)))
744.42/263.17	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.42/263.17	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.42/263.17	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.42/263.17	   mark(U23(X)) -> active(U23(mark(X)))
744.42/263.17	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.42/263.17	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.42/263.17	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.42/263.17	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.42/263.17	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.42/263.17	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.42/263.17	   mark(U36(X)) -> active(U36(mark(X)))
744.42/263.17	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.42/263.17	   mark(U42(X)) -> active(U42(mark(X)))
744.42/263.17	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.42/263.17	   mark(U62(X)) -> active(U62(mark(X)))
744.42/263.17	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.42/263.17	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.42/263.17	   active(U72(tt, N)) -> mark(N)
744.42/263.17	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.42/263.17	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.42/263.17	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.42/263.17	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.42/263.17	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.42/263.17	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.42/263.17	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.42/263.17	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.42/263.17	   mark(s(X)) -> active(s(mark(X)))
744.42/263.17	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.42/263.17	   mark(U92(X)) -> active(U92(mark(X)))
744.42/263.17	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.42/263.17	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.42/263.17	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.42/263.17	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.42/263.17	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.42/263.17	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.42/263.17	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.42/263.17	   mark(U51(X)) -> active(U51(mark(X)))
744.42/263.17	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.42/263.17	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.42/263.17	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.42/263.17	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.42/263.17	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.42/263.17	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.42/263.17	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.42/263.17	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.42/263.17	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.42/263.17	   mark(isNatKind(X)) -> active(isNatKind(X))
744.42/263.17	   mark(isNat(X)) -> active(isNat(X))
744.42/263.17	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.42/263.17	   mark(tt) -> active(tt)
744.42/263.17	   mark(0) -> active(0)
744.42/263.17	   U61(X1, mark(X2)) -> U61(X1, X2)
744.42/263.17	   U61(mark(X1), X2) -> U61(X1, X2)
744.42/263.17	   U61(active(X1), X2) -> U61(X1, X2)
744.42/263.17	   U61(X1, active(X2)) -> U61(X1, X2)
744.42/263.17	   active(U16(tt)) -> mark(tt)
744.42/263.17	   active(U23(tt)) -> mark(tt)
744.42/263.17	   active(U36(tt)) -> mark(tt)
744.42/263.17	   active(U42(tt)) -> mark(tt)
744.42/263.17	   active(U51(tt)) -> mark(tt)
744.42/263.17	   active(U62(tt)) -> mark(tt)
744.42/263.17	   active(U92(tt)) -> mark(0)
744.42/263.17	   active(isNat(0)) -> mark(tt)
744.42/263.17	   active(isNatKind(0)) -> mark(tt)
744.42/263.17	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.42/263.17	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.42/263.17	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.42/263.17	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.42/263.17	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.42/263.17	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.42/263.17	   plus(X1, mark(X2)) -> plus(X1, X2)
744.42/263.17	   plus(mark(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(active(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(X1, active(X2)) -> plus(X1, X2)
744.42/263.17	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U15(X1, mark(X2)) -> U15(X1, X2)
744.42/263.17	   U15(mark(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(active(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(X1, active(X2)) -> U15(X1, X2)
744.42/263.17	   U16(active(X)) -> U16(X)
744.42/263.17	   U16(mark(X)) -> U16(X)
744.42/263.17	   U22(X1, mark(X2)) -> U22(X1, X2)
744.42/263.17	   U22(mark(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(active(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(X1, active(X2)) -> U22(X1, X2)
744.42/263.17	   U23(active(X)) -> U23(X)
744.42/263.17	   U23(mark(X)) -> U23(X)
744.42/263.17	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U35(X1, mark(X2)) -> U35(X1, X2)
744.42/263.17	   U35(mark(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(active(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(X1, active(X2)) -> U35(X1, X2)
744.42/263.17	   U36(active(X)) -> U36(X)
744.42/263.17	   U36(mark(X)) -> U36(X)
744.42/263.17	   U42(active(X)) -> U42(X)
744.42/263.17	   U42(mark(X)) -> U42(X)
744.42/263.17	   U62(active(X)) -> U62(X)
744.42/263.17	   U62(mark(X)) -> U62(X)
744.42/263.17	   U72(X1, mark(X2)) -> U72(X1, X2)
744.42/263.17	   U72(mark(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(active(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(X1, active(X2)) -> U72(X1, X2)
744.42/263.17	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.42/263.17	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.42/263.17	   s(active(X)) -> s(X)
744.42/263.17	   s(mark(X)) -> s(X)
744.42/263.17	   U92(active(X)) -> U92(X)
744.42/263.17	   U92(mark(X)) -> U92(X)
744.42/263.17	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U21(X1, mark(X2)) -> U21(X1, X2)
744.42/263.17	   U21(mark(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(active(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(X1, active(X2)) -> U21(X1, X2)
744.42/263.17	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U41(X1, mark(X2)) -> U41(X1, X2)
744.42/263.17	   U41(mark(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(active(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(X1, active(X2)) -> U41(X1, X2)
744.42/263.17	   U51(active(X)) -> U51(X)
744.42/263.17	   U51(mark(X)) -> U51(X)
744.42/263.17	   U71(X1, mark(X2)) -> U71(X1, X2)
744.42/263.17	   U71(mark(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(active(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(X1, active(X2)) -> U71(X1, X2)
744.42/263.17	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U91(X1, mark(X2)) -> U91(X1, X2)
744.42/263.17	   U91(mark(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(active(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(X1, active(X2)) -> U91(X1, X2)
744.42/263.17	   x(X1, mark(X2)) -> x(X1, X2)
744.42/263.17	   x(mark(X1), X2) -> x(X1, X2)
744.42/263.17	   x(active(X1), X2) -> x(X1, X2)
744.42/263.17	   x(X1, active(X2)) -> x(X1, X2)
744.42/263.17	
744.42/263.17	The set Q consists of the following terms:
744.42/263.17	
744.42/263.17	   active(U101(tt, x0, x1))
744.42/263.17	   active(U102(tt, x0, x1))
744.42/263.17	   active(U103(tt, x0, x1))
744.42/263.17	   active(U104(tt, x0, x1))
744.42/263.17	   active(U11(tt, x0, x1))
744.42/263.17	   active(U12(tt, x0, x1))
744.42/263.17	   active(U13(tt, x0, x1))
744.42/263.17	   active(U14(tt, x0, x1))
744.42/263.17	   active(U15(tt, x0))
744.42/263.17	   active(U16(tt))
744.42/263.17	   active(U21(tt, x0))
744.42/263.17	   active(U22(tt, x0))
744.42/263.17	   active(U23(tt))
744.42/263.17	   active(U31(tt, x0, x1))
744.42/263.17	   active(U32(tt, x0, x1))
744.42/263.17	   active(U33(tt, x0, x1))
744.42/263.17	   active(U34(tt, x0, x1))
744.42/263.17	   active(U35(tt, x0))
744.42/263.17	   active(U36(tt))
