/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 20 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) NumRed [SOUND, 0 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) AND (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) MNOCProof [EQUIVALENT, 0 ms] (18) QDP (19) InductionCalculusProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 0 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) AND (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QReductionProof [EQUIVALENT, 0 ms] (29) QDP (30) TransformationProof [EQUIVALENT, 0 ms] (31) QDP (32) DependencyGraphProof [EQUIVALENT, 0 ms] (33) AND (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QReductionProof [EQUIVALENT, 0 ms] (38) QDP (39) TransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) TransformationProof [EQUIVALENT, 0 ms] (42) QDP (43) DependencyGraphProof [EQUIVALENT, 0 ms] (44) QDP (45) TransformationProof [EQUIVALENT, 0 ms] (46) QDP (47) TransformationProof [EQUIVALENT, 0 ms] (48) QDP (49) DependencyGraphProof [EQUIVALENT, 0 ms] (50) QDP (51) TransformationProof [EQUIVALENT, 0 ms] (52) QDP (53) TransformationProof [EQUIVALENT, 0 ms] (54) QDP (55) TransformationProof [EQUIVALENT, 0 ms] (56) QDP (57) DependencyGraphProof [EQUIVALENT, 0 ms] (58) QDP (59) TransformationProof [EQUIVALENT, 0 ms] (60) QDP (61) QDPSizeChangeProof [EQUIVALENT, 0 ms] (62) YES (63) QDP (64) UsableRulesProof [EQUIVALENT, 0 ms] (65) QDP (66) TransformationProof [EQUIVALENT, 0 ms] (67) QDP (68) DependencyGraphProof [EQUIVALENT, 0 ms] (69) AND (70) QDP (71) TransformationProof [EQUIVALENT, 0 ms] (72) QDP (73) TransformationProof [EQUIVALENT, 0 ms] (74) QDP (75) TransformationProof [EQUIVALENT, 0 ms] (76) QDP (77) TransformationProof [EQUIVALENT, 0 ms] (78) QDP (79) TransformationProof [EQUIVALENT, 0 ms] (80) QDP (81) DependencyGraphProof [EQUIVALENT, 0 ms] (82) QDP (83) TransformationProof [EQUIVALENT, 0 ms] (84) QDP (85) TransformationProof [EQUIVALENT, 0 ms] (86) QDP (87) DependencyGraphProof [EQUIVALENT, 0 ms] (88) QDP (89) QDPOrderProof [EQUIVALENT, 0 ms] (90) QDP (91) DependencyGraphProof [EQUIVALENT, 0 ms] (92) TRUE (93) QDP (94) TransformationProof [EQUIVALENT, 0 ms] (95) QDP (96) DependencyGraphProof [EQUIVALENT, 0 ms] (97) AND (98) QDP (99) TransformationProof [EQUIVALENT, 0 ms] (100) QDP (101) TransformationProof [EQUIVALENT, 0 ms] (102) QDP (103) TransformationProof [EQUIVALENT, 0 ms] (104) QDP (105) TransformationProof [EQUIVALENT, 0 ms] (106) QDP (107) TransformationProof [EQUIVALENT, 0 ms] (108) QDP (109) TransformationProof [EQUIVALENT, 0 ms] (110) QDP (111) TransformationProof [EQUIVALENT, 0 ms] (112) QDP (113) DependencyGraphProof [EQUIVALENT, 0 ms] (114) QDP (115) TransformationProof [EQUIVALENT, 0 ms] (116) QDP (117) QDPOrderProof [EQUIVALENT, 0 ms] (118) QDP (119) DependencyGraphProof [EQUIVALENT, 0 ms] (120) TRUE (121) QDP (122) InductionCalculusProof [EQUIVALENT, 0 ms] (123) QDP (124) QDP (125) UsableRulesProof [EQUIVALENT, 0 ms] (126) QDP (127) QReductionProof [EQUIVALENT, 0 ms] (128) QDP (129) TransformationProof [EQUIVALENT, 0 ms] (130) QDP (131) DependencyGraphProof [EQUIVALENT, 0 ms] (132) AND (133) QDP (134) UsableRulesProof [EQUIVALENT, 0 ms] (135) QDP (136) QReductionProof [EQUIVALENT, 0 ms] (137) QDP (138) TransformationProof [EQUIVALENT, 0 ms] (139) QDP (140) DependencyGraphProof [EQUIVALENT, 0 ms] (141) AND (142) QDP (143) UsableRulesProof [EQUIVALENT, 0 ms] (144) QDP (145) QReductionProof [EQUIVALENT, 0 ms] (146) QDP (147) TransformationProof [EQUIVALENT, 0 ms] (148) QDP (149) TransformationProof [EQUIVALENT, 0 ms] (150) QDP (151) DependencyGraphProof [EQUIVALENT, 0 ms] (152) QDP (153) TransformationProof [EQUIVALENT, 0 ms] (154) QDP (155) TransformationProof [EQUIVALENT, 0 ms] (156) QDP (157) TransformationProof [EQUIVALENT, 0 ms] (158) QDP (159) DependencyGraphProof [EQUIVALENT, 0 ms] (160) QDP (161) TransformationProof [EQUIVALENT, 0 ms] (162) QDP (163) TransformationProof [EQUIVALENT, 0 ms] (164) QDP (165) TransformationProof [EQUIVALENT, 0 ms] (166) QDP (167) DependencyGraphProof [EQUIVALENT, 0 ms] (168) QDP (169) QDPSizeChangeProof [EQUIVALENT, 0 ms] (170) YES (171) QDP (172) UsableRulesProof [EQUIVALENT, 0 ms] (173) QDP (174) TransformationProof [EQUIVALENT, 0 ms] (175) QDP (176) DependencyGraphProof [EQUIVALENT, 0 ms] (177) AND (178) QDP (179) TransformationProof [EQUIVALENT, 0 ms] (180) QDP (181) TransformationProof [EQUIVALENT, 0 ms] (182) QDP (183) TransformationProof [EQUIVALENT, 0 ms] (184) QDP (185) TransformationProof [EQUIVALENT, 0 ms] (186) QDP (187) TransformationProof [EQUIVALENT, 0 ms] (188) QDP (189) DependencyGraphProof [EQUIVALENT, 0 ms] (190) QDP (191) TransformationProof [EQUIVALENT, 0 ms] (192) QDP (193) TransformationProof [EQUIVALENT, 0 ms] (194) QDP (195) DependencyGraphProof [EQUIVALENT, 0 ms] (196) QDP (197) QDPOrderProof [EQUIVALENT, 0 ms] (198) QDP (199) DependencyGraphProof [EQUIVALENT, 0 ms] (200) TRUE (201) QDP (202) TransformationProof [EQUIVALENT, 0 ms] (203) QDP (204) DependencyGraphProof [EQUIVALENT, 0 ms] (205) AND (206) QDP (207) TransformationProof [EQUIVALENT, 0 ms] (208) QDP (209) TransformationProof [EQUIVALENT, 0 ms] (210) QDP (211) TransformationProof [EQUIVALENT, 0 ms] (212) QDP (213) TransformationProof [EQUIVALENT, 0 ms] (214) QDP (215) TransformationProof [EQUIVALENT, 0 ms] (216) QDP (217) TransformationProof [EQUIVALENT, 0 ms] (218) QDP (219) TransformationProof [EQUIVALENT, 0 ms] (220) QDP (221) DependencyGraphProof [EQUIVALENT, 0 ms] (222) QDP (223) TransformationProof [EQUIVALENT, 0 ms] (224) QDP (225) QDPOrderProof [EQUIVALENT, 0 ms] (226) QDP (227) DependencyGraphProof [EQUIVALENT, 0 ms] (228) TRUE (229) QDP (230) InductionCalculusProof [EQUIVALENT, 0 ms] (231) QDP (232) QDP (233) UsableRulesProof [EQUIVALENT, 0 ms] (234) QDP (235) QReductionProof [EQUIVALENT, 0 ms] (236) QDP (237) TransformationProof [EQUIVALENT, 0 ms] (238) QDP (239) DependencyGraphProof [EQUIVALENT, 0 ms] (240) QDP (241) TransformationProof [EQUIVALENT, 0 ms] (242) QDP (243) DependencyGraphProof [EQUIVALENT, 0 ms] (244) QDP (245) TransformationProof [EQUIVALENT, 0 ms] (246) QDP (247) TransformationProof [EQUIVALENT, 0 ms] (248) QDP (249) DependencyGraphProof [EQUIVALENT, 0 ms] (250) AND (251) QDP (252) UsableRulesProof [EQUIVALENT, 0 ms] (253) QDP (254) QReductionProof [EQUIVALENT, 0 ms] (255) QDP (256) TransformationProof [EQUIVALENT, 0 ms] (257) QDP (258) TransformationProof [EQUIVALENT, 0 ms] (259) QDP (260) TransformationProof [EQUIVALENT, 0 ms] (261) QDP (262) TransformationProof [EQUIVALENT, 0 ms] (263) QDP (264) DependencyGraphProof [EQUIVALENT, 0 ms] (265) QDP (266) TransformationProof [EQUIVALENT, 0 ms] (267) QDP (268) TransformationProof [EQUIVALENT, 0 ms] (269) QDP (270) TransformationProof [EQUIVALENT, 0 ms] (271) QDP (272) DependencyGraphProof [EQUIVALENT, 0 ms] (273) QDP (274) QDPSizeChangeProof [EQUIVALENT, 0 ms] (275) YES (276) QDP (277) UsableRulesProof [EQUIVALENT, 0 ms] (278) QDP (279) QReductionProof [EQUIVALENT, 0 ms] (280) QDP (281) TransformationProof [EQUIVALENT, 0 ms] (282) QDP (283) TransformationProof [EQUIVALENT, 0 ms] (284) QDP (285) TransformationProof [EQUIVALENT, 0 ms] (286) QDP (287) DependencyGraphProof [EQUIVALENT, 0 ms] (288) QDP (289) TransformationProof [EQUIVALENT, 0 ms] (290) QDP (291) TransformationProof [EQUIVALENT, 0 ms] (292) QDP (293) TransformationProof [EQUIVALENT, 0 ms] (294) QDP (295) DependencyGraphProof [EQUIVALENT, 0 ms] (296) QDP (297) QDPSizeChangeProof [EQUIVALENT, 0 ms] (298) YES (299) QDP (300) UsableRulesProof [EQUIVALENT, 0 ms] (301) QDP (302) TransformationProof [EQUIVALENT, 0 ms] (303) QDP (304) TransformationProof [EQUIVALENT, 0 ms] (305) QDP (306) TransformationProof [EQUIVALENT, 0 ms] (307) QDP (308) TransformationProof [EQUIVALENT, 0 ms] (309) QDP (310) TransformationProof [EQUIVALENT, 0 ms] (311) QDP (312) TransformationProof [EQUIVALENT, 0 ms] (313) QDP (314) TransformationProof [EQUIVALENT, 0 ms] (315) QDP (316) DependencyGraphProof [EQUIVALENT, 0 ms] (317) QDP (318) TransformationProof [EQUIVALENT, 0 ms] (319) QDP (320) TransformationProof [EQUIVALENT, 0 ms] (321) QDP (322) TransformationProof [EQUIVALENT, 0 ms] (323) QDP (324) TransformationProof [EQUIVALENT, 0 ms] (325) QDP (326) TransformationProof [EQUIVALENT, 0 ms] (327) QDP (328) TransformationProof [EQUIVALENT, 0 ms] (329) QDP (330) TransformationProof [EQUIVALENT, 0 ms] (331) QDP (332) TransformationProof [EQUIVALENT, 0 ms] (333) QDP (334) TransformationProof [EQUIVALENT, 0 ms] (335) QDP (336) DependencyGraphProof [EQUIVALENT, 0 ms] (337) QDP (338) TransformationProof [EQUIVALENT, 0 ms] (339) QDP (340) DependencyGraphProof [EQUIVALENT, 0 ms] (341) AND (342) QDP (343) TransformationProof [EQUIVALENT, 0 ms] (344) QDP (345) TransformationProof [EQUIVALENT, 0 ms] (346) QDP (347) TransformationProof [EQUIVALENT, 0 ms] (348) QDP (349) TransformationProof [EQUIVALENT, 0 ms] (350) QDP (351) DependencyGraphProof [EQUIVALENT, 0 ms] (352) QDP (353) QDPOrderProof [EQUIVALENT, 15 ms] (354) QDP (355) DependencyGraphProof [EQUIVALENT, 0 ms] (356) TRUE (357) QDP (358) TransformationProof [EQUIVALENT, 0 ms] (359) QDP (360) DependencyGraphProof [EQUIVALENT, 0 ms] (361) QDP (362) QDPOrderProof [EQUIVALENT, 18 ms] (363) QDP (364) DependencyGraphProof [EQUIVALENT, 0 ms] (365) TRUE (366) QDP (367) TransformationProof [EQUIVALENT, 0 ms] (368) QDP (369) DependencyGraphProof [EQUIVALENT, 0 ms] (370) AND (371) QDP (372) TransformationProof [EQUIVALENT, 0 ms] (373) QDP (374) TransformationProof [EQUIVALENT, 0 ms] (375) QDP (376) TransformationProof [EQUIVALENT, 0 ms] (377) QDP (378) TransformationProof [EQUIVALENT, 0 ms] (379) QDP (380) QDPOrderProof [EQUIVALENT, 97 ms] (381) QDP (382) DependencyGraphProof [EQUIVALENT, 0 ms] (383) TRUE (384) QDP (385) QDPOrderProof [EQUIVALENT, 167 ms] (386) QDP (387) DependencyGraphProof [EQUIVALENT, 0 ms] (388) TRUE (389) QDP (390) InductionCalculusProof [EQUIVALENT, 0 ms] (391) QDP (392) QDP (393) QDPSizeChangeProof [EQUIVALENT, 0 ms] (394) YES (395) QDP (396) QDPSizeChangeProof [EQUIVALENT, 0 ms] (397) YES (398) QDP (399) DependencyGraphProof [EQUIVALENT, 0 ms] (400) AND (401) QDP (402) TransformationProof [EQUIVALENT, 0 ms] (403) QDP (404) TransformationProof [EQUIVALENT, 0 ms] (405) QDP (406) QDPSizeChangeProof [EQUIVALENT, 0 ms] (407) YES (408) QDP (409) QDPSizeChangeProof [EQUIVALENT, 0 ms] (410) YES (411) QDP (412) DependencyGraphProof [EQUIVALENT, 0 ms] (413) AND (414) QDP (415) MRRProof [EQUIVALENT, 0 ms] (416) QDP (417) PisEmptyProof [EQUIVALENT, 0 ms] (418) YES (419) QDP (420) QDPSizeChangeProof [EQUIVALENT, 0 ms] (421) YES (422) QDP (423) QDPSizeChangeProof [EQUIVALENT, 0 ms] (424) YES (425) QDP (426) QDPSizeChangeProof [EQUIVALENT, 0 ms] (427) YES (428) QDP (429) QDPSizeChangeProof [EQUIVALENT, 0 ms] (430) YES (431) QDP (432) QDPSizeChangeProof [EQUIVALENT, 0 ms] (433) YES (434) Narrow [COMPLETE, 0 ms] (435) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" is transformed to "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); primDivNatS0 x y False = Zero; " The following If expression "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" is transformed to "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); primModNatS0 x y False = Succ x; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "absReal x|x >= 0x|otherwise`negate` x; " is transformed to "absReal x = absReal2 x; " "absReal1 x True = x; absReal1 x False = absReal0 x otherwise; " "absReal0 x True = `negate` x; " "absReal2 x = absReal1 x (x >= 0); " The following Function with conditions "gcd' x 0 = x; gcd' x y = gcd' y (x `rem` y); " is transformed to "gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; " "gcd'0 x y = gcd' y (x `rem` y); " "gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; " "gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; " The following Function with conditions "gcd 0 0 = error []; gcd x y = gcd' (abs x) (abs y) where { gcd' x 0 = x; gcd' x y = gcd' y (x `rem` y); } ; " is transformed to "gcd yz zu = gcd3 yz zu; gcd x y = gcd0 x y; " "gcd0 x y = gcd' (abs x) (abs y) where { gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; ; gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; } ; " "gcd1 True yz zu = error []; gcd1 zv zw zx = gcd0 zw zx; " "gcd2 True yz zu = gcd1 (zu == 0) yz zu; gcd2 zy zz vuu = gcd0 zz vuu; " "gcd3 yz zu = gcd2 (yz == 0) yz zu; gcd3 vuv vuw = gcd0 vuv vuw; " The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where { d = gcd x y; } ; " is transformed to "reduce x y = reduce2 x y; " "reduce2 x y = reduce1 x y (y == 0) where { d = gcd x y; ; reduce0 x y True = x `quot` d :% (y `quot` d); ; reduce1 x y True = error []; reduce1 x y False = reduce0 x y otherwise; } ; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "gcd' (abs x) (abs y) where { gcd' x xz = gcd'2 x xz; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x xz = x; gcd'1 yu yv yw = gcd'0 yv yw; ; gcd'2 x xz = gcd'1 (xz == 0) x xz; gcd'2 yx yy = gcd'0 yx yy; } " are unpacked to the following functions on top level "gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz; gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy; " "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); " "gcd0Gcd' x xz = gcd0Gcd'2 x xz; gcd0Gcd' x y = gcd0Gcd'0 x y; " "gcd0Gcd'1 True x xz = x; gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw; " The bindings of the following Let/Where expression "reduce1 x y (y == 0) where { d = gcd x y; ; reduce0 x y True = x `quot` d :% (y `quot` d); ; reduce1 x y True = error []; reduce1 x y False = reduce0 x y otherwise; } " are unpacked to the following functions on top level "reduce2Reduce1 vux vuy x y True = error []; reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise; " "reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy); " "reduce2D vux vuy = gcd vux vuy; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="subtract",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="subtract vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="subtract vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="flip (-) vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="(-) vuz4 vuz3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="vuz4 + (negate vuz3)",fontsize=16,color="burlywood",shape="box"];6384[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];7 -> 6384[label="",style="solid", color="burlywood", weight=9]; 6384 -> 8[label="",style="solid", color="burlywood", weight=3]; 8[label="vuz40 :% vuz41 + (negate vuz3)",fontsize=16,color="burlywood",shape="box"];6385[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];8 -> 6385[label="",style="solid", color="burlywood", weight=9]; 6385 -> 9[label="",style="solid", color="burlywood", weight=3]; 9[label="vuz40 :% vuz41 + (negate vuz30 :% vuz31)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10[label="vuz40 :% vuz41 + (negate vuz30) :% vuz31",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11[label="vuz40 :% vuz41 + primNegInt vuz30 :% vuz31",fontsize=16,color="burlywood",shape="box"];6386[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];11 -> 6386[label="",style="solid", color="burlywood", weight=9]; 6386 -> 12[label="",style="solid", color="burlywood", weight=3]; 6387[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];11 -> 6387[label="",style="solid", color="burlywood", weight=9]; 6387 -> 13[label="",style="solid", color="burlywood", weight=3]; 12[label="vuz40 :% vuz41 + primNegInt (Pos vuz300) :% vuz31",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vuz40 :% vuz41 + primNegInt (Neg vuz300) :% vuz31",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="vuz40 :% vuz41 + Neg vuz300 :% vuz31",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="vuz40 :% vuz41 + Pos vuz300 :% vuz31",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="reduce (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="reduce (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="reduce2 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="reduce2 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz41 * vuz31 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz41 * vuz31 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (primEqInt (vuz41 * vuz31) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 23[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (primEqInt (vuz41 * vuz31) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 24[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (primMulInt vuz41 vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (primMulInt vuz41 vuz31) (primEqInt (primMulInt vuz41 vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6388[label="vuz41/Pos 