744.42/263.17	   active(U41(tt, x0))
744.42/263.17	   active(U42(tt))
744.42/263.17	   active(U51(tt))
744.42/263.17	   active(U61(tt, x0))
744.42/263.17	   active(U62(tt))
744.42/263.17	   active(U71(tt, x0))
744.42/263.17	   active(U72(tt, x0))
744.42/263.17	   active(U81(tt, x0, x1))
744.42/263.17	   active(U82(tt, x0, x1))
744.42/263.17	   active(U83(tt, x0, x1))
744.42/263.17	   active(U84(tt, x0, x1))
744.42/263.17	   active(U91(tt, x0))
744.42/263.17	   active(U92(tt))
744.42/263.17	   active(isNat(0))
744.42/263.17	   active(isNat(plus(x0, x1)))
744.42/263.17	   active(isNat(s(x0)))
744.42/263.17	   active(isNat(x(x0, x1)))
744.42/263.17	   active(isNatKind(0))
744.42/263.17	   active(isNatKind(plus(x0, x1)))
744.42/263.17	   active(isNatKind(s(x0)))
744.42/263.17	   active(isNatKind(x(x0, x1)))
744.42/263.17	   active(plus(x0, 0))
744.42/263.17	   active(plus(x0, s(x1)))
744.42/263.17	   active(x(x0, 0))
744.42/263.17	   active(x(x0, s(x1)))
744.42/263.17	   mark(U101(x0, x1, x2))
744.42/263.17	   mark(tt)
744.42/263.17	   mark(U102(x0, x1, x2))
744.42/263.17	   mark(isNatKind(x0))
744.42/263.17	   mark(U103(x0, x1, x2))
744.42/263.17	   mark(isNat(x0))
744.42/263.17	   mark(U104(x0, x1, x2))
744.42/263.17	   mark(plus(x0, x1))
744.42/263.17	   mark(x(x0, x1))
744.42/263.17	   mark(U11(x0, x1, x2))
744.42/263.17	   mark(U12(x0, x1, x2))
744.42/263.17	   mark(U13(x0, x1, x2))
744.42/263.17	   mark(U14(x0, x1, x2))
744.42/263.17	   mark(U15(x0, x1))
744.42/263.17	   mark(U16(x0))
744.42/263.17	   mark(U21(x0, x1))
744.42/263.17	   mark(U22(x0, x1))
744.42/263.17	   mark(U23(x0))
744.42/263.17	   mark(U31(x0, x1, x2))
744.42/263.17	   mark(U32(x0, x1, x2))
744.42/263.17	   mark(U33(x0, x1, x2))
744.42/263.17	   mark(U34(x0, x1, x2))
744.42/263.17	   mark(U35(x0, x1))
744.42/263.17	   mark(U36(x0))
744.42/263.17	   mark(U41(x0, x1))
744.42/263.17	   mark(U42(x0))
744.42/263.17	   mark(U51(x0))
744.42/263.17	   mark(U61(x0, x1))
744.42/263.17	   mark(U62(x0))
744.42/263.17	   mark(U71(x0, x1))
744.42/263.17	   mark(U72(x0, x1))
744.42/263.17	   mark(U81(x0, x1, x2))
744.42/263.17	   mark(U82(x0, x1, x2))
744.42/263.17	   mark(U83(x0, x1, x2))
744.42/263.17	   mark(U84(x0, x1, x2))
744.42/263.17	   mark(s(x0))
744.42/263.17	   mark(U91(x0, x1))
744.42/263.17	   mark(U92(x0))
744.42/263.17	   mark(0)
744.42/263.17	   U101(mark(x0), x1, x2)
744.42/263.17	   U101(x0, mark(x1), x2)
744.42/263.17	   U101(x0, x1, mark(x2))
744.42/263.17	   U101(active(x0), x1, x2)
744.42/263.17	   U101(x0, active(x1), x2)
744.42/263.17	   U101(x0, x1, active(x2))
744.42/263.17	   U102(mark(x0), x1, x2)
744.42/263.17	   U102(x0, mark(x1), x2)
744.42/263.17	   U102(x0, x1, mark(x2))
744.42/263.17	   U102(active(x0), x1, x2)
744.42/263.17	   U102(x0, active(x1), x2)
744.42/263.17	   U102(x0, x1, active(x2))
744.42/263.17	   isNatKind(mark(x0))
744.42/263.17	   isNatKind(active(x0))
744.42/263.17	   U103(mark(x0), x1, x2)
744.42/263.17	   U103(x0, mark(x1), x2)
744.42/263.17	   U103(x0, x1, mark(x2))
744.42/263.17	   U103(active(x0), x1, x2)
744.42/263.17	   U103(x0, active(x1), x2)
744.42/263.17	   U103(x0, x1, active(x2))
744.42/263.17	   isNat(mark(x0))
744.42/263.17	   isNat(active(x0))
744.42/263.17	   U104(mark(x0), x1, x2)
744.42/263.17	   U104(x0, mark(x1), x2)
744.42/263.17	   U104(x0, x1, mark(x2))
744.42/263.17	   U104(active(x0), x1, x2)
744.42/263.17	   U104(x0, active(x1), x2)
744.42/263.17	   U104(x0, x1, active(x2))
744.42/263.17	   plus(mark(x0), x1)
744.42/263.17	   plus(x0, mark(x1))
744.42/263.17	   plus(active(x0), x1)
744.42/263.17	   plus(x0, active(x1))
744.42/263.17	   x(mark(x0), x1)
744.42/263.17	   x(x0, mark(x1))
744.42/263.17	   x(active(x0), x1)
744.42/263.17	   x(x0, active(x1))
744.42/263.17	   U11(mark(x0), x1, x2)
744.42/263.17	   U11(x0, mark(x1), x2)
744.42/263.17	   U11(x0, x1, mark(x2))
744.42/263.17	   U11(active(x0), x1, x2)
744.42/263.17	   U11(x0, active(x1), x2)
744.42/263.17	   U11(x0, x1, active(x2))
744.42/263.17	   U12(mark(x0), x1, x2)
744.42/263.17	   U12(x0, mark(x1), x2)
744.42/263.17	   U12(x0, x1, mark(x2))
744.42/263.17	   U12(active(x0), x1, x2)
744.42/263.17	   U12(x0, active(x1), x2)
744.42/263.17	   U12(x0, x1, active(x2))
744.42/263.17	   U13(mark(x0), x1, x2)
744.42/263.17	   U13(x0, mark(x1), x2)
744.42/263.17	   U13(x0, x1, mark(x2))
744.42/263.17	   U13(active(x0), x1, x2)
744.42/263.17	   U13(x0, active(x1), x2)
744.42/263.17	   U13(x0, x1, active(x2))
744.42/263.17	   U14(mark(x0), x1, x2)
744.42/263.17	   U14(x0, mark(x1), x2)
744.42/263.17	   U14(x0, x1, mark(x2))
744.42/263.17	   U14(active(x0), x1, x2)
744.42/263.17	   U14(x0, active(x1), x2)
744.42/263.17	   U14(x0, x1, active(x2))
744.42/263.17	   U15(mark(x0), x1)
744.42/263.17	   U15(x0, mark(x1))
744.42/263.17	   U15(active(x0), x1)
744.42/263.17	   U15(x0, active(x1))
744.42/263.17	   U16(mark(x0))
744.42/263.17	   U16(active(x0))
744.42/263.17	   U21(mark(x0), x1)
744.42/263.17	   U21(x0, mark(x1))
744.42/263.17	   U21(active(x0), x1)
744.42/263.17	   U21(x0, active(x1))
744.42/263.17	   U22(mark(x0), x1)
744.42/263.17	   U22(x0, mark(x1))
744.42/263.17	   U22(active(x0), x1)
744.42/263.17	   U22(x0, active(x1))
744.42/263.17	   U23(mark(x0))
744.42/263.17	   U23(active(x0))
744.42/263.17	   U31(mark(x0), x1, x2)
744.42/263.17	   U31(x0, mark(x1), x2)
744.42/263.17	   U31(x0, x1, mark(x2))
744.42/263.17	   U31(active(x0), x1, x2)
744.42/263.17	   U31(x0, active(x1), x2)
744.42/263.17	   U31(x0, x1, active(x2))
744.42/263.17	   U32(mark(x0), x1, x2)
744.42/263.17	   U32(x0, mark(x1), x2)
744.42/263.17	   U32(x0, x1, mark(x2))
744.42/263.17	   U32(active(x0), x1, x2)
744.42/263.17	   U32(x0, active(x1), x2)
744.42/263.17	   U32(x0, x1, active(x2))
744.42/263.17	   U33(mark(x0), x1, x2)
744.42/263.17	   U33(x0, mark(x1), x2)
744.42/263.17	   U33(x0, x1, mark(x2))
744.42/263.17	   U33(active(x0), x1, x2)
744.42/263.17	   U33(x0, active(x1), x2)
744.42/263.17	   U33(x0, x1, active(x2))
744.42/263.17	   U34(mark(x0), x1, x2)
744.42/263.17	   U34(x0, mark(x1), x2)
744.42/263.17	   U34(x0, x1, mark(x2))
744.42/263.17	   U34(active(x0), x1, x2)
744.42/263.17	   U34(x0, active(x1), x2)
744.42/263.17	   U34(x0, x1, active(x2))
744.42/263.17	   U35(mark(x0), x1)
744.42/263.17	   U35(x0, mark(x1))
744.42/263.17	   U35(active(x0), x1)
744.42/263.17	   U35(x0, active(x1))
744.42/263.17	   U36(mark(x0))
744.42/263.17	   U36(active(x0))
744.42/263.17	   U41(mark(x0), x1)
744.42/263.17	   U41(x0, mark(x1))
744.42/263.17	   U41(active(x0), x1)
744.42/263.17	   U41(x0, active(x1))
744.42/263.17	   U42(mark(x0))
744.42/263.17	   U42(active(x0))
744.42/263.17	   U51(mark(x0))
744.42/263.17	   U51(active(x0))
744.42/263.17	   U61(mark(x0), x1)
744.42/263.17	   U61(x0, mark(x1))
744.42/263.17	   U61(active(x0), x1)
744.42/263.17	   U61(x0, active(x1))
744.42/263.17	   U62(mark(x0))
744.42/263.17	   U62(active(x0))
744.42/263.17	   U71(mark(x0), x1)
744.42/263.17	   U71(x0, mark(x1))
744.42/263.17	   U71(active(x0), x1)
744.42/263.17	   U71(x0, active(x1))
744.42/263.17	   U72(mark(x0), x1)
744.42/263.17	   U72(x0, mark(x1))
744.42/263.17	   U72(active(x0), x1)
744.42/263.17	   U72(x0, active(x1))
744.42/263.17	   U81(mark(x0), x1, x2)
744.42/263.17	   U81(x0, mark(x1), x2)
744.42/263.17	   U81(x0, x1, mark(x2))
744.42/263.17	   U81(active(x0), x1, x2)
744.42/263.17	   U81(x0, active(x1), x2)
744.42/263.17	   U81(x0, x1, active(x2))
744.42/263.17	   U82(mark(x0), x1, x2)
744.42/263.17	   U82(x0, mark(x1), x2)
744.42/263.17	   U82(x0, x1, mark(x2))
744.42/263.17	   U82(active(x0), x1, x2)
744.42/263.17	   U82(x0, active(x1), x2)
744.42/263.17	   U82(x0, x1, active(x2))
744.42/263.17	   U83(mark(x0), x1, x2)
744.42/263.17	   U83(x0, mark(x1), x2)
744.42/263.17	   U83(x0, x1, mark(x2))
744.42/263.17	   U83(active(x0), x1, x2)
744.42/263.17	   U83(x0, active(x1), x2)
744.42/263.17	   U83(x0, x1, active(x2))
744.42/263.17	   U84(mark(x0), x1, x2)
744.42/263.17	   U84(x0, mark(x1), x2)
744.42/263.17	   U84(x0, x1, mark(x2))
744.42/263.17	   U84(active(x0), x1, x2)
744.42/263.17	   U84(x0, active(x1), x2)