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color="burlywood", weight=9]; 6391 -> 29[label="",style="solid", color="burlywood", weight=3]; 26[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (vuz40 * vuz31 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (primEqInt (primMulInt (Pos vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6392[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];26 -> 6392[label="",style="solid", color="burlywood", weight=9]; 6392 -> 30[label="",style="solid", color="burlywood", weight=3]; 6393[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];26 -> 6393[label="",style="solid", color="burlywood", weight=9]; 6393 -> 31[label="",style="solid", color="burlywood", weight=3]; 27[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (vuz40 * vuz31 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (primEqInt (primMulInt 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weight=3]; 6397[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];28 -> 6397[label="",style="solid", color="burlywood", weight=9]; 6397 -> 35[label="",style="solid", color="burlywood", weight=3]; 29[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (vuz40 * vuz31 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (primEqInt (primMulInt (Neg vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6398[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 6398[label="",style="solid", color="burlywood", weight=9]; 6398 -> 36[label="",style="solid", color="burlywood", weight=3]; 6399[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 6399[label="",style="solid", color="burlywood", weight=9]; 6399 -> 37[label="",style="solid", color="burlywood", weight=3]; 30[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Pos 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40[label="",style="solid", color="black", weight=3]; 33[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (primEqInt (primMulInt (Neg vuz410) (Neg vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3]; 34[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (primEqInt (primMulInt (Pos vuz410) (Pos vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3]; 35[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (primEqInt 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51[label="",style="solid", color="burlywood", weight=3]; 41[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6406[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];41 -> 6406[label="",style="solid", color="burlywood", weight=9]; 6406 -> 52[label="",style="solid", color="burlywood", weight=3]; 6407[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 6407[label="",style="solid", color="burlywood", weight=9]; 6407 -> 53[label="",style="solid", color="burlywood", weight=3]; 42[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 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6419[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 6419[label="",style="solid", color="burlywood", weight=9]; 6419 -> 65[label="",style="solid", color="burlywood", weight=3]; 48[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6420[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];48 -> 6420[label="",style="solid", color="burlywood", weight=9]; 6420 -> 66[label="",style="solid", color="burlywood", weight=3]; 6421[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 6421[label="",style="solid", color="burlywood", weight=9]; 6421 -> 67[label="",style="solid", color="burlywood", weight=3]; 49[label="reduce2Reduce1 (vuz40 * 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6427[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 6427[label="",style="solid", color="burlywood", weight=9]; 6427 -> 73[label="",style="solid", color="burlywood", weight=3]; 52[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6428[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];52 -> 6428[label="",style="solid", color="burlywood", weight=9]; 6428 -> 74[label="",style="solid", color="burlywood", weight=3]; 6429[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 6429[label="",style="solid", color="burlywood", weight=9]; 6429 -> 75[label="",style="solid", color="burlywood", weight=3]; 53[label="reduce2Reduce1 (vuz40 * 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6435[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 6435[label="",style="solid", color="burlywood", weight=9]; 6435 -> 81[label="",style="solid", color="burlywood", weight=3]; 56[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6436[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];56 -> 6436[label="",style="solid", color="burlywood", weight=9]; 6436 -> 82[label="",style="solid", color="burlywood", weight=3]; 6437[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 6437[label="",style="solid", color="burlywood", weight=9]; 6437 -> 83[label="",style="solid", color="burlywood", weight=3]; 57[label="reduce2Reduce1 (vuz40 * 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6443[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 6443[label="",style="solid", color="burlywood", weight=9]; 6443 -> 89[label="",style="solid", color="burlywood", weight=3]; 60[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6444[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];60 -> 6444[label="",style="solid", color="burlywood", weight=9]; 6444 -> 90[label="",style="solid", color="burlywood", weight=3]; 6445[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 6445[label="",style="solid", color="burlywood", weight=9]; 6445 -> 91[label="",style="solid", color="burlywood", weight=3]; 61[label="reduce2Reduce1 (vuz40 * 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-> 107[label="",style="solid", color="black", weight=3]; 76[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];76 -> 108[label="",style="solid", color="black", weight=3]; 77[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];77 -> 109[label="",style="solid", color="black", weight=3]; 78[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) 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color="black", weight=3]; 89[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];89 -> 121[label="",style="solid", color="black", weight=3]; 90[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];90 -> 122[label="",style="solid", color="black", weight=3]; 91[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];91 -> 123[label="",style="solid", color="black", weight=3]; 92[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];92 -> 124[label="",style="solid", color="black", weight=3]; 93[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];93 -> 125[label="",style="solid", color="black", weight=3]; 94 -> 1965[label="",style="dashed", color="red", weight=0]; 94[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];94 -> 1966[label="",style="dashed", color="magenta", weight=3]; 94 -> 1967[label="",style="dashed", color="magenta", weight=3]; 94 -> 1968[label="",style="dashed", color="magenta", weight=3]; 94 -> 1969[label="",style="dashed", color="magenta", weight=3]; 94 -> 1970[label="",style="dashed", color="magenta", weight=3]; 94 -> 1971[label="",style="dashed", color="magenta", weight=3]; 94 -> 1972[label="",style="dashed", color="magenta", weight=3]; 95[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];95 -> 128[label="",style="solid", color="black", weight=3]; 96[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];96 -> 129[label="",style="solid", color="black", weight=3]; 97[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];97 -> 130[label="",style="solid", color="black", weight=3]; 98 -> 1032[label="",style="dashed", color="red", weight=0]; 98[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];98 -> 1033[label="",style="dashed", color="magenta", weight=3]; 98 -> 1034[label="",style="dashed", color="magenta", weight=3]; 98 -> 1035[label="",style="dashed", color="magenta", weight=3]; 98 -> 1036[label="",style="dashed", color="magenta", weight=3]; 98 -> 1037[label="",style="dashed", color="magenta", weight=3]; 98 -> 1038[label="",style="dashed", color="magenta", weight=3]; 98 -> 1039[label="",style="dashed", color="magenta", weight=3]; 99[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];99 -> 133[label="",style="solid", color="black", weight=3]; 100[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];100 -> 134[label="",style="solid", color="black", weight=3]; 101[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];101 -> 135[label="",style="solid", color="black", weight=3]; 102 -> 1075[label="",style="dashed", color="red", weight=0]; 102[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];102 -> 1076[label="",style="dashed", color="magenta", weight=3]; 102 -> 1077[label="",style="dashed", color="magenta", weight=3]; 102 -> 1078[label="",style="dashed", color="magenta", weight=3]; 102 -> 1079[label="",style="dashed", color="magenta", weight=3]; 102 -> 1080[label="",style="dashed", color="magenta", weight=3]; 102 -> 1081[label="",style="dashed", color="magenta", weight=3]; 102 -> 1082[label="",style="dashed", color="magenta", weight=3]; 103[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];103 -> 138[label="",style="solid", color="black", weight=3]; 104[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];104 -> 139[label="",style="solid", color="black", weight=3]; 105[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];105 -> 140[label="",style="solid", color="black", weight=3]; 106 -> 1128[label="",style="dashed", color="red", weight=0]; 106[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];106 -> 1129[label="",style="dashed", color="magenta", weight=3]; 106 -> 1130[label="",style="dashed", color="magenta", weight=3]; 106 -> 1131[label="",style="dashed", color="magenta", weight=3]; 106 -> 1132[label="",style="dashed", color="magenta", weight=3]; 106 -> 1133[label="",style="dashed", color="magenta", weight=3]; 106 -> 1134[label="",style="dashed", color="magenta", weight=3]; 106 -> 1135[label="",style="dashed", color="magenta", weight=3]; 107[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];107 -> 143[label="",style="solid", color="black", weight=3]; 108[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];108 -> 144[label="",style="solid", color="black", weight=3]; 109[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];109 -> 145[label="",style="solid", color="black", weight=3]; 110 -> 1188[label="",style="dashed", color="red", weight=0]; 110[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];110 -> 1189[label="",style="dashed", color="magenta", weight=3]; 110 -> 1190[label="",style="dashed", color="magenta", weight=3]; 110 -> 1191[label="",style="dashed", color="magenta", weight=3]; 110 -> 1192[label="",style="dashed", color="magenta", weight=3]; 110 -> 1193[label="",style="dashed", color="magenta", weight=3]; 110 -> 1194[label="",style="dashed", color="magenta", weight=3]; 110 -> 1195[label="",style="dashed", color="magenta", weight=3]; 111[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];111 -> 148[label="",style="solid", color="black", weight=3]; 112[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];112 -> 149[label="",style="solid", color="black", weight=3]; 113[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];113 -> 150[label="",style="solid", color="black", weight=3]; 114 -> 1361[label="",style="dashed", color="red", weight=0]; 114[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];114 -> 1362[label="",style="dashed", color="magenta", weight=3]; 114 -> 1363[label="",style="dashed", color="magenta", weight=3]; 114 -> 1364[label="",style="dashed", color="magenta", weight=3]; 114 -> 1365[label="",style="dashed", color="magenta", weight=3]; 114 -> 1366[label="",style="dashed", color="magenta", weight=3]; 114 -> 1367[label="",style="dashed", color="magenta", weight=3]; 114 -> 1368[label="",style="dashed", color="magenta", weight=3]; 115[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];115 -> 153[label="",style="solid", color="black", weight=3]; 116[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];116 -> 154[label="",style="solid", color="black", weight=3]; 117[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];117 -> 155[label="",style="solid", color="black", weight=3]; 118 -> 1541[label="",style="dashed", color="red", weight=0]; 118[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];118 -> 1542[label="",style="dashed", color="magenta", weight=3]; 118 -> 1543[label="",style="dashed", color="magenta", weight=3]; 118 -> 1544[label="",style="dashed", color="magenta", weight=3]; 118 -> 1545[label="",style="dashed", color="magenta", weight=3]; 118 -> 1546[label="",style="dashed", color="magenta", weight=3]; 118 -> 1547[label="",style="dashed", color="magenta", weight=3]; 118 -> 1548[label="",style="dashed", color="magenta", weight=3]; 119[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];119 -> 158[label="",style="solid", color="black", weight=3]; 120[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];120 -> 159[label="",style="solid", color="black", weight=3]; 121[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];121 -> 160[label="",style="solid", color="black", weight=3]; 122 -> 1724[label="",style="dashed", color="red", weight=0]; 122[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];122 -> 1725[label="",style="dashed", color="magenta", weight=3]; 122 -> 1726[label="",style="dashed", color="magenta", weight=3]; 122 -> 1727[label="",style="dashed", color="magenta", weight=3]; 122 -> 1728[label="",style="dashed", color="magenta", weight=3]; 122 -> 1729[label="",style="dashed", color="magenta", weight=3]; 122 -> 1730[label="",style="dashed", color="magenta", weight=3]; 122 -> 1731[label="",style="dashed", color="magenta", weight=3]; 123[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];123 -> 163[label="",style="solid", color="black", weight=3]; 124[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];124 -> 164[label="",style="solid", color="black", weight=3]; 125[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];125 -> 165[label="",style="solid", color="black", weight=3]; 1966[label="vuz4100",fontsize=16,color="green",shape="box"];1967 -> 1354[label="",style="dashed", color="red", weight=0]; 1967[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1967 -> 2129[label="",style="dashed", color="magenta", weight=3]; 1967 -> 2130[label="",style="dashed", color="magenta", weight=3]; 1968[label="vuz300",fontsize=16,color="green",shape="box"];1969[label="vuz40",fontsize=16,color="green",shape="box"];1970 -> 1354[label="",style="dashed", color="red", weight=0]; 1970[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1970 -> 2131[label="",style="dashed", color="magenta", weight=3]; 1970 -> 2132[label="",style="dashed", color="magenta", weight=3]; 1971[label="vuz3100",fontsize=16,color="green",shape="box"];1972 -> 1354[label="",style="dashed", color="red", weight=0]; 1972[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1972 -> 2133[label="",style="dashed", color="magenta", weight=3]; 1972 -> 2134[label="",style="dashed", color="magenta", weight=3]; 1965[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos vuz145) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6448[label="vuz145/Succ vuz1450",fontsize=10,color="white",style="solid",shape="box"];1965 -> 6448[label="",style="solid", color="burlywood", weight=9]; 6448 -> 2135[label="",style="solid", color="burlywood", weight=3]; 6449[label="vuz145/Zero",fontsize=10,color="white",style="solid",shape="box"];1965 -> 6449[label="",style="solid", color="burlywood", weight=9]; 6449 -> 2136[label="",style="solid", color="burlywood", weight=3]; 128[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];128 -> 168[label="",style="solid", color="black", weight=3]; 129[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];129 -> 169[label="",style="solid", color="black", weight=3]; 130[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];130 -> 170[label="",style="solid", color="black", weight=3]; 1033[label="vuz4100",fontsize=16,color="green",shape="box"];1034 -> 1016[label="",style="dashed", color="red", weight=0]; 1034[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1034 -> 1070[label="",style="dashed", color="magenta", weight=3]; 1035[label="vuz3100",fontsize=16,color="green",shape="box"];1036[label="vuz300",fontsize=16,color="green",shape="box"];1037[label="vuz40",fontsize=16,color="green",shape="box"];1038 -> 1016[label="",style="dashed", color="red", weight=0]; 1038[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1038 -> 1071[label="",style="dashed", color="magenta", weight=3]; 1039 -> 1016[label="",style="dashed", color="red", weight=0]; 1039[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1039 -> 1072[label="",style="dashed", color="magenta", weight=3]; 1032[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg vuz69) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6450[label="vuz69/Succ vuz690",fontsize=10,color="white",style="solid",shape="box"];1032 -> 6450[label="",style="solid", color="burlywood", weight=9]; 6450 -> 1073[label="",style="solid", color="burlywood", weight=3]; 6451[label="vuz69/Zero",fontsize=10,color="white",style="solid",shape="box"];1032 -> 6451[label="",style="solid", color="burlywood", weight=9]; 6451 -> 1074[label="",style="solid", color="burlywood", weight=3]; 133[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];133 -> 173[label="",style="solid", color="black", weight=3]; 134[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];134 -> 174[label="",style="solid", color="black", weight=3]; 135[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];135 -> 175[label="",style="solid", color="black", weight=3]; 1076[label="vuz4100",fontsize=16,color="green",shape="box"];1077[label="vuz300",fontsize=16,color="green",shape="box"];1078[label="vuz40",fontsize=16,color="green",shape="box"];1079 -> 1016[label="",style="dashed", color="red", weight=0]; 1079[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1079 -> 1113[label="",style="dashed", color="magenta", weight=3]; 1079 -> 1114[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1016[label="",style="dashed", color="red", weight=0]; 1080[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1080 -> 1115[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1116[label="",style="dashed", color="magenta", weight=3]; 1081[label="vuz3100",fontsize=16,color="green",shape="box"];1082 -> 1016[label="",style="dashed", color="red", weight=0]; 1082[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1082 -> 1117[label="",style="dashed", color="magenta", weight=3]; 1082 -> 1118[label="",style="dashed", color="magenta", weight=3]; 1075[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg vuz72) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6452[label="vuz72/Succ vuz720",fontsize=10,color="white",style="solid",shape="box"];1075 -> 6452[label="",style="solid", color="burlywood", weight=9]; 6452 -> 1119[label="",style="solid", color="burlywood", weight=3]; 6453[label="vuz72/Zero",fontsize=10,color="white",style="solid",shape="box"];1075 -> 6453[label="",style="solid", color="burlywood", weight=9]; 6453 -> 1120[label="",style="solid", color="burlywood", weight=3]; 138[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];138 -> 178[label="",style="solid", color="black", weight=3]; 139[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];139 -> 179[label="",style="solid", color="black", weight=3]; 140[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];140 -> 180[label="",style="solid", color="black", weight=3]; 1129[label="vuz300",fontsize=16,color="green",shape="box"];1130[label="vuz40",fontsize=16,color="green",shape="box"];1131 -> 1016[label="",style="dashed", color="red", weight=0]; 1131[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1131 -> 1166[label="",style="dashed", color="magenta", weight=3]; 1132[label="vuz3100",fontsize=16,color="green",shape="box"];1133[label="vuz4100",fontsize=16,color="green",shape="box"];1134 -> 1016[label="",style="dashed", color="red", weight=0]; 1134[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1134 -> 1167[label="",style="dashed", color="magenta", weight=3]; 1135 -> 1016[label="",style="dashed", color="red", weight=0]; 1135[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1135 -> 1168[label="",style="dashed", color="magenta", weight=3]; 1128[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos vuz75) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6454[label="vuz75/Succ vuz750",fontsize=10,color="white",style="solid",shape="box"];1128 -> 6454[label="",style="solid", color="burlywood", weight=9]; 6454 -> 1169[label="",style="solid", color="burlywood", weight=3]; 6455[label="vuz75/Zero",fontsize=10,color="white",style="solid",shape="box"];1128 -> 6455[label="",style="solid", color="burlywood", weight=9]; 6455 -> 1170[label="",style="solid", color="burlywood", weight=3]; 143[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];143 -> 183[label="",style="solid", color="black", weight=3]; 144[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];144 -> 184[label="",style="solid", color="black", weight=3]; 145[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];145 -> 185[label="",style="solid", color="black", weight=3]; 1189 -> 1016[label="",style="dashed", color="red", weight=0]; 1189[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1189 -> 1339[label="",style="dashed", color="magenta", weight=3]; 1189 -> 1340[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1016[label="",style="dashed", color="red", weight=0]; 1190[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1190 -> 1341[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1342[label="",style="dashed", color="magenta", weight=3]; 1191[label="vuz40",fontsize=16,color="green",shape="box"];1192 -> 1016[label="",style="dashed", color="red", weight=0]; 1192[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1192 -> 1343[label="",style="dashed", color="magenta", weight=3]; 1192 -> 1344[label="",style="dashed", color="magenta", weight=3]; 1193[label="vuz3100",fontsize=16,color="green",shape="box"];1194[label="vuz300",fontsize=16,color="green",shape="box"];1195[label="vuz4100",fontsize=16,color="green",shape="box"];1188[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos vuz78) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6456[label="vuz78/Succ vuz780",fontsize=10,color="white",style="solid",shape="box"];1188 -> 6456[label="",style="solid", color="burlywood", weight=9]; 6456 -> 1345[label="",style="solid", color="burlywood", weight=3]; 6457[label="vuz78/Zero",fontsize=10,color="white",style="solid",shape="box"];1188 -> 6457[label="",style="solid", color="burlywood", weight=9]; 6457 -> 1346[label="",style="solid", color="burlywood", weight=3]; 148[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];148 -> 188[label="",style="solid", color="black", weight=3]; 149[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];149 -> 189[label="",style="solid", color="black", weight=3]; 150[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];150 -> 190[label="",style="solid", color="black", weight=3]; 1362[label="vuz3100",fontsize=16,color="green",shape="box"];1363[label="vuz40",fontsize=16,color="green",shape="box"];1364 -> 1016[label="",style="dashed", color="red", weight=0]; 1364[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1364 -> 1519[label="",style="dashed", color="magenta", weight=3]; 1365[label="vuz4100",fontsize=16,color="green",shape="box"];1366 -> 1016[label="",style="dashed", color="red", weight=0]; 1366[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1366 -> 1520[label="",style="dashed", color="magenta", weight=3]; 1367[label="vuz300",fontsize=16,color="green",shape="box"];1368 -> 1016[label="",style="dashed", color="red", weight=0]; 1368[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1368 -> 1521[label="",style="dashed", color="magenta", weight=3]; 1361[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg vuz93) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6458[label="vuz93/Succ vuz930",fontsize=10,color="white",style="solid",shape="box"];1361 -> 6458[label="",style="solid", color="burlywood", weight=9]; 6458 -> 1522[label="",style="solid", color="burlywood", weight=3]; 6459[label="vuz93/Zero",fontsize=10,color="white",style="solid",shape="box"];1361 -> 6459[label="",style="solid", color="burlywood", weight=9]; 6459 -> 1523[label="",style="solid", color="burlywood", weight=3]; 153[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];153 -> 193[label="",style="solid", color="black", weight=3]; 154[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];154 -> 194[label="",style="solid", color="black", weight=3]; 155[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];155 -> 195[label="",style="solid", color="black", weight=3]; 1542 -> 1354[label="",style="dashed", color="red", weight=0]; 1542[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1542 -> 1699[label="",style="dashed", color="magenta", weight=3]; 1542 -> 1700[label="",style="dashed", color="magenta", weight=3]; 1543[label="vuz4100",fontsize=16,color="green",shape="box"];1544[label="vuz40",fontsize=16,color="green",shape="box"];1545[label="vuz300",fontsize=16,color="green",shape="box"];1546 -> 1354[label="",style="dashed", color="red", weight=0]; 1546[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1546 -> 1701[label="",style="dashed", color="magenta", weight=3]; 1546 -> 1702[label="",style="dashed", color="magenta", weight=3]; 1547 -> 1354[label="",style="dashed", color="red", weight=0]; 1547[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1547 -> 1703[label="",style="dashed", color="magenta", weight=3]; 1547 -> 1704[label="",style="dashed", color="magenta", weight=3]; 1548[label="vuz3100",fontsize=16,color="green",shape="box"];1541[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg vuz108) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6460[label="vuz108/Succ vuz1080",fontsize=10,color="white",style="solid",shape="box"];1541 -> 6460[label="",style="solid", color="burlywood", weight=9]; 6460 -> 1705[label="",style="solid", color="burlywood", weight=3]; 6461[label="vuz108/Zero",fontsize=10,color="white",style="solid",shape="box"];1541 -> 6461[label="",style="solid", color="burlywood", weight=9]; 6461 -> 1706[label="",style="solid", color="burlywood", weight=3]; 158[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];158 -> 198[label="",style="solid", color="black", weight=3]; 159[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];159 -> 199[label="",style="solid", color="black", weight=3]; 160[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];160 -> 200[label="",style="solid", color="black", weight=3]; 1725[label="vuz40",fontsize=16,color="green",shape="box"];1726 -> 1354[label="",style="dashed", color="red", weight=0]; 1726[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1726 -> 1875[label="",style="dashed", color="magenta", weight=3]; 1726 -> 1876[label="",style="dashed", color="magenta", weight=3]; 1727[label="vuz3100",fontsize=16,color="green",shape="box"];1728 -> 1354[label="",style="dashed", color="red", weight=0]; 1728[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1728 -> 1877[label="",style="dashed", color="magenta", weight=3]; 1728 -> 1878[label="",style="dashed", color="magenta", weight=3]; 1729[label="vuz4100",fontsize=16,color="green",shape="box"];1730 -> 1354[label="",style="dashed", color="red", weight=0]; 1730[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1730 -> 1879[label="",style="dashed", color="magenta", weight=3]; 1730 -> 1880[label="",style="dashed", color="magenta", weight=3]; 1731[label="vuz300",fontsize=16,color="green",shape="box"];1724[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos vuz123) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6462[label="vuz123/Succ vuz1230",fontsize=10,color="white",style="solid",shape="box"];1724 -> 6462[label="",style="solid", color="burlywood", weight=9]; 6462 -> 1881[label="",style="solid", color="burlywood", weight=3]; 6463[label="vuz123/Zero",fontsize=10,color="white",style="solid",shape="box"];1724 -> 6463[label="",style="solid", color="burlywood", weight=9]; 6463 -> 1882[label="",style="solid", color="burlywood", weight=3]; 163[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];163 -> 203[label="",style="solid", color="black", weight=3]; 164[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];164 -> 204[label="",style="solid", color="black", weight=3]; 165[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];165 -> 205[label="",style="solid", color="black", weight=3]; 2129[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2130 -> 681[label="",style="dashed", color="red", weight=0]; 2130[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2130 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2150[label="",style="dashed", color="magenta", weight=3]; 1354[label="primPlusNat vuz660 vuz3100",fontsize=16,color="burlywood",shape="triangle"];6464[label="vuz660/Succ vuz6600",fontsize=10,color="white",style="solid",shape="box"];1354 -> 6464[label="",style="solid", color="burlywood", weight=9]; 6464 -> 1536[label="",style="solid", color="burlywood", weight=3]; 6465[label="vuz660/Zero",fontsize=10,color="white",style="solid",shape="box"];1354 -> 6465[label="",style="solid", color="burlywood", weight=9]; 6465 -> 1537[label="",style="solid", color="burlywood", weight=3]; 2131[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2132 -> 681[label="",style="dashed", color="red", weight=0]; 2132[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2132 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2132 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2133[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2134 -> 681[label="",style="dashed", color="red", weight=0]; 2134[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2134 -> 2153[label="",style="dashed", color="magenta", weight=3]; 2134 -> 2154[label="",style="dashed", color="magenta", weight=3]; 2135[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2135 -> 2155[label="",style="solid", color="black", weight=3]; 2136[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2136 -> 2156[label="",style="solid", color="black", weight=3]; 168[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];168 -> 209[label="",style="solid", color="black", weight=3]; 169[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];169 -> 210[label="",style="solid", color="black", weight=3]; 170[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];170 -> 211[label="",style="solid", color="black", weight=3]; 1070 -> 681[label="",style="dashed", color="red", weight=0]; 1070[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1070 -> 1121[label="",style="dashed", color="magenta", weight=3]; 1016[label="primPlusNat vuz66 (Succ vuz3100)",fontsize=16,color="burlywood",shape="triangle"];6466[label="vuz66/Succ vuz660",fontsize=10,color="white",style="solid",shape="box"];1016 -> 6466[label="",style="solid", color="burlywood", weight=9]; 6466 -> 1122[label="",style="solid", color="burlywood", weight=3]; 6467[label="vuz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1016 -> 6467[label="",style="solid", color="burlywood", weight=9]; 6467 -> 1123[label="",style="solid", color="burlywood", weight=3]; 1071 -> 681[label="",style="dashed", color="red", weight=0]; 1071[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1071 -> 1124[label="",style="dashed", color="magenta", weight=3]; 1072 -> 681[label="",style="dashed", color="red", weight=0]; 1072[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1072 -> 1125[label="",style="dashed", color="magenta", weight=3]; 1073[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1073 -> 1126[label="",style="solid", color="black", weight=3]; 1074[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1074 -> 1127[label="",style="solid", color="black", weight=3]; 173[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];173 -> 215[label="",style="solid", color="black", weight=3]; 174[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];174 -> 216[label="",style="solid", color="black", weight=3]; 175[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];175 -> 217[label="",style="solid", color="black", weight=3]; 1113 -> 681[label="",style="dashed", color="red", weight=0]; 1113[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1113 -> 1171[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1172[label="",style="dashed", color="magenta", weight=3]; 1114[label="vuz3100",fontsize=16,color="green",shape="box"];1115 -> 681[label="",style="dashed", color="red", weight=0]; 1115[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1115 -> 1173[label="",style="dashed", color="magenta", weight=3]; 1115 -> 1174[label="",style="dashed", color="magenta", weight=3]; 1116[label="vuz3100",fontsize=16,color="green",shape="box"];1117 -> 681[label="",style="dashed", color="red", weight=0]; 1117[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1117 -> 1175[label="",style="dashed", color="magenta", weight=3]; 1117 -> 1176[label="",style="dashed", color="magenta", weight=3]; 