744.42/263.17	   U84(x0, x1, active(x2))
744.42/263.17	   s(mark(x0))
744.42/263.17	   s(active(x0))
744.42/263.17	   U91(mark(x0), x1)
744.42/263.17	   U91(x0, mark(x1))
744.42/263.17	   U91(active(x0), x1)
744.42/263.17	   U91(x0, active(x1))
744.42/263.17	   U92(mark(x0))
744.42/263.17	   U92(active(x0))
744.42/263.17	
744.42/263.17	We have to consider all minimal (P,Q,R)-chains.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(377) DependencyGraphProof (EQUIVALENT)
744.42/263.17	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(378)
744.42/263.17	Obligation:
744.42/263.17	Q DP problem:
744.42/263.17	The TRS P consists of the following rules:
744.42/263.17	
744.42/263.17	   MARK(U23(X)) -> MARK(X)
744.42/263.17	   MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.17	
744.42/263.17	The TRS R consists of the following rules:
744.42/263.17	
744.42/263.17	   mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3))
744.42/263.17	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
744.42/263.17	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
744.42/263.17	   mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3))
744.42/263.17	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
744.42/263.17	   mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3))
744.42/263.17	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
744.42/263.17	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
744.42/263.17	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3))
744.42/263.17	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U13(X1, X2, X3)) -> active(U13(mark(X1), X2, X3))
744.42/263.17	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U14(X1, X2, X3)) -> active(U14(mark(X1), X2, X3))
744.42/263.17	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
744.42/263.17	   mark(U15(X1, X2)) -> active(U15(mark(X1), X2))
744.42/263.17	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
744.42/263.17	   mark(U16(X)) -> active(U16(mark(X)))
744.42/263.17	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
744.42/263.17	   mark(U22(X1, X2)) -> active(U22(mark(X1), X2))
744.42/263.17	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
744.42/263.17	   mark(U23(X)) -> active(U23(mark(X)))
744.42/263.17	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U32(X1, X2, X3)) -> active(U32(mark(X1), X2, X3))
744.42/263.17	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U33(X1, X2, X3)) -> active(U33(mark(X1), X2, X3))
744.42/263.17	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
744.42/263.17	   mark(U34(X1, X2, X3)) -> active(U34(mark(X1), X2, X3))
744.42/263.17	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
744.42/263.17	   mark(U35(X1, X2)) -> active(U35(mark(X1), X2))
744.42/263.17	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
744.42/263.17	   mark(U36(X)) -> active(U36(mark(X)))
744.42/263.17	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
744.42/263.17	   mark(U42(X)) -> active(U42(mark(X)))
744.42/263.17	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
744.42/263.17	   mark(U62(X)) -> active(U62(mark(X)))
744.42/263.17	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
744.42/263.17	   mark(U72(X1, X2)) -> active(U72(mark(X1), X2))
744.42/263.17	   active(U72(tt, N)) -> mark(N)
744.42/263.17	   mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3))
744.42/263.17	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
744.42/263.17	   mark(U82(X1, X2, X3)) -> active(U82(mark(X1), X2, X3))
744.42/263.17	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
744.42/263.17	   mark(U83(X1, X2, X3)) -> active(U83(mark(X1), X2, X3))
744.42/263.17	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
744.42/263.17	   mark(U84(X1, X2, X3)) -> active(U84(mark(X1), X2, X3))
744.42/263.17	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
744.42/263.17	   mark(s(X)) -> active(s(mark(X)))
744.42/263.17	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
744.42/263.17	   mark(U92(X)) -> active(U92(mark(X)))
744.42/263.17	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
744.42/263.17	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
744.42/263.17	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
744.42/263.17	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
744.42/263.17	   mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3))
744.42/263.17	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
744.42/263.17	   mark(U41(X1, X2)) -> active(U41(mark(X1), X2))
744.42/263.17	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
744.42/263.17	   mark(U51(X)) -> active(U51(mark(X)))
744.42/263.17	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
744.42/263.17	   mark(U61(X1, X2)) -> active(U61(mark(X1), X2))
744.42/263.17	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
744.42/263.17	   mark(U71(X1, X2)) -> active(U71(mark(X1), X2))
744.42/263.17	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
744.42/263.17	   mark(U81(X1, X2, X3)) -> active(U81(mark(X1), X2, X3))
744.42/263.17	   active(x(N, 0)) -> mark(U91(isNat(N), N))
744.42/263.17	   mark(U91(X1, X2)) -> active(U91(mark(X1), X2))
744.42/263.17	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
744.42/263.17	   mark(isNatKind(X)) -> active(isNatKind(X))
744.42/263.17	   mark(isNat(X)) -> active(isNat(X))
744.42/263.17	   mark(x(X1, X2)) -> active(x(mark(X1), mark(X2)))
744.42/263.17	   mark(tt) -> active(tt)
744.42/263.17	   mark(0) -> active(0)
744.42/263.17	   U61(X1, mark(X2)) -> U61(X1, X2)
744.42/263.17	   U61(mark(X1), X2) -> U61(X1, X2)
744.42/263.17	   U61(active(X1), X2) -> U61(X1, X2)
744.42/263.17	   U61(X1, active(X2)) -> U61(X1, X2)
744.42/263.17	   active(U16(tt)) -> mark(tt)
744.42/263.17	   active(U23(tt)) -> mark(tt)
744.42/263.17	   active(U36(tt)) -> mark(tt)
744.42/263.17	   active(U42(tt)) -> mark(tt)
744.42/263.17	   active(U51(tt)) -> mark(tt)
744.42/263.17	   active(U62(tt)) -> mark(tt)
744.42/263.17	   active(U92(tt)) -> mark(0)
744.42/263.17	   active(isNat(0)) -> mark(tt)
744.42/263.17	   active(isNatKind(0)) -> mark(tt)
744.42/263.17	   U102(X1, mark(X2), X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(mark(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, X2, mark(X3)) -> U102(X1, X2, X3)
744.42/263.17	   U102(active(X1), X2, X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, active(X2), X3) -> U102(X1, X2, X3)
744.42/263.17	   U102(X1, X2, active(X3)) -> U102(X1, X2, X3)
744.42/263.17	   U103(X1, mark(X2), X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(mark(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, X2, mark(X3)) -> U103(X1, X2, X3)
744.42/263.17	   U103(active(X1), X2, X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, active(X2), X3) -> U103(X1, X2, X3)
744.42/263.17	   U103(X1, X2, active(X3)) -> U103(X1, X2, X3)
744.42/263.17	   U104(X1, mark(X2), X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(mark(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, X2, mark(X3)) -> U104(X1, X2, X3)
744.42/263.17	   U104(active(X1), X2, X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, active(X2), X3) -> U104(X1, X2, X3)
744.42/263.17	   U104(X1, X2, active(X3)) -> U104(X1, X2, X3)
744.42/263.17	   plus(X1, mark(X2)) -> plus(X1, X2)
744.42/263.17	   plus(mark(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(active(X1), X2) -> plus(X1, X2)
744.42/263.17	   plus(X1, active(X2)) -> plus(X1, X2)
744.42/263.17	   U12(X1, mark(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(mark(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, mark(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U12(active(X1), X2, X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, active(X2), X3) -> U12(X1, X2, X3)
744.42/263.17	   U12(X1, X2, active(X3)) -> U12(X1, X2, X3)
744.42/263.17	   U13(X1, mark(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(mark(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, mark(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U13(active(X1), X2, X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, active(X2), X3) -> U13(X1, X2, X3)