1118[label="vuz3100",fontsize=16,color="green",shape="box"];1119[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1119 -> 1177[label="",style="solid", color="black", weight=3]; 1120[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1120 -> 1178[label="",style="solid", color="black", weight=3]; 178[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];178 -> 221[label="",style="solid", color="black", weight=3]; 179[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];179 -> 222[label="",style="solid", color="black", weight=3]; 180[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];180 -> 223[label="",style="solid", color="black", weight=3]; 1166 -> 681[label="",style="dashed", color="red", weight=0]; 1166[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1166 -> 1347[label="",style="dashed", color="magenta", weight=3]; 1167 -> 681[label="",style="dashed", color="red", weight=0]; 1167[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1167 -> 1348[label="",style="dashed", color="magenta", weight=3]; 1168 -> 681[label="",style="dashed", color="red", weight=0]; 1168[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1168 -> 1349[label="",style="dashed", color="magenta", weight=3]; 1169[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1169 -> 1350[label="",style="solid", color="black", weight=3]; 1170[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1170 -> 1351[label="",style="solid", color="black", weight=3]; 183[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];183 -> 227[label="",style="solid", color="black", weight=3]; 184[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];184 -> 228[label="",style="solid", color="black", weight=3]; 185[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];185 -> 229[label="",style="solid", color="black", weight=3]; 1339 -> 681[label="",style="dashed", color="red", weight=0]; 1339[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1339 -> 1524[label="",style="dashed", color="magenta", weight=3]; 1339 -> 1525[label="",style="dashed", color="magenta", weight=3]; 1340[label="vuz3100",fontsize=16,color="green",shape="box"];1341 -> 681[label="",style="dashed", color="red", weight=0]; 1341[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1341 -> 1526[label="",style="dashed", color="magenta", weight=3]; 1341 -> 1527[label="",style="dashed", color="magenta", weight=3]; 1342[label="vuz3100",fontsize=16,color="green",shape="box"];1343 -> 681[label="",style="dashed", color="red", weight=0]; 1343[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1343 -> 1528[label="",style="dashed", color="magenta", weight=3]; 1343 -> 1529[label="",style="dashed", color="magenta", weight=3]; 1344[label="vuz3100",fontsize=16,color="green",shape="box"];1345[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1345 -> 1530[label="",style="solid", color="black", weight=3]; 1346[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1346 -> 1531[label="",style="solid", color="black", weight=3]; 188[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];188 -> 233[label="",style="solid", color="black", weight=3]; 189[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];189 -> 234[label="",style="solid", color="black", weight=3]; 190[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];190 -> 235[label="",style="solid", color="black", weight=3]; 1519 -> 681[label="",style="dashed", color="red", weight=0]; 1519[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1519 -> 1707[label="",style="dashed", color="magenta", weight=3]; 1520 -> 681[label="",style="dashed", color="red", weight=0]; 1520[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1520 -> 1708[label="",style="dashed", color="magenta", weight=3]; 1521 -> 681[label="",style="dashed", color="red", weight=0]; 1521[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1521 -> 1709[label="",style="dashed", color="magenta", weight=3]; 1522[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1522 -> 1710[label="",style="solid", color="black", weight=3]; 1523[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1523 -> 1711[label="",style="solid", color="black", weight=3]; 193[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];193 -> 239[label="",style="solid", color="black", weight=3]; 194[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];194 -> 240[label="",style="solid", color="black", weight=3]; 195[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];195 -> 241[label="",style="solid", color="black", weight=3]; 1699[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1700 -> 681[label="",style="dashed", color="red", weight=0]; 1700[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1700 -> 1883[label="",style="dashed", color="magenta", weight=3]; 1700 -> 1884[label="",style="dashed", color="magenta", weight=3]; 1701[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1702 -> 681[label="",style="dashed", color="red", weight=0]; 1702[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1702 -> 1885[label="",style="dashed", color="magenta", weight=3]; 1702 -> 1886[label="",style="dashed", color="magenta", weight=3]; 1703[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1704 -> 681[label="",style="dashed", color="red", weight=0]; 1704[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1704 -> 1887[label="",style="dashed", color="magenta", weight=3]; 1704 -> 1888[label="",style="dashed", color="magenta", weight=3]; 1705[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1705 -> 1889[label="",style="solid", color="black", weight=3]; 1706[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1706 -> 1890[label="",style="solid", color="black", weight=3]; 198[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];198 -> 245[label="",style="solid", color="black", weight=3]; 199[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];199 -> 246[label="",style="solid", color="black", weight=3]; 200[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];200 -> 247[label="",style="solid", color="black", weight=3]; 1875[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1876 -> 681[label="",style="dashed", color="red", weight=0]; 1876[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1876 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1877[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1878 -> 681[label="",style="dashed", color="red", weight=0]; 1878[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1878 -> 1918[label="",style="dashed", color="magenta", weight=3]; 1879[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1880 -> 681[label="",style="dashed", color="red", weight=0]; 1880[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1880 -> 1919[label="",style="dashed", color="magenta", weight=3]; 1881[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1881 -> 1920[label="",style="solid", color="black", weight=3]; 1882[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1882 -> 1921[label="",style="solid", color="black", weight=3]; 203[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];203 -> 251[label="",style="solid", color="black", weight=3]; 204[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];204 -> 252[label="",style="solid", color="black", weight=3]; 205[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];205 -> 253[label="",style="solid", color="black", weight=3]; 2149[label="vuz3100",fontsize=16,color="green",shape="box"];2150[label="vuz4100",fontsize=16,color="green",shape="box"];681[label="primMulNat vuz41000 (Succ vuz3100)",fontsize=16,color="burlywood",shape="triangle"];6468[label="vuz41000/Succ vuz410000",fontsize=10,color="white",style="solid",shape="box"];681 -> 6468[label="",style="solid", color="burlywood", weight=9]; 6468 -> 781[label="",style="solid", color="burlywood", weight=3]; 6469[label="vuz41000/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 6469[label="",style="solid", color="burlywood", weight=9]; 6469 -> 782[label="",style="solid", color="burlywood", weight=3]; 1536[label="primPlusNat (Succ vuz6600) vuz3100",fontsize=16,color="burlywood",shape="box"];6470[label="vuz3100/Succ vuz31000",fontsize=10,color="white",style="solid",shape="box"];1536 -> 6470[label="",style="solid", color="burlywood", weight=9]; 6470 -> 1717[label="",style="solid", color="burlywood", weight=3]; 6471[label="vuz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];1536 -> 6471[label="",style="solid", color="burlywood", weight=9]; 6471 -> 1718[label="",style="solid", color="burlywood", weight=3]; 1537[label="primPlusNat Zero vuz3100",fontsize=16,color="burlywood",shape="box"];6472[label="vuz3100/Succ vuz31000",fontsize=10,color="white",style="solid",shape="box"];1537 -> 6472[label="",style="solid", color="burlywood", weight=9]; 6472 -> 1719[label="",style="solid", color="burlywood", weight=3]; 6473[label="vuz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];1537 -> 6473[label="",style="solid", color="burlywood", weight=9]; 6473 -> 1720[label="",style="solid", color="burlywood", weight=3]; 2151[label="vuz3100",fontsize=16,color="green",shape="box"];2152[label="vuz4100",fontsize=16,color="green",shape="box"];2153[label="vuz3100",fontsize=16,color="green",shape="box"];2154[label="vuz4100",fontsize=16,color="green",shape="box"];2155[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (Pos Zero))",fontsize=16,color="black",shape="box"];2155 -> 2170[label="",style="solid", color="black", weight=3]; 2156[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];2156 -> 2171[label="",style="solid", color="black", weight=3]; 209[label="error []",fontsize=16,color="black",shape="triangle"];209 -> 257[label="",style="solid", color="black", weight=3]; 210 -> 209[label="",style="dashed", color="red", weight=0]; 210[label="error []",fontsize=16,color="magenta"];211 -> 209[label="",style="dashed", color="red", weight=0]; 211[label="error []",fontsize=16,color="magenta"];1121[label="vuz4100",fontsize=16,color="green",shape="box"];1122[label="primPlusNat (Succ vuz660) (Succ vuz3100)",fontsize=16,color="black",shape="box"];1122 -> 1179[label="",style="solid", color="black", weight=3]; 1123[label="primPlusNat Zero (Succ vuz3100)",fontsize=16,color="black",shape="box"];1123 -> 1180[label="",style="solid", color="black", weight=3]; 1124[label="vuz4100",fontsize=16,color="green",shape="box"];1125[label="vuz4100",fontsize=16,color="green",shape="box"];1126[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (Pos Zero))",fontsize=16,color="black",shape="box"];1126 -> 1181[label="",style="solid", color="black", weight=3]; 1127[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1127 -> 1182[label="",style="solid", color="black", weight=3]; 215 -> 209[label="",style="dashed", color="red", weight=0]; 215[label="error []",fontsize=16,color="magenta"];216 -> 209[label="",style="dashed", color="red", weight=0]; 216[label="error []",fontsize=16,color="magenta"];217 -> 209[label="",style="dashed", color="red", weight=0]; 217[label="error []",fontsize=16,color="magenta"];1171[label="vuz3100",fontsize=16,color="green",shape="box"];1172[label="vuz4100",fontsize=16,color="green",shape="box"];1173[label="vuz3100",fontsize=16,color="green",shape="box"];1174[label="vuz4100",fontsize=16,color="green",shape="box"];1175[label="vuz3100",fontsize=16,color="green",shape="box"];1176[label="vuz4100",fontsize=16,color="green",shape="box"];1177[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (Pos Zero))",fontsize=16,color="black",shape="box"];1177 -> 1352[label="",style="solid", color="black", weight=3]; 1178[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1178 -> 1353[label="",style="solid", color="black", weight=3]; 221 -> 209[label="",style="dashed", color="red", weight=0]; 221[label="error []",fontsize=16,color="magenta"];222 -> 209[label="",style="dashed", color="red", weight=0]; 222[label="error []",fontsize=16,color="magenta"];223 -> 209[label="",style="dashed", color="red", weight=0]; 223[label="error []",fontsize=16,color="magenta"];1347[label="vuz4100",fontsize=16,color="green",shape="box"];1348[label="vuz4100",fontsize=16,color="green",shape="box"];1349[label="vuz4100",fontsize=16,color="green",shape="box"];1350[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (Pos Zero))",fontsize=16,color="black",shape="box"];1350 -> 1532[label="",style="solid", color="black", weight=3]; 1351[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1351 -> 1533[label="",style="solid", color="black", weight=3]; 227 -> 209[label="",style="dashed", color="red", weight=0]; 227[label="error []",fontsize=16,color="magenta"];228 -> 209[label="",style="dashed", color="red", weight=0]; 228[label="error []",fontsize=16,color="magenta"];229 -> 209[label="",style="dashed", color="red", weight=0]; 229[label="error []",fontsize=16,color="magenta"];1524[label="vuz3100",fontsize=16,color="green",shape="box"];1525[label="vuz4100",fontsize=16,color="green",shape="box"];1526[label="vuz3100",fontsize=16,color="green",shape="box"];1527[label="vuz4100",fontsize=16,color="green",shape="box"];1528[label="vuz3100",fontsize=16,color="green",shape="box"];1529[label="vuz4100",fontsize=16,color="green",shape="box"];1530[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (Pos Zero))",fontsize=16,color="black",shape="box"];1530 -> 1712[label="",style="solid", color="black", weight=3]; 1531[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1531 -> 1713[label="",style="solid", color="black", weight=3]; 233 -> 209[label="",style="dashed", color="red", weight=0]; 233[label="error []",fontsize=16,color="magenta"];234 -> 209[label="",style="dashed", color="red", weight=0]; 234[label="error []",fontsize=16,color="magenta"];235 -> 209[label="",style="dashed", color="red", weight=0]; 235[label="error []",fontsize=16,color="magenta"];1707[label="vuz4100",fontsize=16,color="green",shape="box"];1708[label="vuz4100",fontsize=16,color="green",shape="box"];1709[label="vuz4100",fontsize=16,color="green",shape="box"];1710[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (Pos Zero))",fontsize=16,color="black",shape="box"];1710 -> 1891[label="",style="solid", color="black", weight=3]; 1711[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1711 -> 1892[label="",style="solid", color="black", weight=3]; 239 -> 209[label="",style="dashed", color="red", weight=0]; 239[label="error []",fontsize=16,color="magenta"];240 -> 209[label="",style="dashed", color="red", weight=0]; 240[label="error []",fontsize=16,color="magenta"];241 -> 209[label="",style="dashed", color="red", weight=0]; 241[label="error []",fontsize=16,color="magenta"];1883[label="vuz3100",fontsize=16,color="green",shape="box"];1884[label="vuz4100",fontsize=16,color="green",shape="box"];1885[label="vuz3100",fontsize=16,color="green",shape="box"];1886[label="vuz4100",fontsize=16,color="green",shape="box"];1887[label="vuz3100",fontsize=16,color="green",shape="box"];1888[label="vuz4100",fontsize=16,color="green",shape="box"];1889[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (Pos Zero))",fontsize=16,color="black",shape="box"];1889 -> 1922[label="",style="solid", color="black", weight=3]; 1890[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1890 -> 1923[label="",style="solid", color="black", weight=3]; 245 -> 209[label="",style="dashed", color="red", weight=0]; 245[label="error []",fontsize=16,color="magenta"];246 -> 209[label="",style="dashed", color="red", weight=0]; 246[label="error []",fontsize=16,color="magenta"];247 -> 209[label="",style="dashed", color="red", weight=0]; 247[label="error []",fontsize=16,color="magenta"];1917[label="vuz4100",fontsize=16,color="green",shape="box"];1918[label="vuz4100",fontsize=16,color="green",shape="box"];1919[label="vuz4100",fontsize=16,color="green",shape="box"];1920[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (Pos Zero))",fontsize=16,color="black",shape="box"];1920 -> 1942[label="",style="solid", color="black", weight=3]; 1921[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1921 -> 1943[label="",style="solid", color="black", weight=3]; 251 -> 209[label="",style="dashed", color="red", weight=0]; 251[label="error []",fontsize=16,color="magenta"];252 -> 209[label="",style="dashed", color="red", weight=0]; 252[label="error []",fontsize=16,color="magenta"];253 -> 209[label="",style="dashed", color="red", weight=0]; 253[label="error []",fontsize=16,color="magenta"];781[label="primMulNat (Succ vuz410000) (Succ vuz3100)",fontsize=16,color="black",shape="box"];781 -> 899[label="",style="solid", color="black", weight=3]; 782[label="primMulNat Zero (Succ vuz3100)",fontsize=16,color="black",shape="box"];782 -> 900[label="",style="solid", color="black", weight=3]; 1717[label="primPlusNat (Succ vuz6600) (Succ vuz31000)",fontsize=16,color="black",shape="box"];1717 -> 1895[label="",style="solid", color="black", weight=3]; 1718[label="primPlusNat (Succ vuz6600) Zero",fontsize=16,color="black",shape="box"];1718 -> 1896[label="",style="solid", color="black", weight=3]; 1719[label="primPlusNat Zero (Succ vuz31000)",fontsize=16,color="black",shape="box"];1719 -> 1897[label="",style="solid", color="black", weight=3]; 1720[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1720 -> 1898[label="",style="solid", color="black", weight=3]; 2170[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) False",fontsize=16,color="black",shape="box"];2170 -> 2187[label="",style="solid", color="black", weight=3]; 2171[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2171 -> 2188[label="",style="solid", color="black", weight=3]; 257[label="error []",fontsize=16,color="red",shape="box"];1179[label="Succ (Succ (primPlusNat vuz660 vuz3100))",fontsize=16,color="green",shape="box"];1179 -> 1354[label="",style="dashed", color="green", weight=3]; 1180[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1181[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) False",fontsize=16,color="black",shape="box"];1181 -> 1355[label="",style="solid", color="black", weight=3]; 1182[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1182 -> 1356[label="",style="solid", color="black", weight=3]; 1352[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) False",fontsize=16,color="black",shape="box"];1352 -> 1534[label="",style="solid", color="black", weight=3]; 1353[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1353 -> 1535[label="",style="solid", color="black", weight=3]; 1532[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) False",fontsize=16,color="black",shape="box"];1532 -> 1714[label="",style="solid", color="black", weight=3]; 1533[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1533 -> 1715[label="",style="solid", color="black", weight=3]; 1712[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) False",fontsize=16,color="black",shape="box"];1712 -> 1893[label="",style="solid", color="black", weight=3]; 1713[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1713 -> 1894[label="",style="solid", color="black", weight=3]; 1891[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) False",fontsize=16,color="black",shape="box"];1891 -> 1924[label="",style="solid", color="black", weight=3]; 1892[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1892 -> 1925[label="",style="solid", color="black", weight=3]; 1922[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) False",fontsize=16,color="black",shape="box"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1923[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];1923 -> 1945[label="",style="solid", color="black", weight=3]; 1942[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) False",fontsize=16,color="black",shape="box"];1942 -> 2137[label="",style="solid", color="black", weight=3]; 1943[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];1943 -> 2138[label="",style="solid", color="black", weight=3]; 899 -> 1016[label="",style="dashed", color="red", weight=0]; 899[label="primPlusNat (primMulNat vuz410000 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];899 -> 1017[label="",style="dashed", color="magenta", weight=3]; 900[label="Zero",fontsize=16,color="green",shape="box"];1895[label="Succ (Succ (primPlusNat vuz6600 vuz31000))",fontsize=16,color="green",shape="box"];1895 -> 1927[label="",style="dashed", color="green", weight=3]; 1896[label="Succ vuz6600",fontsize=16,color="green",shape="box"];1897[label="Succ vuz31000",fontsize=16,color="green",shape="box"];1898[label="Zero",fontsize=16,color="green",shape="box"];2187[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) otherwise",fontsize=16,color="black",shape="box"];2187 -> 2206[label="",style="solid", color="black", weight=3]; 2188 -> 209[label="",style="dashed", color="red", weight=0]; 2188[label="error []",fontsize=16,color="magenta"];1355[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) otherwise",fontsize=16,color="black",shape="box"];1355 -> 1538[label="",style="solid", color="black", weight=3]; 1356 -> 209[label="",style="dashed", color="red", weight=0]; 1356[label="error []",fontsize=16,color="magenta"];1534[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) otherwise",fontsize=16,color="black",shape="box"];1534 -> 1716[label="",style="solid", color="black", weight=3]; 1535 -> 209[label="",style="dashed", color="red", weight=0]; 1535[label="error []",fontsize=16,color="magenta"];1714[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) otherwise",fontsize=16,color="black",shape="box"];1714 -> 1899[label="",style="solid", color="black", weight=3]; 1715 -> 209[label="",style="dashed", color="red", weight=0]; 1715[label="error []",fontsize=16,color="magenta"];1893[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) otherwise",fontsize=16,color="black",shape="box"];1893 -> 1926[label="",style="solid", color="black", weight=3]; 1894 -> 209[label="",style="dashed", color="red", weight=0]; 1894[label="error []",fontsize=16,color="magenta"];1924[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) otherwise",fontsize=16,color="black",shape="box"];1924 -> 1946[label="",style="solid", color="black", weight=3]; 1925 -> 209[label="",style="dashed", color="red", weight=0]; 1925[label="error []",fontsize=16,color="magenta"];1944[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) otherwise",fontsize=16,color="black",shape="box"];1944 -> 2139[label="",style="solid", color="black", weight=3]; 1945 -> 209[label="",style="dashed", color="red", weight=0]; 1945[label="error []",fontsize=16,color="magenta"];2137[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) otherwise",fontsize=16,color="black",shape="box"];2137 -> 2157[label="",style="solid", color="black", weight=3]; 2138 -> 209[label="",style="dashed", color="red", weight=0]; 2138[label="error []",fontsize=16,color="magenta"];1017 -> 681[label="",style="dashed", color="red", weight=0]; 1017[label="primMulNat vuz410000 (Succ vuz3100)",fontsize=16,color="magenta"];1017 -> 1183[label="",style="dashed", color="magenta", weight=3]; 1927 -> 1354[label="",style="dashed", color="red", weight=0]; 1927[label="primPlusNat vuz6600 vuz31000",fontsize=16,color="magenta"];1927 -> 1948[label="",style="dashed", color="magenta", weight=3]; 1927 -> 1949[label="",style="dashed", color="magenta", weight=3]; 2206[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2206 -> 2222[label="",style="solid", color="black", weight=3]; 1538[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1538 -> 1721[label="",style="solid", color="black", weight=3]; 1716[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1716 -> 1900[label="",style="solid", color="black", weight=3]; 1899[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1899 -> 1928[label="",style="solid", color="black", weight=3]; 1926[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1926 -> 1947[label="",style="solid", color="black", weight=3]; 1946[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1946 -> 2140[label="",style="solid", color="black", weight=3]; 2139[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];2139 -> 2158[label="",style="solid", color="black", weight=3]; 2157[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];2157 -> 2172[label="",style="solid", color="black", weight=3]; 1183[label="vuz410000",fontsize=16,color="green",shape="box"];1948[label="vuz31000",fontsize=16,color="green",shape="box"];1949[label="vuz6600",fontsize=16,color="green",shape="box"];2222[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) :% (Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="green",shape="box"];2222 -> 2237[label="",style="dashed", color="green", weight=3]; 2222 -> 2238[label="",style="dashed", color="green", weight=3]; 1721[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) :% (Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="green",shape="box"];1721 -> 1901[label="",style="dashed", color="green", weight=3]; 1721 -> 1902[label="",style="dashed", color="green", weight=3]; 1900[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) :% (Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="green",shape="box"];1900 -> 1929[label="",style="dashed", color="green", weight=3]; 1900 -> 1930[label="",style="dashed", color="green", weight=3]; 1928[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) :% (Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="green",shape="box"];1928 -> 1950[label="",style="dashed", color="green", weight=3]; 1928 -> 1951[label="",style="dashed", color="green", weight=3]; 1947[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) :% (Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="green",shape="box"];1947 -> 2141[label="",style="dashed", color="green", weight=3]; 1947 -> 2142[label="",style="dashed", color="green", weight=3]; 2140[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) :% (Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="green",shape="box"];2140 -> 2159[label="",style="dashed", color="green", weight=3]; 2140 -> 2160[label="",style="dashed", color="green", weight=3]; 2158[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) :% (Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="green",shape="box"];2158 -> 2173[label="",style="dashed", color="green", weight=3]; 2158 -> 2174[label="",style="dashed", color="green", weight=3]; 2172[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) :% (Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="green",shape="box"];2172 -> 2189[label="",style="dashed", color="green", weight=3]; 2172 -> 2190[label="",style="dashed", color="green", weight=3]; 2237[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2237 -> 2250[label="",style="solid", color="black", weight=3]; 2238[label="Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2238 -> 2251[label="",style="solid", color="black", weight=3]; 1901[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1901 -> 1931[label="",style="solid", color="black", weight=3]; 1902[label="Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1902 -> 1932[label="",style="solid", color="black", weight=3]; 1929[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1929 -> 1952[label="",style="solid", color="black", weight=3]; 1930[label="Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1930 -> 1953[label="",style="solid", color="black", weight=3]; 1950[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1950 -> 2143[label="",style="solid", color="black", weight=3]; 1951[label="Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1951 -> 2144[label="",style="solid", color="black", weight=3]; 2141[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2141 -> 2161[label="",style="solid", color="black", weight=3]; 2142[label="Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2142 -> 2162[label="",style="solid", color="black", weight=3]; 2159[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2159 -> 2175[label="",style="solid", color="black", weight=3]; 2160[label="Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2160 -> 2176[label="",style="solid", color="black", weight=3]; 2173[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2173 -> 2191[label="",style="solid", color="black", weight=3]; 2174[label="Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2174 -> 2192[label="",style="solid", color="black", weight=3]; 2189[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2189 -> 2207[label="",style="solid", color="black", weight=3]; 2190[label="Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2190 -> 2208[label="",style="solid", color="black", weight=3]; 2250[label="primQuotInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2250 -> 2262[label="",style="solid", color="black", weight=3]; 2251 -> 5046[label="",style="dashed", color="red", weight=0]; 2251[label="primQuotInt (Pos vuz143) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="magenta"];2251 -> 5047[label="",style="dashed", color="magenta", weight=3]; 2251 -> 5048[label="",style="dashed", color="magenta", weight=3]; 1931[label="primQuotInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="black",shape="box"];1931 -> 1960[label="",style="solid", color="black", weight=3]; 1932 -> 3509[label="",style="dashed", color="red", weight=0]; 1932[label="primQuotInt (Neg vuz67) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="magenta"];1932 -> 3510[label="",style="dashed", color="magenta", weight=3]; 1932 -> 3511[label="",style="dashed", color="magenta", weight=3]; 1952[label="primQuotInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="black",shape="box"];1952 -> 2145[label="",style="solid", color="black", weight=3]; 1953 -> 3509[label="",style="dashed", color="red", weight=0]; 1953[label="primQuotInt (Neg vuz70) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="magenta"];1953 -> 3512[label="",style="dashed", color="magenta", weight=3]; 1953 -> 3513[label="",style="dashed", color="magenta", weight=3]; 2143[label="primQuotInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="black",shape="box"];2143 -> 2163[label="",style="solid", color="black", weight=3]; 2144 -> 5046[label="",style="dashed", color="red", weight=0]; 2144[label="primQuotInt (Pos vuz73) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="magenta"];2144 -> 5049[label="",style="dashed", color="magenta", weight=3]; 2161[label="primQuotInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="black",shape="box"];2161 -> 2177[label="",style="solid", color="black", weight=3]; 2162 -> 5046[label="",style="dashed", color="red", weight=0]; 2162[label="primQuotInt (Pos vuz76) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="magenta"];2162 -> 5050[label="",style="dashed", color="magenta", weight=3]; 2162 -> 5051[label="",style="dashed", color="magenta", weight=3]; 2175[label="primQuotInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="black",shape="box"];2175 -> 2193[label="",style="solid", color="black", weight=3]; 2176 -> 3509[label="",style="dashed", color="red", weight=0]; 2176[label="primQuotInt (Neg vuz91) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="magenta"];2176 -> 3514[label="",style="dashed", color="magenta", weight=3]; 2176 -> 3515[label="",style="dashed", color="magenta", weight=3]; 2191[label="primQuotInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="black",shape="box"];2191 -> 2209[label="",style="solid", color="black", weight=3]; 2192 -> 3509[label="",style="dashed", color="red", weight=0]; 2192[label="primQuotInt (Neg vuz106) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="magenta"];2192 -> 3516[label="",style="dashed", color="magenta", weight=3]; 2192 -> 3517[label="",style="dashed", color="magenta", weight=3]; 2207[label="primQuotInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="black",shape="box"];2207 -> 2223[label="",style="solid", color="black", weight=3]; 2208 -> 5046[label="",style="dashed", color="red", weight=0]; 2208[label="primQuotInt (Pos vuz121) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="magenta"];2208 -> 5052[label="",style="dashed", color="magenta", weight=3]; 2208 -> 5053[label="",style="dashed", color="magenta", weight=3]; 2262[label="primQuotInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2262 -> 2270[label="",style="solid", color="black", weight=3]; 5047[label="reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5047 -> 5683[label="",style="solid", color="black", weight=3]; 5048[label="vuz143",fontsize=16,color="green",shape="box"];5046[label="primQuotInt (Pos vuz73) vuz346",fontsize=16,color="burlywood",shape="triangle"];6474[label="vuz346/Pos vuz3460",fontsize=10,color="white",style="solid",shape="box"];5046 -> 6474[label="",style="solid", color="burlywood", weight=9]; 6474 -> 5684[label="",style="solid", color="burlywood", weight=3]; 6475[label="vuz346/Neg vuz3460",fontsize=10,color="white",style="solid",shape="box"];5046 -> 6475[label="",style="solid", color="burlywood", weight=9]; 6475 -> 5685[label="",style="solid", color="burlywood", weight=3]; 1960[label="primQuotInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];1960 -> 2147[label="",style="solid", color="black", weight=3]; 3510[label="reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];3510 -> 4084[label="",style="solid", color="black", weight=3]; 3511[label="vuz67",fontsize=16,color="green",shape="box"];3509[label="primQuotInt (Neg vuz280) vuz281",fontsize=16,color="burlywood",shape="triangle"];6476[label="vuz281/Pos