744.42/263.17	   U13(X1, X2, active(X3)) -> U13(X1, X2, X3)
744.42/263.17	   U14(X1, mark(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(mark(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, mark(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U14(active(X1), X2, X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, active(X2), X3) -> U14(X1, X2, X3)
744.42/263.17	   U14(X1, X2, active(X3)) -> U14(X1, X2, X3)
744.42/263.17	   U15(X1, mark(X2)) -> U15(X1, X2)
744.42/263.17	   U15(mark(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(active(X1), X2) -> U15(X1, X2)
744.42/263.17	   U15(X1, active(X2)) -> U15(X1, X2)
744.42/263.17	   U16(active(X)) -> U16(X)
744.42/263.17	   U16(mark(X)) -> U16(X)
744.42/263.17	   U22(X1, mark(X2)) -> U22(X1, X2)
744.42/263.17	   U22(mark(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(active(X1), X2) -> U22(X1, X2)
744.42/263.17	   U22(X1, active(X2)) -> U22(X1, X2)
744.42/263.17	   U23(active(X)) -> U23(X)
744.42/263.17	   U23(mark(X)) -> U23(X)
744.42/263.17	   U32(X1, mark(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(mark(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, mark(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U32(active(X1), X2, X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, active(X2), X3) -> U32(X1, X2, X3)
744.42/263.17	   U32(X1, X2, active(X3)) -> U32(X1, X2, X3)
744.42/263.17	   U33(X1, mark(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(mark(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, mark(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U33(active(X1), X2, X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, active(X2), X3) -> U33(X1, X2, X3)
744.42/263.17	   U33(X1, X2, active(X3)) -> U33(X1, X2, X3)
744.42/263.17	   U34(X1, mark(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(mark(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, mark(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U34(active(X1), X2, X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, active(X2), X3) -> U34(X1, X2, X3)
744.42/263.17	   U34(X1, X2, active(X3)) -> U34(X1, X2, X3)
744.42/263.17	   U35(X1, mark(X2)) -> U35(X1, X2)
744.42/263.17	   U35(mark(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(active(X1), X2) -> U35(X1, X2)
744.42/263.17	   U35(X1, active(X2)) -> U35(X1, X2)
744.42/263.17	   U36(active(X)) -> U36(X)
744.42/263.17	   U36(mark(X)) -> U36(X)
744.42/263.17	   U42(active(X)) -> U42(X)
744.42/263.17	   U42(mark(X)) -> U42(X)
744.42/263.17	   U62(active(X)) -> U62(X)
744.42/263.17	   U62(mark(X)) -> U62(X)
744.42/263.17	   U72(X1, mark(X2)) -> U72(X1, X2)
744.42/263.17	   U72(mark(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(active(X1), X2) -> U72(X1, X2)
744.42/263.17	   U72(X1, active(X2)) -> U72(X1, X2)
744.42/263.17	   U101(X1, mark(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(mark(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, mark(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U101(active(X1), X2, X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, active(X2), X3) -> U101(X1, X2, X3)
744.42/263.17	   U101(X1, X2, active(X3)) -> U101(X1, X2, X3)
744.42/263.17	   U82(X1, mark(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(mark(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, mark(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U82(active(X1), X2, X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, active(X2), X3) -> U82(X1, X2, X3)
744.42/263.17	   U82(X1, X2, active(X3)) -> U82(X1, X2, X3)
744.42/263.17	   U83(X1, mark(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(mark(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, mark(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U83(active(X1), X2, X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, active(X2), X3) -> U83(X1, X2, X3)
744.42/263.17	   U83(X1, X2, active(X3)) -> U83(X1, X2, X3)
744.42/263.17	   U84(X1, mark(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(mark(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, mark(X3)) -> U84(X1, X2, X3)
744.42/263.17	   U84(active(X1), X2, X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, active(X2), X3) -> U84(X1, X2, X3)
744.42/263.17	   U84(X1, X2, active(X3)) -> U84(X1, X2, X3)
744.42/263.17	   s(active(X)) -> s(X)
744.42/263.17	   s(mark(X)) -> s(X)
744.42/263.17	   U92(active(X)) -> U92(X)
744.42/263.17	   U92(mark(X)) -> U92(X)
744.42/263.17	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
744.42/263.17	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
744.42/263.17	   U21(X1, mark(X2)) -> U21(X1, X2)
744.42/263.17	   U21(mark(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(active(X1), X2) -> U21(X1, X2)
744.42/263.17	   U21(X1, active(X2)) -> U21(X1, X2)
744.42/263.17	   U31(X1, mark(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(mark(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, mark(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U31(active(X1), X2, X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, active(X2), X3) -> U31(X1, X2, X3)
744.42/263.17	   U31(X1, X2, active(X3)) -> U31(X1, X2, X3)
744.42/263.17	   U41(X1, mark(X2)) -> U41(X1, X2)
744.42/263.17	   U41(mark(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(active(X1), X2) -> U41(X1, X2)
744.42/263.17	   U41(X1, active(X2)) -> U41(X1, X2)
744.42/263.17	   U51(active(X)) -> U51(X)
744.42/263.17	   U51(mark(X)) -> U51(X)
744.42/263.17	   U71(X1, mark(X2)) -> U71(X1, X2)
744.42/263.17	   U71(mark(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(active(X1), X2) -> U71(X1, X2)
744.42/263.17	   U71(X1, active(X2)) -> U71(X1, X2)
744.42/263.17	   U81(X1, mark(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(mark(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, mark(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U81(active(X1), X2, X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, active(X2), X3) -> U81(X1, X2, X3)
744.42/263.17	   U81(X1, X2, active(X3)) -> U81(X1, X2, X3)
744.42/263.17	   U91(X1, mark(X2)) -> U91(X1, X2)
744.42/263.17	   U91(mark(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(active(X1), X2) -> U91(X1, X2)
744.42/263.17	   U91(X1, active(X2)) -> U91(X1, X2)
744.42/263.17	   x(X1, mark(X2)) -> x(X1, X2)
744.42/263.17	   x(mark(X1), X2) -> x(X1, X2)
744.42/263.17	   x(active(X1), X2) -> x(X1, X2)
744.42/263.17	   x(X1, active(X2)) -> x(X1, X2)
744.42/263.17	
744.42/263.17	The set Q consists of the following terms:
744.42/263.17	
744.42/263.17	   active(U101(tt, x0, x1))
744.42/263.17	   active(U102(tt, x0, x1))
744.42/263.17	   active(U103(tt, x0, x1))
744.42/263.17	   active(U104(tt, x0, x1))
744.42/263.17	   active(U11(tt, x0, x1))
744.42/263.17	   active(U12(tt, x0, x1))
744.42/263.17	   active(U13(tt, x0, x1))
744.42/263.17	   active(U14(tt, x0, x1))
744.42/263.17	   active(U15(tt, x0))
744.42/263.17	   active(U16(tt))
744.42/263.17	   active(U21(tt, x0))
744.42/263.17	   active(U22(tt, x0))
744.42/263.17	   active(U23(tt))
744.42/263.17	   active(U31(tt, x0, x1))
744.42/263.17	   active(U32(tt, x0, x1))
744.42/263.17	   active(U33(tt, x0, x1))
744.42/263.17	   active(U34(tt, x0, x1))
744.42/263.17	   active(U35(tt, x0))
744.42/263.17	   active(U36(tt))
744.42/263.17	   active(U41(tt, x0))
744.42/263.17	   active(U42(tt))
744.42/263.17	   active(U51(tt))
744.42/263.17	   active(U61(tt, x0))
744.42/263.17	   active(U62(tt))
744.42/263.17	   active(U71(tt, x0))
744.42/263.17	   active(U72(tt, x0))
744.42/263.17	   active(U81(tt, x0, x1))
744.42/263.17	   active(U82(tt, x0, x1))
744.42/263.17	   active(U83(tt, x0, x1))
744.42/263.17	   active(U84(tt, x0, x1))
744.42/263.17	   active(U91(tt, x0))
744.42/263.17	   active(U92(tt))
744.42/263.17	   active(isNat(0))
744.42/263.17	   active(isNat(plus(x0, x1)))
744.42/263.17	   active(isNat(s(x0)))
744.42/263.17	   active(isNat(x(x0, x1)))
744.42/263.17	   active(isNatKind(0))
744.42/263.17	   active(isNatKind(plus(x0, x1)))
744.42/263.17	   active(isNatKind(s(x0)))
744.42/263.17	   active(isNatKind(x(x0, x1)))
744.42/263.17	   active(plus(x0, 0))
744.42/263.17	   active(plus(x0, s(x1)))
744.42/263.17	   active(x(x0, 0))
744.42/263.17	   active(x(x0, s(x1)))
744.42/263.17	   mark(U101(x0, x1, x2))
744.42/263.17	   mark(tt)
744.42/263.17	   mark(U102(x0, x1, x2))
744.42/263.17	   mark(isNatKind(x0))
744.42/263.17	   mark(U103(x0, x1, x2))
744.42/263.17	   mark(isNat(x0))
744.42/263.17	   mark(U104(x0, x1, x2))
744.42/263.17	   mark(plus(x0, x1))
744.42/263.17	   mark(x(x0, x1))
744.42/263.17	   mark(U11(x0, x1, x2))
744.42/263.17	   mark(U12(x0, x1, x2))
744.42/263.17	   mark(U13(x0, x1, x2))
744.42/263.17	   mark(U14(x0, x1, x2))
744.42/263.17	   mark(U15(x0, x1))
744.42/263.17	   mark(U16(x0))
744.42/263.17	   mark(U21(x0, x1))
744.42/263.17	   mark(U22(x0, x1))
744.42/263.17	   mark(U23(x0))
744.42/263.17	   mark(U31(x0, x1, x2))
744.42/263.17	   mark(U32(x0, x1, x2))
744.42/263.17	   mark(U33(x0, x1, x2))
744.42/263.17	   mark(U34(x0, x1, x2))
744.42/263.17	   mark(U35(x0, x1))
744.42/263.17	   mark(U36(x0))
744.42/263.17	   mark(U41(x0, x1))
744.42/263.17	   mark(U42(x0))
744.42/263.17	   mark(U51(x0))
744.42/263.17	   mark(U61(x0, x1))
744.42/263.17	   mark(U62(x0))
744.42/263.17	   mark(U71(x0, x1))
744.42/263.17	   mark(U72(x0, x1))
744.42/263.17	   mark(U81(x0, x1, x2))
744.42/263.17	   mark(U82(x0, x1, x2))
744.42/263.17	   mark(U83(x0, x1, x2))
744.42/263.17	   mark(U84(x0, x1, x2))
744.42/263.17	   mark(s(x0))
744.42/263.17	   mark(U91(x0, x1))
744.42/263.17	   mark(U92(x0))
744.42/263.17	   mark(0)
744.42/263.17	   U101(mark(x0), x1, x2)
744.42/263.17	   U101(x0, mark(x1), x2)
744.42/263.17	   U101(x0, x1, mark(x2))
744.42/263.17	   U101(active(x0), x1, x2)
744.42/263.17	   U101(x0, active(x1), x2)
744.42/263.17	   U101(x0, x1, active(x2))
744.42/263.17	   U102(mark(x0), x1, x2)
744.42/263.17	   U102(x0, mark(x1), x2)
744.42/263.17	   U102(x0, x1, mark(x2))
744.42/263.17	   U102(active(x0), x1, x2)
744.42/263.17	   U102(x0, active(x1), x2)
744.42/263.17	   U102(x0, x1, active(x2))
744.42/263.17	   isNatKind(mark(x0))
744.42/263.17	   isNatKind(active(x0))
744.42/263.17	   U103(mark(x0), x1, x2)
744.42/263.17	   U103(x0, mark(x1), x2)
744.42/263.17	   U103(x0, x1, mark(x2))
744.42/263.17	   U103(active(x0), x1, x2)
744.42/263.17	   U103(x0, active(x1), x2)
744.42/263.17	   U103(x0, x1, active(x2))
744.42/263.17	   isNat(mark(x0))
744.42/263.17	   isNat(active(x0))
744.42/263.17	   U104(mark(x0), x1, x2)
744.42/263.17	   U104(x0, mark(x1), x2)
744.42/263.17	   U104(x0, x1, mark(x2))
744.42/263.17	   U104(active(x0), x1, x2)
744.42/263.17	   U104(x0, active(x1), x2)
744.42/263.17	   U104(x0, x1, active(x2))
744.42/263.17	   plus(mark(x0), x1)
744.42/263.17	   plus(x0, mark(x1))
744.42/263.17	   plus(active(x0), x1)
744.42/263.17	   plus(x0, active(x1))
744.42/263.17	   x(mark(x0), x1)
744.42/263.17	   x(x0, mark(x1))
744.42/263.17	   x(active(x0), x1)
744.42/263.17	   x(x0, active(x1))
744.42/263.17	   U11(mark(x0), x1, x2)
744.42/263.17	   U11(x0, mark(x1), x2)
744.42/263.17	   U11(x0, x1, mark(x2))
744.42/263.17	   U11(active(x0), x1, x2)
744.42/263.17	   U11(x0, active(x1), x2)
744.42/263.17	   U11(x0, x1, active(x2))
744.42/263.17	   U12(mark(x0), x1, x2)
744.42/263.17	   U12(x0, mark(x1), x2)
744.42/263.17	   U12(x0, x1, mark(x2))
744.42/263.17	   U12(active(x0), x1, x2)
744.42/263.17	   U12(x0, active(x1), x2)
744.42/263.17	   U12(x0, x1, active(x2))
744.42/263.17	   U13(mark(x0), x1, x2)
744.42/263.17	   U13(x0, mark(x1), x2)
744.42/263.17	   U13(x0, x1, mark(x2))
744.42/263.17	   U13(active(x0), x1, x2)
744.42/263.17	   U13(x0, active(x1), x2)
744.42/263.17	   U13(x0, x1, active(x2))
744.42/263.17	   U14(mark(x0), x1, x2)
744.42/263.17	   U14(x0, mark(x1), x2)
744.42/263.17	   U14(x0, x1, mark(x2))
744.42/263.17	   U14(active(x0), x1, x2)
744.42/263.17	   U14(x0, active(x1), x2)
744.42/263.17	   U14(x0, x1, active(x2))
744.42/263.17	   U15(mark(x0), x1)
744.42/263.17	   U15(x0, mark(x1))
744.42/263.17	   U15(active(x0), x1)
744.42/263.17	   U15(x0, active(x1))
744.42/263.17	   U16(mark(x0))
744.42/263.17	   U16(active(x0))
744.42/263.17	   U21(mark(x0), x1)
744.42/263.17	   U21(x0, mark(x1))
744.42/263.17	   U21(active(x0), x1)
744.42/263.17	   U21(x0, active(x1))
744.42/263.17	   U22(mark(x0), x1)
744.42/263.17	   U22(x0, mark(x1))
744.42/263.17	   U22(active(x0), x1)
744.42/263.17	   U22(x0, active(x1))
744.42/263.17	   U23(mark(x0))
744.42/263.17	   U23(active(x0))
744.42/263.17	   U31(mark(x0), x1, x2)
744.42/263.17	   U31(x0, mark(x1), x2)
744.42/263.17	   U31(x0, x1, mark(x2))
744.42/263.17	   U31(active(x0), x1, x2)
744.42/263.17	   U31(x0, active(x1), x2)
744.42/263.17	   U31(x0, x1, active(x2))
744.42/263.17	   U32(mark(x0), x1, x2)
744.42/263.17	   U32(x0, mark(x1), x2)
744.42/263.17	   U32(x0, x1, mark(x2))
744.42/263.17	   U32(active(x0), x1, x2)
744.42/263.17	   U32(x0, active(x1), x2)
744.42/263.17	   U32(x0, x1, active(x2))
744.42/263.17	   U33(mark(x0), x1, x2)
744.42/263.17	   U33(x0, mark(x1), x2)
744.42/263.17	   U33(x0, x1, mark(x2))
744.42/263.17	   U33(active(x0), x1, x2)
744.42/263.17	   U33(x0, active(x1), x2)
744.42/263.17	   U33(x0, x1, active(x2))
744.42/263.17	   U34(mark(x0), x1, x2)
744.42/263.17	   U34(x0, mark(x1), x2)
744.42/263.17	   U34(x0, x1, mark(x2))
744.42/263.17	   U34(active(x0), x1, x2)
744.42/263.17	   U34(x0, active(x1), x2)
744.42/263.17	   U34(x0, x1, active(x2))
744.42/263.17	   U35(mark(x0), x1)
744.42/263.17	   U35(x0, mark(x1))
744.42/263.17	   U35(active(x0), x1)
744.42/263.17	   U35(x0, active(x1))
744.42/263.17	   U36(mark(x0))
744.42/263.17	   U36(active(x0))
744.42/263.17	   U41(mark(x0), x1)
744.42/263.17	   U41(x0, mark(x1))
744.42/263.17	   U41(active(x0), x1)
744.42/263.17	   U41(x0, active(x1))
744.42/263.17	   U42(mark(x0))
744.42/263.17	   U42(active(x0))
744.42/263.17	   U51(mark(x0))
744.42/263.17	   U51(active(x0))
744.42/263.17	   U61(mark(x0), x1)
744.42/263.17	   U61(x0, mark(x1))
744.42/263.17	   U61(active(x0), x1)
744.42/263.17	   U61(x0, active(x1))
744.42/263.17	   U62(mark(x0))
744.42/263.17	   U62(active(x0))
744.42/263.17	   U71(mark(x0), x1)
744.42/263.17	   U71(x0, mark(x1))
744.42/263.17	   U71(active(x0), x1)
744.42/263.17	   U71(x0, active(x1))
744.42/263.17	   U72(mark(x0), x1)
744.42/263.17	   U72(x0, mark(x1))
744.42/263.17	   U72(active(x0), x1)
744.42/263.17	   U72(x0, active(x1))
744.42/263.17	   U81(mark(x0), x1, x2)
744.42/263.17	   U81(x0, mark(x1), x2)
744.42/263.17	   U81(x0, x1, mark(x2))
744.42/263.17	   U81(active(x0), x1, x2)
744.42/263.17	   U81(x0, active(x1), x2)
744.42/263.17	   U81(x0, x1, active(x2))
744.42/263.17	   U82(mark(x0), x1, x2)
744.42/263.17	   U82(x0, mark(x1), x2)
744.42/263.17	   U82(x0, x1, mark(x2))
744.42/263.17	   U82(active(x0), x1, x2)
744.42/263.17	   U82(x0, active(x1), x2)
744.42/263.17	   U82(x0, x1, active(x2))
744.42/263.17	   U83(mark(x0), x1, x2)
744.42/263.17	   U83(x0, mark(x1), x2)
744.42/263.17	   U83(x0, x1, mark(x2))
744.42/263.17	   U83(active(x0), x1, x2)
744.42/263.17	   U83(x0, active(x1), x2)
744.42/263.17	   U83(x0, x1, active(x2))
744.42/263.17	   U84(mark(x0), x1, x2)
744.42/263.17	   U84(x0, mark(x1), x2)
744.42/263.17	   U84(x0, x1, mark(x2))
744.42/263.17	   U84(active(x0), x1, x2)
744.42/263.17	   U84(x0, active(x1), x2)
744.42/263.17	   U84(x0, x1, active(x2))
744.42/263.17	   s(mark(x0))
744.42/263.17	   s(active(x0))
744.42/263.17	   U91(mark(x0), x1)
744.42/263.17	   U91(x0, mark(x1))
744.42/263.17	   U91(active(x0), x1)
744.42/263.17	   U91(x0, active(x1))
744.42/263.17	   U92(mark(x0))
744.42/263.17	   U92(active(x0))
744.42/263.17	
744.42/263.17	We have to consider all minimal (P,Q,R)-chains.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(379) UsableRulesProof (EQUIVALENT)
744.42/263.17	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.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(380)
744.42/263.17	Obligation:
744.42/263.17	Q DP problem:
744.42/263.17	The TRS P consists of the following rules:
744.42/263.17	
744.42/263.17	   MARK(U23(X)) -> MARK(X)
744.42/263.17	   MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.17	
744.42/263.17	R is empty.