vuz2810",fontsize=10,color="white",style="solid",shape="box"];3509 -> 6476[label="",style="solid", color="burlywood", weight=9]; 6476 -> 4085[label="",style="solid", color="burlywood", weight=3]; 6477[label="vuz281/Neg vuz2810",fontsize=10,color="white",style="solid",shape="box"];3509 -> 6477[label="",style="solid", color="burlywood", weight=9]; 6477 -> 4086[label="",style="solid", color="burlywood", weight=3]; 2145[label="primQuotInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2145 -> 2165[label="",style="solid", color="black", weight=3]; 3512[label="reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];3512 -> 4087[label="",style="solid", color="black", weight=3]; 3513[label="vuz70",fontsize=16,color="green",shape="box"];2163[label="primQuotInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2163 -> 2179[label="",style="solid", color="black", weight=3]; 5049[label="reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5049 -> 5686[label="",style="solid", color="black", weight=3]; 2177[label="primQuotInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2177 -> 2195[label="",style="solid", color="black", weight=3]; 5050[label="reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5050 -> 5687[label="",style="solid", color="black", weight=3]; 5051[label="vuz76",fontsize=16,color="green",shape="box"];2193[label="primQuotInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2193 -> 2211[label="",style="solid", color="black", weight=3]; 3514[label="reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];3514 -> 4088[label="",style="solid", color="black", weight=3]; 3515[label="vuz91",fontsize=16,color="green",shape="box"];2209[label="primQuotInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2209 -> 2225[label="",style="solid", color="black", weight=3]; 3516[label="reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];3516 -> 4089[label="",style="solid", color="black", weight=3]; 3517[label="vuz106",fontsize=16,color="green",shape="box"];2223[label="primQuotInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2223 -> 2239[label="",style="solid", color="black", weight=3]; 5052[label="reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5052 -> 5688[label="",style="solid", color="black", weight=3]; 5053[label="vuz121",fontsize=16,color="green",shape="box"];2270[label="primQuotInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6478[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];2270 -> 6478[label="",style="solid", color="burlywood", weight=9]; 6478 -> 2276[label="",style="solid", color="burlywood", weight=3]; 6479[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];2270 -> 6479[label="",style="solid", color="burlywood", weight=9]; 6479 -> 2277[label="",style="solid", color="burlywood", weight=3]; 5683[label="gcd (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5683 -> 5695[label="",style="solid", color="black", weight=3]; 5684[label="primQuotInt (Pos vuz73) (Pos vuz3460)",fontsize=16,color="burlywood",shape="box"];6480[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5684 -> 6480[label="",style="solid", color="burlywood", weight=9]; 6480 -> 5696[label="",style="solid", color="burlywood", weight=3]; 6481[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5684 -> 6481[label="",style="solid", color="burlywood", weight=9]; 6481 -> 5697[label="",style="solid", color="burlywood", weight=3]; 5685[label="primQuotInt (Pos vuz73) (Neg vuz3460)",fontsize=16,color="burlywood",shape="box"];6482[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5685 -> 6482[label="",style="solid", color="burlywood", weight=9]; 6482 -> 5698[label="",style="solid", color="burlywood", weight=3]; 6483[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5685 -> 6483[label="",style="solid", color="burlywood", weight=9]; 6483 -> 5699[label="",style="solid", color="burlywood", weight=3]; 2147[label="primQuotInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6484[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];2147 -> 6484[label="",style="solid", color="burlywood", weight=9]; 6484 -> 2167[label="",style="solid", color="burlywood", weight=3]; 6485[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];2147 -> 6485[label="",style="solid", color="burlywood", weight=9]; 6485 -> 2168[label="",style="solid", color="burlywood", weight=3]; 4084[label="gcd (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4084 -> 4093[label="",style="solid", color="black", weight=3]; 4085[label="primQuotInt (Neg vuz280) (Pos vuz2810)",fontsize=16,color="burlywood",shape="box"];6486[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4085 -> 6486[label="",style="solid", color="burlywood", weight=9]; 6486 -> 4094[label="",style="solid", color="burlywood", weight=3]; 6487[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4085 -> 6487[label="",style="solid", color="burlywood", weight=9]; 6487 -> 4095[label="",style="solid", color="burlywood", weight=3]; 4086[label="primQuotInt (Neg vuz280) (Neg vuz2810)",fontsize=16,color="burlywood",shape="box"];6488[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4086 -> 6488[label="",style="solid", color="burlywood", weight=9]; 6488 -> 4096[label="",style="solid", color="burlywood", weight=3]; 6489[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4086 -> 6489[label="",style="solid", color="burlywood", weight=9]; 6489 -> 4097[label="",style="solid", color="burlywood", weight=3]; 2165[label="primQuotInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="burlywood",shape="box"];6490[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];2165 -> 6490[label="",style="solid", color="burlywood", weight=9]; 6490 -> 2181[label="",style="solid", color="burlywood", weight=3]; 6491[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];2165 -> 6491[label="",style="solid", color="burlywood", weight=9]; 6491 -> 2182[label="",style="solid", color="burlywood", weight=3]; 4087[label="gcd (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4087 -> 4098[label="",style="solid", color="black", weight=3]; 2179[label="primQuotInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="burlywood",shape="box"];6492[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];2179 -> 6492[label="",style="solid", color="burlywood", weight=9]; 6492 -> 2197[label="",style="solid", color="burlywood", weight=3]; 6493[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];2179 -> 6493[label="",style="solid", color="burlywood", weight=9]; 6493 -> 2198[label="",style="solid", color="burlywood", weight=3]; 5686[label="gcd (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5686 -> 5700[label="",style="solid", color="black", weight=3]; 2195[label="primQuotInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="burlywood",shape="box"];6494[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];2195 -> 6494[label="",style="solid", color="burlywood", weight=9]; 6494 -> 2213[label="",style="solid", color="burlywood", weight=3]; 6495[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];2195 -> 6495[label="",style="solid", color="burlywood", weight=9]; 6495 -> 2214[label="",style="solid", color="burlywood", weight=3]; 5687[label="gcd (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5687 -> 5701[label="",style="solid", color="black", weight=3]; 2211[label="primQuotInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="burlywood",shape="box"];6496[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2211 -> 6496[label="",style="solid", color="burlywood", weight=9]; 6496 -> 2227[label="",style="solid", color="burlywood", weight=3]; 6497[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2211 -> 6497[label="",style="solid", color="burlywood", weight=9]; 6497 -> 2228[label="",style="solid", color="burlywood", weight=3]; 4088[label="gcd (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4088 -> 4099[label="",style="solid", color="black", weight=3]; 2225[label="primQuotInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="burlywood",shape="box"];6498[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];2225 -> 6498[label="",style="solid", color="burlywood", weight=9]; 6498 -> 2241[label="",style="solid", color="burlywood", weight=3]; 6499[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];2225 -> 6499[label="",style="solid", color="burlywood", weight=9]; 6499 -> 2242[label="",style="solid", color="burlywood", weight=3]; 4089[label="gcd (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4089 -> 4100[label="",style="solid", color="black", weight=3]; 2239[label="primQuotInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="burlywood",shape="box"];6500[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];2239 -> 6500[label="",style="solid", color="burlywood", weight=9]; 6500 -> 2252[label="",style="solid", color="burlywood", weight=3]; 6501[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];2239 -> 6501[label="",style="solid", color="burlywood", weight=9]; 6501 -> 2253[label="",style="solid", color="burlywood", weight=3]; 5688[label="gcd (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5688 -> 5702[label="",style="solid", color="black", weight=3]; 2276[label="primQuotInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2276 -> 2282[label="",style="solid", color="black", weight=3]; 2277[label="primQuotInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2277 -> 2283[label="",style="solid", color="black", weight=3]; 5695[label="gcd3 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5695 -> 5711[label="",style="solid", color="black", weight=3]; 5696[label="primQuotInt (Pos vuz73) (Pos (Succ vuz34600))",fontsize=16,color="black",shape="box"];5696 -> 5712[label="",style="solid", color="black", weight=3]; 5697[label="primQuotInt (Pos vuz73) (Pos Zero)",fontsize=16,color="black",shape="box"];5697 -> 5713[label="",style="solid", color="black", weight=3]; 5698[label="primQuotInt (Pos vuz73) (Neg (Succ vuz34600))",fontsize=16,color="black",shape="box"];5698 -> 5714[label="",style="solid", color="black", weight=3]; 5699[label="primQuotInt (Pos vuz73) (Neg Zero)",fontsize=16,color="black",shape="box"];5699 -> 5715[label="",style="solid", color="black", weight=3]; 2167[label="primQuotInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2167 -> 2184[label="",style="solid", color="black", weight=3]; 2168[label="primQuotInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2168 -> 2185[label="",style="solid", color="black", weight=3]; 4093[label="gcd3 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4093 -> 4106[label="",style="solid", color="black", weight=3]; 4094[label="primQuotInt (Neg vuz280) (Pos (Succ vuz28100))",fontsize=16,color="black",shape="box"];4094 -> 4107[label="",style="solid", color="black", weight=3]; 4095[label="primQuotInt (Neg vuz280) (Pos Zero)",fontsize=16,color="black",shape="box"];4095 -> 4108[label="",style="solid", color="black", weight=3]; 4096[label="primQuotInt (Neg vuz280) (Neg (Succ vuz28100))",fontsize=16,color="black",shape="box"];4096 -> 4109[label="",style="solid", color="black", weight=3]; 4097[label="primQuotInt (Neg vuz280) (Neg Zero)",fontsize=16,color="black",shape="box"];4097 -> 4110[label="",style="solid", color="black", weight=3]; 2181[label="primQuotInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2181 -> 2200[label="",style="solid", color="black", weight=3]; 2182[label="primQuotInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2182 -> 2201[label="",style="solid", color="black", weight=3]; 4098[label="gcd3 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4098 -> 4111[label="",style="solid", color="black", weight=3]; 2197[label="primQuotInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2197 -> 2216[label="",style="solid", color="black", weight=3]; 2198[label="primQuotInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2198 -> 2217[label="",style="solid", color="black", weight=3]; 5700[label="gcd3 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5700 -> 5716[label="",style="solid", color="black", weight=3]; 2213[label="primQuotInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2213 -> 2230[label="",style="solid", color="black", weight=3]; 2214[label="primQuotInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2214 -> 2231[label="",style="solid", color="black", weight=3]; 5701[label="gcd3 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5701 -> 5717[label="",style="solid", color="black", weight=3]; 2227[label="primQuotInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2227 -> 2244[label="",style="solid", color="black", weight=3]; 2228[label="primQuotInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2228 -> 2245[label="",style="solid", color="black", weight=3]; 4099[label="gcd3 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4099 -> 4112[label="",style="solid", color="black", weight=3]; 2241[label="primQuotInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2241 -> 2255[label="",style="solid", color="black", weight=3]; 2242[label="primQuotInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2242 -> 2256[label="",style="solid", color="black", weight=3]; 4100[label="gcd3 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4100 -> 4113[label="",style="solid", color="black", weight=3]; 2252[label="primQuotInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2252 -> 2264[label="",style="solid", color="black", weight=3]; 2253[label="primQuotInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2253 -> 2265[label="",style="solid", color="black", weight=3]; 5702[label="gcd3 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5702 -> 5718[label="",style="solid", color="black", weight=3]; 2282 -> 2289[label="",style="dashed", color="red", weight=0]; 2282[label="primQuotInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2282 -> 2290[label="",style="dashed", color="magenta", weight=3]; 2282 -> 2291[label="",style="dashed", color="magenta", weight=3]; 2283 -> 2292[label="",style="dashed", color="red", weight=0]; 2283[label="primQuotInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2283 -> 2293[label="",style="dashed", color="magenta", weight=3]; 2283 -> 2294[label="",style="dashed", color="magenta", weight=3]; 5711[label="gcd2 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12) == fromInt (Pos Zero)) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5711 -> 5735[label="",style="solid", color="black", weight=3]; 5712[label="Pos (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5712 -> 5736[label="",style="dashed", color="green", weight=3]; 5713 -> 4108[label="",style="dashed", color="red", weight=0]; 5713[label="error []",fontsize=16,color="magenta"];5714[label="Neg (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5714 -> 5737[label="",style="dashed", color="green", weight=3]; 5715 -> 4108[label="",style="dashed", color="red", weight=0]; 5715[label="error []",fontsize=16,color="magenta"];2184 -> 2203[label="",style="dashed", color="red", weight=0]; 2184[label="primQuotInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2184 -> 2204[label="",style="dashed", color="magenta", weight=3]; 2184 -> 2205[label="",style="dashed", color="magenta", weight=3]; 2185 -> 2219[label="",style="dashed", color="red", weight=0]; 2185[label="primQuotInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2185 -> 2220[label="",style="dashed", color="magenta", weight=3]; 2185 -> 2221[label="",style="dashed", color="magenta", weight=3]; 4106[label="gcd2 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23) == fromInt (Pos Zero)) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4106 -> 4128[label="",style="solid", color="black", weight=3]; 4107[label="Neg (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4107 -> 4129[label="",style="dashed", color="green", weight=3]; 4108[label="error []",fontsize=16,color="black",shape="triangle"];4108 -> 4130[label="",style="solid", color="black", weight=3]; 4109[label="Pos (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4109 -> 4131[label="",style="dashed", color="green", weight=3]; 4110 -> 4108[label="",style="dashed", color="red", weight=0]; 4110[label="error []",fontsize=16,color="magenta"];2200 -> 2234[label="",style="dashed", color="red", weight=0]; 2200[label="primQuotInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2200 -> 2235[label="",style="dashed", color="magenta", weight=3]; 2200 -> 2236[label="",style="dashed", color="magenta", weight=3]; 2201 -> 2247[label="",style="dashed", color="red", weight=0]; 2201[label="primQuotInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2201 -> 2248[label="",style="dashed", color="magenta", weight=3]; 2201 -> 