744.42/263.17	The set Q consists of the following terms:
744.42/263.17	
744.42/263.17	   active(U101(tt, x0, x1))
744.42/263.17	   active(U102(tt, x0, x1))
744.42/263.17	   active(U103(tt, x0, x1))
744.42/263.17	   active(U104(tt, x0, x1))
744.42/263.17	   active(U11(tt, x0, x1))
744.42/263.17	   active(U12(tt, x0, x1))
744.42/263.17	   active(U13(tt, x0, x1))
744.42/263.17	   active(U14(tt, x0, x1))
744.42/263.17	   active(U15(tt, x0))
744.42/263.17	   active(U16(tt))
744.42/263.17	   active(U21(tt, x0))
744.42/263.17	   active(U22(tt, x0))
744.42/263.17	   active(U23(tt))
744.42/263.17	   active(U31(tt, x0, x1))
744.42/263.17	   active(U32(tt, x0, x1))
744.42/263.17	   active(U33(tt, x0, x1))
744.42/263.17	   active(U34(tt, x0, x1))
744.42/263.17	   active(U35(tt, x0))
744.42/263.17	   active(U36(tt))
744.42/263.17	   active(U41(tt, x0))
744.42/263.17	   active(U42(tt))
744.42/263.17	   active(U51(tt))
744.42/263.17	   active(U61(tt, x0))
744.42/263.17	   active(U62(tt))
744.42/263.17	   active(U71(tt, x0))
744.42/263.17	   active(U72(tt, x0))
744.42/263.17	   active(U81(tt, x0, x1))
744.42/263.17	   active(U82(tt, x0, x1))
744.42/263.17	   active(U83(tt, x0, x1))
744.42/263.17	   active(U84(tt, x0, x1))
744.42/263.17	   active(U91(tt, x0))
744.42/263.17	   active(U92(tt))
744.42/263.17	   active(isNat(0))
744.42/263.17	   active(isNat(plus(x0, x1)))
744.42/263.17	   active(isNat(s(x0)))
744.42/263.17	   active(isNat(x(x0, x1)))
744.42/263.17	   active(isNatKind(0))
744.42/263.17	   active(isNatKind(plus(x0, x1)))
744.42/263.17	   active(isNatKind(s(x0)))
744.42/263.17	   active(isNatKind(x(x0, x1)))
744.42/263.17	   active(plus(x0, 0))
744.42/263.17	   active(plus(x0, s(x1)))
744.42/263.17	   active(x(x0, 0))
744.42/263.17	   active(x(x0, s(x1)))
744.42/263.17	   mark(U101(x0, x1, x2))
744.42/263.17	   mark(tt)
744.42/263.17	   mark(U102(x0, x1, x2))
744.42/263.17	   mark(isNatKind(x0))
744.42/263.17	   mark(U103(x0, x1, x2))
744.42/263.17	   mark(isNat(x0))
744.42/263.17	   mark(U104(x0, x1, x2))
744.42/263.17	   mark(plus(x0, x1))
744.42/263.17	   mark(x(x0, x1))
744.42/263.17	   mark(U11(x0, x1, x2))
744.42/263.17	   mark(U12(x0, x1, x2))
744.42/263.17	   mark(U13(x0, x1, x2))
744.42/263.17	   mark(U14(x0, x1, x2))
744.42/263.17	   mark(U15(x0, x1))
744.42/263.17	   mark(U16(x0))
744.42/263.17	   mark(U21(x0, x1))
744.42/263.17	   mark(U22(x0, x1))
744.42/263.17	   mark(U23(x0))
744.42/263.17	   mark(U31(x0, x1, x2))
744.42/263.17	   mark(U32(x0, x1, x2))
744.42/263.17	   mark(U33(x0, x1, x2))
744.42/263.17	   mark(U34(x0, x1, x2))
744.42/263.17	   mark(U35(x0, x1))
744.42/263.17	   mark(U36(x0))
744.42/263.17	   mark(U41(x0, x1))
744.42/263.17	   mark(U42(x0))
744.42/263.17	   mark(U51(x0))
744.42/263.17	   mark(U61(x0, x1))
744.42/263.17	   mark(U62(x0))
744.42/263.17	   mark(U71(x0, x1))
744.42/263.17	   mark(U72(x0, x1))
744.42/263.17	   mark(U81(x0, x1, x2))
744.42/263.17	   mark(U82(x0, x1, x2))
744.42/263.17	   mark(U83(x0, x1, x2))
744.42/263.17	   mark(U84(x0, x1, x2))
744.42/263.17	   mark(s(x0))
744.42/263.17	   mark(U91(x0, x1))
744.42/263.17	   mark(U92(x0))
744.42/263.17	   mark(0)
744.42/263.17	   U101(mark(x0), x1, x2)
744.42/263.17	   U101(x0, mark(x1), x2)
744.42/263.17	   U101(x0, x1, mark(x2))
744.42/263.17	   U101(active(x0), x1, x2)
744.42/263.17	   U101(x0, active(x1), x2)
744.42/263.17	   U101(x0, x1, active(x2))
744.42/263.17	   U102(mark(x0), x1, x2)
744.42/263.17	   U102(x0, mark(x1), x2)
744.42/263.17	   U102(x0, x1, mark(x2))
744.42/263.17	   U102(active(x0), x1, x2)
744.42/263.17	   U102(x0, active(x1), x2)
744.42/263.17	   U102(x0, x1, active(x2))
744.42/263.17	   isNatKind(mark(x0))
744.42/263.17	   isNatKind(active(x0))
744.42/263.17	   U103(mark(x0), x1, x2)
744.42/263.17	   U103(x0, mark(x1), x2)
744.42/263.17	   U103(x0, x1, mark(x2))
744.42/263.17	   U103(active(x0), x1, x2)
744.42/263.17	   U103(x0, active(x1), x2)
744.42/263.17	   U103(x0, x1, active(x2))
744.42/263.17	   isNat(mark(x0))
744.42/263.17	   isNat(active(x0))
744.42/263.17	   U104(mark(x0), x1, x2)
744.42/263.17	   U104(x0, mark(x1), x2)
744.42/263.17	   U104(x0, x1, mark(x2))
744.42/263.17	   U104(active(x0), x1, x2)
744.42/263.17	   U104(x0, active(x1), x2)
744.42/263.17	   U104(x0, x1, active(x2))
744.42/263.17	   plus(mark(x0), x1)
744.42/263.17	   plus(x0, mark(x1))
744.42/263.17	   plus(active(x0), x1)
744.42/263.17	   plus(x0, active(x1))
744.42/263.17	   x(mark(x0), x1)
744.42/263.17	   x(x0, mark(x1))
744.42/263.17	   x(active(x0), x1)
744.42/263.17	   x(x0, active(x1))
744.42/263.17	   U11(mark(x0), x1, x2)
744.42/263.17	   U11(x0, mark(x1), x2)
744.42/263.17	   U11(x0, x1, mark(x2))
744.42/263.17	   U11(active(x0), x1, x2)
744.42/263.17	   U11(x0, active(x1), x2)
744.42/263.17	   U11(x0, x1, active(x2))
744.42/263.17	   U12(mark(x0), x1, x2)
744.42/263.17	   U12(x0, mark(x1), x2)
744.42/263.17	   U12(x0, x1, mark(x2))
744.42/263.17	   U12(active(x0), x1, x2)
744.42/263.17	   U12(x0, active(x1), x2)
744.42/263.17	   U12(x0, x1, active(x2))
744.42/263.17	   U13(mark(x0), x1, x2)
744.42/263.17	   U13(x0, mark(x1), x2)
744.42/263.17	   U13(x0, x1, mark(x2))
744.42/263.17	   U13(active(x0), x1, x2)
744.42/263.17	   U13(x0, active(x1), x2)
744.42/263.17	   U13(x0, x1, active(x2))
744.42/263.17	   U14(mark(x0), x1, x2)
744.42/263.17	   U14(x0, mark(x1), x2)
744.42/263.17	   U14(x0, x1, mark(x2))
744.42/263.17	   U14(active(x0), x1, x2)
744.42/263.17	   U14(x0, active(x1), x2)
744.42/263.17	   U14(x0, x1, active(x2))
744.42/263.17	   U15(mark(x0), x1)
744.42/263.17	   U15(x0, mark(x1))
744.42/263.17	   U15(active(x0), x1)
744.42/263.17	   U15(x0, active(x1))
744.42/263.17	   U16(mark(x0))
744.42/263.17	   U16(active(x0))
744.42/263.17	   U21(mark(x0), x1)
744.42/263.17	   U21(x0, mark(x1))
744.42/263.17	   U21(active(x0), x1)
744.42/263.17	   U21(x0, active(x1))
744.42/263.17	   U22(mark(x0), x1)
744.42/263.17	   U22(x0, mark(x1))
744.42/263.17	   U22(active(x0), x1)
744.42/263.17	   U22(x0, active(x1))
744.42/263.17	   U23(mark(x0))
744.42/263.17	   U23(active(x0))
744.42/263.17	   U31(mark(x0), x1, x2)
744.42/263.17	   U31(x0, mark(x1), x2)
744.42/263.17	   U31(x0, x1, mark(x2))
744.42/263.17	   U31(active(x0), x1, x2)
744.42/263.17	   U31(x0, active(x1), x2)
744.42/263.17	   U31(x0, x1, active(x2))
744.42/263.17	   U32(mark(x0), x1, x2)
744.42/263.17	   U32(x0, mark(x1), x2)
744.42/263.17	   U32(x0, x1, mark(x2))
744.42/263.17	   U32(active(x0), x1, x2)
744.42/263.17	   U32(x0, active(x1), x2)
744.42/263.17	   U32(x0, x1, active(x2))
744.42/263.17	   U33(mark(x0), x1, x2)