2249[label="",style="dashed", color="magenta", weight=3]; 4111[label="gcd2 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28) == fromInt (Pos Zero)) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4111 -> 4132[label="",style="solid", color="black", weight=3]; 2216 -> 2259[label="",style="dashed", color="red", weight=0]; 2216[label="primQuotInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ 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2273[label="",style="dashed", color="red", weight=0]; 2230[label="primQuotInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2230 -> 2274[label="",style="dashed", color="magenta", weight=3]; 2230 -> 2275[label="",style="dashed", color="magenta", weight=3]; 2231 -> 2279[label="",style="dashed", color="red", weight=0]; 2231[label="primQuotInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2231 -> 2280[label="",style="dashed", color="magenta", weight=3]; 2231 -> 2281[label="",style="dashed", color="magenta", weight=3]; 5717[label="gcd2 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38) == fromInt (Pos Zero)) (vuz35 * Pos (Succ vuz36) + Pos 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weight=3]; 5737 -> 5754[label="",style="dashed", color="magenta", weight=3]; 2204 -> 681[label="",style="dashed", color="red", weight=0]; 2204[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2204 -> 2325[label="",style="dashed", color="magenta", weight=3]; 2204 -> 2326[label="",style="dashed", color="magenta", weight=3]; 2205 -> 681[label="",style="dashed", color="red", weight=0]; 2205[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2205 -> 2327[label="",style="dashed", color="magenta", weight=3]; 2205 -> 2328[label="",style="dashed", color="magenta", weight=3]; 2203[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2203 -> 2329[label="",style="solid", color="black", weight=3]; 2220 -> 681[label="",style="dashed", color="red", weight=0]; 2220[label="primMulNat vuz200 (Succ 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4129[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="burlywood",shape="triangle"];6502[label="vuz280/Succ vuz2800",fontsize=10,color="white",style="solid",shape="box"];4129 -> 6502[label="",style="solid", color="burlywood", weight=9]; 6502 -> 4145[label="",style="solid", color="burlywood", weight=3]; 6503[label="vuz280/Zero",fontsize=10,color="white",style="solid",shape="box"];4129 -> 6503[label="",style="solid", color="burlywood", weight=9]; 6503 -> 4146[label="",style="solid", color="burlywood", weight=3]; 4130[label="error []",fontsize=16,color="red",shape="box"];4131 -> 4129[label="",style="dashed", color="red", weight=0]; 4131[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="magenta"];4131 -> 4147[label="",style="dashed", color="magenta", weight=3]; 2235 -> 681[label="",style="dashed", color="red", weight=0]; 2235[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2235 -> 2336[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2337[label="",style="dashed", color="magenta", weight=3]; 2236 -> 681[label="",style="dashed", color="red", weight=0]; 2236[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2236 -> 2338[label="",style="dashed", color="magenta", weight=3]; 2236 -> 2339[label="",style="dashed", color="magenta", weight=3]; 2234[label="primQuotInt (primPlusInt (Pos vuz171) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos vuz172) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2234 -> 2340[label="",style="solid", color="black", weight=3]; 2248 -> 681[label="",style="dashed", color="red", weight=0]; 2248[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2248 -> 2341[label="",style="dashed", color="magenta", weight=3]; 2248 -> 2342[label="",style="dashed", color="magenta", weight=3]; 2249 -> 681[label="",style="dashed", color="red", weight=0]; 2249[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2249 -> 2343[label="",style="dashed", color="magenta", weight=3]; 2249 -> 2344[label="",style="dashed", color="magenta", weight=3]; 2247[label="primQuotInt (primPlusInt (Neg vuz173) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg vuz174) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2247 -> 2345[label="",style="solid", color="black", weight=3]; 4132[label="gcd2 (primEqInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (fromInt (Pos Zero))) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4132 -> 4148[label="",style="solid", color="black", weight=3]; 2260 -> 681[label="",style="dashed", color="red", weight=0]; 2260[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2260 -> 2347[label="",style="dashed", color="magenta", weight=3]; 2260 -> 2348[label="",style="dashed", color="magenta", weight=3]; 2261 -> 681[label="",style="dashed", color="red", weight=0]; 2261[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2261 -> 2349[label="",style="dashed", color="magenta", weight=3]; 2261 -> 2350[label="",style="dashed", color="magenta", weight=3]; 2259[label="primQuotInt (primPlusInt (Neg vuz175) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg vuz176) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2259 -> 2351[label="",style="solid", color="black", weight=3]; 2268 -> 681[label="",style="dashed", color="red", weight=0]; 2268[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2268 -> 2352[label="",style="dashed", color="magenta", weight=3]; 2268 -> 2353[label="",style="dashed", color="magenta", weight=3]; 2269 -> 681[label="",style="dashed", color="red", weight=0]; 2269[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2269 -> 2354[label="",style="dashed", color="magenta", weight=3]; 2269 -> 2355[label="",style="dashed", color="magenta", weight=3]; 2267[label="primQuotInt (primPlusInt (Pos vuz177) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos vuz178) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2267 -> 2356[label="",style="solid", color="black", weight=3]; 5738[label="gcd2 (primEqInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (fromInt (Pos Zero))) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5738 -> 5755[label="",style="solid", color="black", weight=3]; 2274 -> 681[label="",style="dashed", color="red", weight=0]; 2274[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2274 -> 2358[label="",style="dashed", color="magenta", weight=3]; 2274 -> 2359[label="",style="dashed", color="magenta", weight=3]; 2275 -> 681[label="",style="dashed", color="red", weight=0]; 2275[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2275 -> 2360[label="",style="dashed", color="magenta", weight=3]; 2275 -> 2361[label="",style="dashed", color="magenta", weight=3]; 2273[label="primQuotInt (primPlusInt (Pos vuz179) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos vuz180) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2273 -> 2362[label="",style="solid", color="black", weight=3]; 2280 -> 681[label="",style="dashed", color="red", weight=0]; 2280[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2280 -> 2363[label="",style="dashed", color="magenta", weight=3]; 2280 -> 2364[label="",style="dashed", color="magenta", weight=3]; 2281 -> 681[label="",style="dashed", color="red", weight=0]; 2281[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2281 -> 2365[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2366[label="",style="dashed", color="magenta", weight=3]; 2279[label="primQuotInt (primPlusInt (Neg vuz181) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg vuz182) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2279 -> 2367[label="",style="solid", color="black", weight=3]; 5739[label="gcd2 (primEqInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (fromInt (Pos Zero))) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5739 -> 5756[label="",style="solid", color="black", weight=3]; 2287 -> 681[label="",style="dashed", color="red", weight=0]; 2287[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2287 -> 2369[label="",style="dashed", color="magenta", weight=3]; 2287 -> 2370[label="",style="dashed", color="magenta", weight=3]; 2288 -> 681[label="",style="dashed", color="red", weight=0]; 2288[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2288 -> 2371[label="",style="dashed", color="magenta", weight=3]; 2288 -> 2372[label="",style="dashed", color="magenta", weight=3]; 2286[label="primQuotInt (primPlusInt (Neg vuz183) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg vuz184) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2286 -> 2373[label="",style="solid", color="black", weight=3]; 2297 -> 681[label="",style="dashed", color="red", weight=0]; 2297[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2297 -> 2374[label="",style="dashed", color="magenta", weight=3]; 2297 -> 2375[label="",style="dashed", color="magenta", weight=3]; 2298 -> 681[label="",style="dashed", color="red", weight=0]; 2298[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2298 -> 2376[label="",style="dashed", color="magenta", weight=3]; 2298 -> 2377[label="",style="dashed", color="magenta", weight=3]; 2296[label="primQuotInt (primPlusInt (Pos vuz189) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos vuz190) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2296 -> 2378[label="",style="solid", color="black", weight=3]; 4133[label="gcd2 (primEqInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (fromInt (Pos Zero))) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4133 -> 4149[label="",style="solid", color="black", weight=3]; 2301 -> 681[label="",style="dashed", color="red", weight=0]; 2301[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2301 -> 2380[label="",style="dashed", color="magenta", weight=3]; 2301 -> 2381[label="",style="dashed", color="magenta", weight=3]; 2302 -> 681[label="",style="dashed", color="red", weight=0]; 2302[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2302 -> 2382[label="",style="dashed", color="magenta", weight=3]; 2302 -> 2383[label="",style="dashed", color="magenta", weight=3]; 2300[label="primQuotInt (primPlusInt (Pos vuz191) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos vuz192) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2300 -> 2384[label="",style="solid", color="black", weight=3]; 2304 -> 681[label="",style="dashed", color="red", weight=0]; 2304[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2304 -> 2385[label="",style="dashed", color="magenta", weight=3]; 2304 -> 2386[label="",style="dashed", color="magenta", weight=3]; 2305 -> 681[label="",style="dashed", color="red", weight=0]; 2305[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2305 -> 2387[label="",style="dashed", color="magenta", weight=3]; 2305 -> 2388[label="",style="dashed", color="magenta", weight=3]; 2303[label="primQuotInt (primPlusInt (Neg vuz193) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg vuz194) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2303 -> 2389[label="",style="solid", color="black", weight=3]; 4134[label="gcd2 (primEqInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (fromInt (Pos Zero))) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4134 -> 4150[label="",style="solid", color="black", weight=3]; 2308 -> 681[label="",style="dashed", color="red", weight=0]; 2308[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2308 -> 2391[label="",style="dashed", color="magenta", weight=3]; 2308 -> 2392[label="",style="dashed", color="magenta", weight=3]; 2309 -> 681[label="",style="dashed", color="red", weight=0]; 2309[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2309 -> 2393[label="",style="dashed", color="magenta", weight=3]; 2309 -> 2394[label="",style="dashed", color="magenta", weight=3]; 2307[label="primQuotInt (primPlusInt (Neg vuz195) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg vuz196) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2307 -> 2395[label="",style="solid", color="black", weight=3]; 2311 -> 681[label="",style="dashed", color="red", weight=0]; 2311[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2311 -> 2396[label="",style="dashed", color="magenta", weight=3]; 2311 -> 2397[label="",style="dashed", color="magenta", weight=3]; 2312 -> 681[label="",style="dashed", color="red", weight=0]; 2312[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2312 -> 2398[label="",style="dashed", color="magenta", weight=3]; 2312 -> 2399[label="",style="dashed", color="magenta", weight=3]; 2310[label="primQuotInt (primPlusInt (Pos vuz197) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos vuz198) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2310 -> 2400[label="",style="solid", color="black", weight=3]; 5740[label="gcd2 (primEqInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (fromInt (Pos Zero))) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5740 -> 5757[label="",style="solid", color="black", weight=3]; 2314[label="vuz10",fontsize=16,color="green",shape="box"];2315[label="vuz90",fontsize=16,color="green",shape="box"];2316[label="vuz10",fontsize=16,color="green",shape="box"];2317[label="vuz90",fontsize=16,color="green",shape="box"];2318[label="primQuotInt (primPlusInt (Pos vuz185) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2318 -> 2402[label="",style="solid", color="black", weight=3]; 2319[label="vuz10",fontsize=16,color="green",shape="box"];2320[label="vuz90",fontsize=16,color="green",shape="box"];2321[label="vuz10",fontsize=16,color="green",shape="box"];2322[label="vuz90",fontsize=16,color="green",shape="box"];2323[label="primQuotInt (primPlusInt (Neg vuz187) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2323 -> 2403[label="",style="solid", color="black", weight=3]; 5750[label="gcd2 (primEqInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5750 -> 5769[label="",style="solid", color="black", weight=3]; 5751[label="vuz34600",fontsize=16,color="green",shape="box"];5752[label="vuz73",fontsize=16,color="green",shape="box"];5753[label="vuz34600",fontsize=16,color="green",shape="box"];5754[label="vuz73",fontsize=16,color="green",shape="box"];2325[label="vuz21",fontsize=16,color="green",shape="box"];2326[label="vuz200",fontsize=16,color="green",shape="box"];2327[label="vuz21",fontsize=16,color="green",shape="box"];2328[label="vuz200",fontsize=16,color="green",shape="box"];2329[label="primQuotInt (primPlusInt (Neg vuz167) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2329 -> 2406[label="",style="solid", color="black", weight=3]; 2330[label="vuz21",fontsize=16,color="green",shape="box"];2331[label="vuz200",fontsize=16,color="green",shape="box"];2332[label="vuz21",fontsize=16,color="green",shape="box"];2333[label="vuz200",fontsize=16,color="green",shape="box"];2334[label="primQuotInt (primPlusInt (Pos vuz169) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2334 -> 2407[label="",style="solid", color="black", weight=3]; 4144[label="gcd2 (primEqInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4144 -> 4160[label="",style="solid", color="black", weight=3]; 4145[label="primDivNatS (Succ vuz2800) (Succ vuz28100)",fontsize=16,color="black",shape="box"];4145 -> 4161[label="",style="solid", color="black", weight=3]; 4146[label="primDivNatS Zero (Succ vuz28100)",fontsize=16,color="black",shape="box"];4146 -> 4162[label="",style="solid", color="black", weight=3]; 4147[label="vuz28100",fontsize=16,color="green",shape="box"];2336[label="vuz26",fontsize=16,color="green",shape="box"];2337[label="vuz250",fontsize=16,color="green",shape="box"];2338[label="vuz26",fontsize=16,color="green",shape="box"];2339[label="vuz250",fontsize=16,color="green",shape="box"];2340[label="primQuotInt (primPlusInt (Pos vuz171) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2340 -> 2410[label="",style="solid", color="black", weight=3]; 2341[label="vuz26",fontsize=16,color="green",shape="box"];2342[label="vuz250",fontsize=16,color="green",shape="box"];2343[label="vuz26",fontsize=16,color="green",shape="box"];2344[label="vuz250",fontsize=16,color="green",shape="box"];2345[label="primQuotInt (primPlusInt (Neg vuz173) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2345 -> 2411[label="",style="solid", color="black", weight=3]; 4148[label="gcd2 (primEqInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4148 -> 4163[label="",style="solid", color="black", weight=3]; 2347[label="vuz31",fontsize=16,color="green",shape="box"];2348[label="vuz300",fontsize=16,color="green",shape="box"];2349[label="vuz31",fontsize=16,color="green",shape="box"];2350[label="vuz300",fontsize=16,color="green",shape="box"];2351[label="primQuotInt (primPlusInt (Neg vuz175) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2351 -> 2414[label="",style="solid", color="black", weight=3]; 