744.42/263.17	   U33(x0, mark(x1), x2)
744.42/263.17	   U33(x0, x1, mark(x2))
744.42/263.17	   U33(active(x0), x1, x2)
744.42/263.17	   U33(x0, active(x1), x2)
744.42/263.17	   U33(x0, x1, active(x2))
744.42/263.17	   U34(mark(x0), x1, x2)
744.42/263.17	   U34(x0, mark(x1), x2)
744.42/263.17	   U34(x0, x1, mark(x2))
744.42/263.17	   U34(active(x0), x1, x2)
744.42/263.17	   U34(x0, active(x1), x2)
744.42/263.17	   U34(x0, x1, active(x2))
744.42/263.17	   U35(mark(x0), x1)
744.42/263.17	   U35(x0, mark(x1))
744.42/263.17	   U35(active(x0), x1)
744.42/263.17	   U35(x0, active(x1))
744.42/263.17	   U36(mark(x0))
744.42/263.17	   U36(active(x0))
744.42/263.17	   U41(mark(x0), x1)
744.42/263.17	   U41(x0, mark(x1))
744.42/263.17	   U41(active(x0), x1)
744.42/263.17	   U41(x0, active(x1))
744.42/263.17	   U42(mark(x0))
744.42/263.17	   U42(active(x0))
744.42/263.17	   U51(mark(x0))
744.42/263.17	   U51(active(x0))
744.42/263.17	   U61(mark(x0), x1)
744.42/263.17	   U61(x0, mark(x1))
744.42/263.17	   U61(active(x0), x1)
744.42/263.17	   U61(x0, active(x1))
744.42/263.17	   U62(mark(x0))
744.42/263.17	   U62(active(x0))
744.42/263.17	   U71(mark(x0), x1)
744.42/263.17	   U71(x0, mark(x1))
744.42/263.17	   U71(active(x0), x1)
744.42/263.17	   U71(x0, active(x1))
744.42/263.17	   U72(mark(x0), x1)
744.42/263.17	   U72(x0, mark(x1))
744.42/263.17	   U72(active(x0), x1)
744.42/263.17	   U72(x0, active(x1))
744.42/263.17	   U81(mark(x0), x1, x2)
744.42/263.17	   U81(x0, mark(x1), x2)
744.42/263.17	   U81(x0, x1, mark(x2))
744.42/263.17	   U81(active(x0), x1, x2)
744.42/263.17	   U81(x0, active(x1), x2)
744.42/263.17	   U81(x0, x1, active(x2))
744.42/263.17	   U82(mark(x0), x1, x2)
744.42/263.17	   U82(x0, mark(x1), x2)
744.42/263.17	   U82(x0, x1, mark(x2))
744.42/263.17	   U82(active(x0), x1, x2)
744.42/263.17	   U82(x0, active(x1), x2)
744.42/263.17	   U82(x0, x1, active(x2))
744.42/263.17	   U83(mark(x0), x1, x2)
744.42/263.17	   U83(x0, mark(x1), x2)
744.42/263.17	   U83(x0, x1, mark(x2))
744.42/263.17	   U83(active(x0), x1, x2)
744.42/263.17	   U83(x0, active(x1), x2)
744.42/263.17	   U83(x0, x1, active(x2))
744.42/263.17	   U84(mark(x0), x1, x2)
744.42/263.17	   U84(x0, mark(x1), x2)
744.42/263.17	   U84(x0, x1, mark(x2))
744.42/263.17	   U84(active(x0), x1, x2)
744.42/263.17	   U84(x0, active(x1), x2)
744.42/263.17	   U84(x0, x1, active(x2))
744.42/263.17	   s(mark(x0))
744.42/263.17	   s(active(x0))
744.42/263.17	   U91(mark(x0), x1)
744.42/263.17	   U91(x0, mark(x1))
744.42/263.17	   U91(active(x0), x1)
744.42/263.17	   U91(x0, active(x1))
744.42/263.17	   U92(mark(x0))
744.42/263.17	   U92(active(x0))
744.42/263.17	
744.42/263.17	We have to consider all minimal (P,Q,R)-chains.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(381) QReductionProof (EQUIVALENT)
744.42/263.17	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
744.42/263.17	
744.42/263.17	   active(U101(tt, x0, x1))
744.42/263.17	   active(U102(tt, x0, x1))
744.42/263.17	   active(U103(tt, x0, x1))
744.42/263.17	   active(U104(tt, x0, x1))
744.42/263.17	   active(U11(tt, x0, x1))
744.42/263.17	   active(U12(tt, x0, x1))
744.42/263.17	   active(U13(tt, x0, x1))
744.42/263.17	   active(U14(tt, x0, x1))
744.42/263.17	   active(U15(tt, x0))
744.42/263.17	   active(U16(tt))
744.42/263.17	   active(U21(tt, x0))
744.42/263.17	   active(U22(tt, x0))
744.42/263.17	   active(U23(tt))
744.42/263.17	   active(U31(tt, x0, x1))
744.42/263.17	   active(U32(tt, x0, x1))
744.42/263.17	   active(U33(tt, x0, x1))
744.42/263.17	   active(U34(tt, x0, x1))
744.42/263.17	   active(U35(tt, x0))
744.42/263.17	   active(U36(tt))
744.42/263.17	   active(U41(tt, x0))
744.42/263.17	   active(U42(tt))
744.42/263.17	   active(U51(tt))
744.42/263.17	   active(U61(tt, x0))
744.42/263.17	   active(U62(tt))
744.42/263.17	   active(U71(tt, x0))
744.42/263.17	   active(U72(tt, x0))
744.42/263.17	   active(U81(tt, x0, x1))
744.42/263.17	   active(U82(tt, x0, x1))
744.42/263.17	   active(U83(tt, x0, x1))
744.42/263.17	   active(U84(tt, x0, x1))
744.42/263.17	   active(U91(tt, x0))
744.42/263.17	   active(U92(tt))
744.42/263.17	   active(isNat(0))
744.42/263.17	   active(isNat(plus(x0, x1)))
744.42/263.17	   active(isNat(s(x0)))
744.42/263.17	   active(isNat(x(x0, x1)))
744.42/263.17	   active(isNatKind(0))
744.42/263.17	   active(isNatKind(plus(x0, x1)))
744.42/263.17	   active(isNatKind(s(x0)))
744.42/263.17	   active(isNatKind(x(x0, x1)))
744.42/263.17	   active(plus(x0, 0))
744.42/263.17	   active(plus(x0, s(x1)))
744.42/263.17	   active(x(x0, 0))
744.42/263.17	   active(x(x0, s(x1)))
744.42/263.17	   mark(U101(x0, x1, x2))
744.42/263.17	   mark(tt)
744.42/263.17	   mark(U102(x0, x1, x2))
744.42/263.17	   mark(isNatKind(x0))
744.42/263.17	   mark(U103(x0, x1, x2))
744.42/263.17	   mark(isNat(x0))
744.42/263.17	   mark(U104(x0, x1, x2))
744.42/263.17	   mark(plus(x0, x1))
744.42/263.17	   mark(x(x0, x1))
744.42/263.17	   mark(U11(x0, x1, x2))
744.42/263.17	   mark(U12(x0, x1, x2))
744.42/263.17	   mark(U13(x0, x1, x2))
744.42/263.17	   mark(U14(x0, x1, x2))
744.42/263.17	   mark(U15(x0, x1))
744.42/263.17	   mark(U16(x0))
744.42/263.17	   mark(U21(x0, x1))
744.42/263.17	   mark(U22(x0, x1))
744.42/263.17	   mark(U23(x0))
744.42/263.17	   mark(U31(x0, x1, x2))
744.42/263.17	   mark(U32(x0, x1, x2))
744.42/263.17	   mark(U33(x0, x1, x2))
744.42/263.17	   mark(U34(x0, x1, x2))
744.42/263.17	   mark(U35(x0, x1))
744.42/263.17	   mark(U36(x0))
744.42/263.17	   mark(U41(x0, x1))
744.42/263.17	   mark(U42(x0))
744.42/263.17	   mark(U51(x0))
744.42/263.17	   mark(U61(x0, x1))
744.42/263.17	   mark(U62(x0))
744.42/263.17	   mark(U71(x0, x1))
744.42/263.17	   mark(U72(x0, x1))
744.42/263.17	   mark(U81(x0, x1, x2))
744.42/263.17	   mark(U82(x0, x1, x2))
744.42/263.17	   mark(U83(x0, x1, x2))
744.42/263.17	   mark(U84(x0, x1, x2))
744.42/263.17	   mark(s(x0))
744.42/263.17	   mark(U91(x0, x1))
744.42/263.17	   mark(U92(x0))
744.42/263.17	   mark(0)
744.42/263.17	   U101(mark(x0), x1, x2)
744.42/263.17	   U101(x0, mark(x1), x2)
744.42/263.17	   U101(x0, x1, mark(x2))
744.42/263.17	   U101(active(x0), x1, x2)
744.42/263.17	   U101(x0, active(x1), x2)
744.42/263.17	   U101(x0, x1, active(x2))
744.42/263.17	   U102(mark(x0), x1, x2)
744.42/263.17	   U102(x0, mark(x1), x2)
744.42/263.17	   U102(x0, x1, mark(x2))
744.42/263.17	   U102(active(x0), x1, x2)
744.42/263.17	   U102(x0, active(x1), x2)
744.42/263.17	   U102(x0, x1, active(x2))
744.42/263.17	   isNatKind(mark(x0))
744.42/263.17	   isNatKind(active(x0))
744.42/263.17	   U103(mark(x0), x1, x2)
744.42/263.17	   U103(x0, mark(x1), x2)
744.42/263.17	   U103(x0, x1, mark(x2))
744.42/263.17	   U103(active(x0), x1, x2)
744.42/263.17	   U103(x0, active(x1), x2)
744.42/263.17	   U103(x0, x1, active(x2))
744.42/263.17	   isNat(mark(x0))
744.42/263.17	   isNat(active(x0))
744.42/263.17	   U104(mark(x0), x1, x2)
744.42/263.17	   U104(x0, mark(x1), x2)
744.42/263.17	   U104(x0, x1, mark(x2))
744.42/263.17	   U104(active(x0), x1, x2)
744.42/263.17	   U104(x0, active(x1), x2)
744.42/263.17	   U104(x0, x1, active(x2))
744.42/263.17	   plus(mark(x0), x1)
744.42/263.17	   plus(x0, mark(x1))
744.42/263.17	   plus(active(x0), x1)
744.42/263.17	   plus(x0, active(x1))
744.42/263.17	   x(mark(x0), x1)
744.42/263.17	   x(x0, mark(x1))
744.42/263.17	   x(active(x0), x1)
744.42/263.17	   x(x0, active(x1))
744.42/263.17	   U11(mark(x0), x1, x2)
744.42/263.17	   U11(x0, mark(x1), x2)
744.42/263.17	   U11(x0, x1, mark(x2))
744.42/263.17	   U11(active(x0), x1, x2)
744.42/263.17	   U11(x0, active(x1), x2)
744.42/263.17	   U11(x0, x1, active(x2))
744.42/263.17	   U12(mark(x0), x1, x2)
744.42/263.17	   U12(x0, mark(x1), x2)
744.42/263.17	   U12(x0, x1, mark(x2))
744.42/263.17	   U12(active(x0), x1, x2)
744.42/263.17	   U12(x0, active(x1), x2)
744.42/263.17	   U12(x0, x1, active(x2))
744.42/263.17	   U13(mark(x0), x1, x2)
744.42/263.17	   U13(x0, mark(x1), x2)
744.42/263.17	   U13(x0, x1, mark(x2))
744.42/263.17	   U13(active(x0), x1, x2)
744.42/263.17	   U13(x0, active(x1), x2)
744.42/263.17	   U13(x0, x1, active(x2))
744.42/263.17	   U14(mark(x0), x1, x2)
744.42/263.17	   U14(x0, mark(x1), x2)
744.42/263.17	   U14(x0, x1, mark(x2))
744.42/263.17	   U14(active(x0), x1, x2)
744.42/263.17	   U14(x0, active(x1), x2)
744.42/263.17	   U14(x0, x1, active(x2))
744.42/263.17	   U16(mark(x0))
744.42/263.17	   U16(active(x0))
744.42/263.17	   U21(mark(x0), x1)
744.42/263.17	   U21(x0, mark(x1))
744.42/263.17	   U21(active(x0), x1)
744.42/263.17	   U21(x0, active(x1))
744.42/263.17	   U22(mark(x0), x1)
744.42/263.17	   U22(x0, mark(x1))
744.42/263.17	   U22(active(x0), x1)
744.42/263.17	   U22(x0, active(x1))
744.42/263.17	   U31(mark(x0), x1, x2)
744.42/263.17	   U31(x0, mark(x1), x2)
744.42/263.17	   U31(x0, x1, mark(x2))
744.42/263.17	   U31(active(x0), x1, x2)
744.42/263.17	   U31(x0, active(x1), x2)
744.42/263.17	   U31(x0, x1, active(x2))
744.42/263.17	   U32(mark(x0), x1, x2)
744.42/263.17	   U32(x0, mark(x1), x2)
744.42/263.17	   U32(x0, x1, mark(x2))
744.42/263.17	   U32(active(x0), x1, x2)
744.42/263.17	   U32(x0, active(x1), x2)
744.42/263.17	   U32(x0, x1, active(x2))
744.42/263.17	   U33(mark(x0), x1, x2)
744.42/263.17	   U33(x0, mark(x1), x2)
744.42/263.17	   U33(x0, x1, mark(x2))
744.42/263.17	   U33(active(x0), x1, x2)
744.42/263.17	   U33(x0, active(x1), x2)
744.42/263.17	   U33(x0, x1, active(x2))
744.42/263.17	   U34(mark(x0), x1, x2)
744.42/263.17	   U34(x0, mark(x1), x2)
744.42/263.17	   U34(x0, x1, mark(x2))
744.42/263.17	   U34(active(x0), x1, x2)
744.42/263.17	   U34(x0, active(x1), x2)
744.42/263.17	   U34(x0, x1, active(x2))
744.42/263.17	   U35(mark(x0), x1)
744.42/263.17	   U35(x0, mark(x1))
744.42/263.17	   U35(active(x0), x1)
744.42/263.17	   U35(x0, active(x1))
744.42/263.17	   U36(mark(x0))
744.42/263.17	   U36(active(x0))
744.42/263.17	   U41(mark(x0), x1)
744.42/263.17	   U41(x0, mark(x1))
744.42/263.17	   U41(active(x0), x1)
744.42/263.17	   U41(x0, active(x1))
744.42/263.17	   U42(mark(x0))
744.42/263.17	   U42(active(x0))
744.42/263.17	   U51(mark(x0))
744.42/263.17	   U51(active(x0))
744.42/263.17	   U61(mark(x0), x1)
744.42/263.17	   U61(x0, mark(x1))
744.42/263.17	   U61(active(x0), x1)
744.42/263.17	   U61(x0, active(x1))
744.42/263.17	   U62(mark(x0))
744.42/263.17	   U62(active(x0))
744.42/263.17	   U71(mark(x0), x1)
744.42/263.17	   U71(x0, mark(x1))
744.42/263.17	   U71(active(x0), x1)
744.42/263.17	   U71(x0, active(x1))
744.42/263.17	   U72(mark(x0), x1)
744.42/263.17	   U72(x0, mark(x1))
744.42/263.17	   U72(active(x0), x1)
744.42/263.17	   U72(x0, active(x1))
744.42/263.17	   U81(mark(x0), x1, x2)
744.42/263.17	   U81(x0, mark(x1), x2)
744.42/263.17	   U81(x0, x1, mark(x2))
744.42/263.17	   U81(active(x0), x1, x2)
744.42/263.17	   U81(x0, active(x1), x2)
744.42/263.17	   U81(x0, x1, active(x2))
744.42/263.17	   U82(mark(x0), x1, x2)
744.42/263.17	   U82(x0, mark(x1), x2)
744.42/263.17	   U82(x0, x1, mark(x2))
744.42/263.17	   U82(active(x0), x1, x2)
744.42/263.17	   U82(x0, active(x1), x2)
744.42/263.17	   U82(x0, x1, active(x2))
744.42/263.17	   U83(mark(x0), x1, x2)
744.42/263.17	   U83(x0, mark(x1), x2)
744.42/263.17	   U83(x0, x1, mark(x2))
744.42/263.17	   U83(active(x0), x1, x2)
744.42/263.17	   U83(x0, active(x1), x2)
744.42/263.17	   U83(x0, x1, active(x2))
744.42/263.17	   U84(mark(x0), x1, x2)
744.42/263.17	   U84(x0, mark(x1), x2)
744.42/263.17	   U84(x0, x1, mark(x2))
744.42/263.17	   U84(active(x0), x1, x2)
744.42/263.17	   U84(x0, active(x1), x2)
744.42/263.17	   U84(x0, x1, active(x2))
744.42/263.17	   s(mark(x0))
744.42/263.17	   s(active(x0))
744.42/263.17	   U91(mark(x0), x1)
744.42/263.17	   U91(x0, mark(x1))
744.42/263.17	   U91(active(x0), x1)
744.42/263.17	   U91(x0, active(x1))
744.42/263.17	   U92(mark(x0))
744.42/263.17	   U92(active(x0))
744.42/263.17	
744.42/263.17	
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(382)
744.42/263.17	Obligation:
744.42/263.17	Q DP problem:
744.42/263.17	The TRS P consists of the following rules:
744.42/263.17	
744.42/263.17	   MARK(U23(X)) -> MARK(X)
744.42/263.17	   MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.17	
744.42/263.17	R is empty.
744.42/263.17	The set Q consists of the following terms:
744.42/263.17	
744.42/263.17	   U15(mark(x0), x1)
744.42/263.17	   U15(x0, mark(x1))
744.42/263.17	   U15(active(x0), x1)
744.42/263.17	   U15(x0, active(x1))
744.42/263.17	   U23(mark(x0))
744.42/263.17	   U23(active(x0))
744.42/263.17	
744.42/263.17	We have to consider all minimal (P,Q,R)-chains.
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(383) QDPSizeChangeProof (EQUIVALENT)
744.42/263.17	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. 
744.42/263.17	
744.42/263.17	From the DPs we obtained the following set of size-change graphs:
744.42/263.17	*MARK(U23(X)) -> MARK(X)
744.42/263.17	The graph contains the following edges 1 > 1
744.42/263.17	
744.42/263.17	
744.42/263.17	*MARK(U15(X1, X2)) -> MARK(X1)
744.42/263.17	The graph contains the following edges 1 > 1
744.42/263.17	
744.42/263.17	
744.42/263.17	----------------------------------------
744.42/263.17	
744.42/263.17	(384)
744.42/263.17	YES
744.49/263.25	EOF