2352[label="vuz31",fontsize=16,color="green",shape="box"];2353[label="vuz300",fontsize=16,color="green",shape="box"];2354[label="vuz31",fontsize=16,color="green",shape="box"];2355[label="vuz300",fontsize=16,color="green",shape="box"];2356[label="primQuotInt (primPlusInt (Pos vuz177) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2356 -> 2415[label="",style="solid", color="black", weight=3]; 5755[label="gcd2 (primEqInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5755 -> 5770[label="",style="solid", color="black", weight=3]; 2358[label="vuz36",fontsize=16,color="green",shape="box"];2359[label="vuz350",fontsize=16,color="green",shape="box"];2360[label="vuz36",fontsize=16,color="green",shape="box"];2361[label="vuz350",fontsize=16,color="green",shape="box"];2362[label="primQuotInt (primPlusInt (Pos vuz179) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2362 -> 2418[label="",style="solid", color="black", weight=3]; 2363[label="vuz36",fontsize=16,color="green",shape="box"];2364[label="vuz350",fontsize=16,color="green",shape="box"];2365[label="vuz36",fontsize=16,color="green",shape="box"];2366[label="vuz350",fontsize=16,color="green",shape="box"];2367[label="primQuotInt (primPlusInt (Neg vuz181) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2367 -> 2419[label="",style="solid", color="black", weight=3]; 5756[label="gcd2 (primEqInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5756 -> 5771[label="",style="solid", color="black", weight=3]; 2369[label="vuz41",fontsize=16,color="green",shape="box"];2370[label="vuz400",fontsize=16,color="green",shape="box"];2371[label="vuz41",fontsize=16,color="green",shape="box"];2372[label="vuz400",fontsize=16,color="green",shape="box"];2373[label="primQuotInt (primPlusInt (Neg vuz183) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2373 -> 2422[label="",style="solid", color="black", weight=3]; 2374[label="vuz41",fontsize=16,color="green",shape="box"];2375[label="vuz400",fontsize=16,color="green",shape="box"];2376[label="vuz41",fontsize=16,color="green",shape="box"];2377[label="vuz400",fontsize=16,color="green",shape="box"];2378[label="primQuotInt (primPlusInt (Pos vuz189) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2378 -> 2423[label="",style="solid", color="black", weight=3]; 4149[label="gcd2 (primEqInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4149 -> 4164[label="",style="solid", color="black", weight=3]; 2380[label="vuz46",fontsize=16,color="green",shape="box"];2381[label="vuz450",fontsize=16,color="green",shape="box"];2382[label="vuz46",fontsize=16,color="green",shape="box"];2383[label="vuz450",fontsize=16,color="green",shape="box"];2384[label="primQuotInt (primPlusInt (Pos vuz191) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2384 -> 2426[label="",style="solid", color="black", weight=3]; 2385[label="vuz46",fontsize=16,color="green",shape="box"];2386[label="vuz450",fontsize=16,color="green",shape="box"];2387[label="vuz46",fontsize=16,color="green",shape="box"];2388[label="vuz450",fontsize=16,color="green",shape="box"];2389[label="primQuotInt (primPlusInt (Neg vuz193) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2389 -> 2427[label="",style="solid", color="black", weight=3]; 4150[label="gcd2 (primEqInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4150 -> 4165[label="",style="solid", color="black", weight=3]; 2391[label="vuz51",fontsize=16,color="green",shape="box"];2392[label="vuz500",fontsize=16,color="green",shape="box"];2393[label="vuz51",fontsize=16,color="green",shape="box"];2394[label="vuz500",fontsize=16,color="green",shape="box"];2395[label="primQuotInt (primPlusInt (Neg vuz195) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2395 -> 2430[label="",style="solid", color="black", weight=3]; 2396[label="vuz51",fontsize=16,color="green",shape="box"];2397[label="vuz500",fontsize=16,color="green",shape="box"];2398[label="vuz51",fontsize=16,color="green",shape="box"];2399[label="vuz500",fontsize=16,color="green",shape="box"];2400[label="primQuotInt (primPlusInt (Pos vuz197) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2400 -> 2431[label="",style="solid", color="black", weight=3]; 5757[label="gcd2 (primEqInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5757 -> 5772[label="",style="solid", color="black", weight=3]; 2402 -> 2434[label="",style="dashed", color="red", weight=0]; 2402[label="primQuotInt (primPlusInt (Pos vuz185) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2402 -> 2435[label="",style="dashed", color="magenta", weight=3]; 2402 -> 2436[label="",style="dashed", color="magenta", weight=3]; 2403 -> 2442[label="",style="dashed", color="red", weight=0]; 2403[label="primQuotInt (primPlusInt (Neg vuz187) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2403 -> 2443[label="",style="dashed", color="magenta", weight=3]; 2403 -> 2444[label="",style="dashed", color="magenta", weight=3]; 5769[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6504[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6504[label="",style="solid", color="burlywood", weight=9]; 6504 -> 5784[label="",style="solid", color="burlywood", weight=3]; 6505[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6505[label="",style="solid", color="burlywood", weight=9]; 6505 -> 5785[label="",style="solid", color="burlywood", weight=3]; 2406 -> 2452[label="",style="dashed", color="red", weight=0]; 2406[label="primQuotInt (primPlusInt (Neg vuz167) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2406 -> 2453[label="",style="dashed", color="magenta", weight=3]; 2406 -> 2454[label="",style="dashed", color="magenta", weight=3]; 2407 -> 2460[label="",style="dashed", color="red", weight=0]; 2407[label="primQuotInt (primPlusInt (Pos vuz169) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2407 -> 2461[label="",style="dashed", color="magenta", weight=3]; 2407 -> 2462[label="",style="dashed", color="magenta", weight=3]; 4160[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6506[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];4160 -> 6506[label="",style="solid", color="burlywood", weight=9]; 6506 -> 4175[label="",style="solid", color="burlywood", weight=3]; 6507[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];4160 -> 6507[label="",style="solid", color="burlywood", weight=9]; 6507 -> 4176[label="",style="solid", color="burlywood", weight=3]; 4161[label="primDivNatS0 vuz2800 vuz28100 (primGEqNatS vuz2800 vuz28100)",fontsize=16,color="burlywood",shape="box"];6508[label="vuz2800/Succ vuz28000",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6508[label="",style="solid", color="burlywood", weight=9]; 6508 -> 4177[label="",style="solid", color="burlywood", weight=3]; 6509[label="vuz2800/Zero",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6509[label="",style="solid", color="burlywood", weight=9]; 6509 -> 4178[label="",style="solid", color="burlywood", weight=3]; 4162[label="Zero",fontsize=16,color="green",shape="box"];2410 -> 2470[label="",style="dashed", color="red", weight=0]; 2410[label="primQuotInt (primPlusInt (Pos vuz171) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2410 -> 2471[label="",style="dashed", color="magenta", weight=3]; 2410 -> 2472[label="",style="dashed", color="magenta", weight=3]; 2411 -> 2478[label="",style="dashed", color="red", weight=0]; 2411[label="primQuotInt (primPlusInt (Neg vuz173) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2411 -> 2479[label="",style="dashed", color="magenta", weight=3]; 2411 -> 2480[label="",style="dashed", color="magenta", weight=3]; 4163[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6510[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6510[label="",style="solid", color="burlywood", weight=9]; 6510 -> 4179[label="",style="solid", color="burlywood", weight=3]; 6511[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6511[label="",style="solid", color="burlywood", weight=9]; 6511 -> 4180[label="",style="solid", color="burlywood", weight=3]; 2414 -> 2488[label="",style="dashed", color="red", weight=0]; 2414[label="primQuotInt (primPlusInt (Neg vuz175) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2414 -> 2489[label="",style="dashed", color="magenta", weight=3]; 2414 -> 2490[label="",style="dashed", color="magenta", weight=3]; 2415 -> 2496[label="",style="dashed", color="red", weight=0]; 2415[label="primQuotInt (primPlusInt (Pos vuz177) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2415 -> 2497[label="",style="dashed", color="magenta", weight=3]; 2415 -> 2498[label="",style="dashed", color="magenta", weight=3]; 5770[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6512[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6512[label="",style="solid", color="burlywood", weight=9]; 6512 -> 5786[label="",style="solid", color="burlywood", weight=3]; 6513[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6513[label="",style="solid", color="burlywood", weight=9]; 6513 -> 5787[label="",style="solid", color="burlywood", weight=3]; 2418 -> 2496[label="",style="dashed", color="red", weight=0]; 2418[label="primQuotInt (primPlusInt (Pos vuz179) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2418 -> 2499[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2500[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2501[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2502[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2503[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2488[label="",style="dashed", color="red", weight=0]; 2419[label="primQuotInt (primPlusInt (Neg vuz181) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2419 -> 2491[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2492[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2493[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2494[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2495[label="",style="dashed", color="magenta", weight=3]; 5771[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="burlywood",shape="box"];6514[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];5771 -> 6514[label="",style="solid", color="burlywood", weight=9]; 6514 -> 5788[label="",style="solid", color="burlywood", weight=3]; 6515[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];5771 -> 6515[label="",style="solid", color="burlywood", weight=9]; 6515 -> 5789[label="",style="solid", color="burlywood", weight=3]; 2422 -> 2478[label="",style="dashed", color="red", weight=0]; 2422[label="primQuotInt (primPlusInt (Neg vuz183) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2422 -> 2481[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2482[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2483[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2484[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2485[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2470[label="",style="dashed", color="red", weight=0]; 2423[label="primQuotInt (primPlusInt (Pos vuz189) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2423 -> 2473[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2474[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2475[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2476[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2477[label="",style="dashed", color="magenta", weight=3]; 4164[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="burlywood",shape="box"];6516[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6516[label="",style="solid", color="burlywood", weight=9]; 6516 -> 4181[label="",style="solid", color="burlywood", weight=3]; 6517[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6517[label="",style="solid", color="burlywood", weight=9]; 6517 -> 4182[label="",style="solid", color="burlywood", weight=3]; 2426 -> 2460[label="",style="dashed", color="red", weight=0]; 2426[label="primQuotInt (primPlusInt (Pos vuz191) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2426 -> 2463[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2464[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2465[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2466[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2467[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2452[label="",style="dashed", color="red", weight=0]; 2427[label="primQuotInt (primPlusInt (Neg vuz193) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2427 -> 2455[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2456[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2457[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2458[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2459[label="",style="dashed", color="magenta", weight=3]; 4165[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="burlywood",shape="box"];6518[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6518[label="",style="solid", color="burlywood", weight=9]; 6518 -> 4183[label="",style="solid", color="burlywood", weight=3]; 6519[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6519[label="",style="solid", color="burlywood", weight=9]; 6519 -> 4184[label="",style="solid", color="burlywood", weight=3]; 2430 -> 2442[label="",style="dashed", color="red", weight=0]; 2430[label="primQuotInt (primPlusInt (Neg vuz195) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2430 -> 2445[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2446[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2447[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2448[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2449[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2434[label="",style="dashed", color="red", weight=0]; 2431[label="primQuotInt (primPlusInt (Pos vuz197) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2431 -> 2437[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2438[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2439[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2440[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2441[label="",style="dashed", color="magenta", weight=3]; 5772[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="burlywood",shape="box"];6520[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6520[label="",style="solid", color="burlywood", weight=9]; 6520 -> 5790[label="",style="solid", color="burlywood", weight=3]; 6521[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6521[label="",style="solid", color="burlywood", weight=9]; 6521 -> 5791[label="",style="solid", color="burlywood", weight=3]; 2435 -> 681[label="",style="dashed", color="red", weight=0]; 2435[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2435 -> 2514[label="",style="dashed", color="magenta", weight=3]; 2435 -> 2515[label="",style="dashed", color="magenta", weight=3]; 2436 -> 681[label="",style="dashed", color="red", weight=0]; 2436[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2436 -> 2516[label="",style="dashed", color="magenta", weight=3]; 2436 -> 2517[label="",style="dashed", color="magenta", weight=3]; 2434[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz199)) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz200)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2434 -> 2518[label="",style="solid", color="black", weight=3]; 2443 -> 681[label="",style="dashed", color="red", weight=0]; 2443[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2443 -> 2519[label="",style="dashed", color="magenta", weight=3]; 2443 -> 2520[label="",style="dashed", color="magenta", weight=3]; 2444 -> 681[label="",style="dashed", color="red", weight=0]; 2444[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2444 -> 2521[label="",style="dashed", color="magenta", weight=3]; 2444 -> 2522[label="",style="dashed", color="magenta", weight=3]; 2442[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz201)) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz202)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2442 -> 2523[label="",style="solid", color="black", weight=3]; 5784[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5784 -> 5806[label="",style="solid", color="black", weight=3]; 5785[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5785 -> 5807[label="",style="solid", color="black", weight=3]; 2453 -> 681[label="",style="dashed", color="red", weight=0]; 2453[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2453 -> 2530[label="",style="dashed", color="magenta", weight=3]; 2453 -> 2531[label="",style="dashed", color="magenta", weight=3]; 2454 -> 681[label="",style="dashed", color="red", weight=0]; 2454[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2454 -> 2532[label="",style="dashed", color="magenta", weight=3]; 2454 -> 2533[label="",style="dashed", color="magenta", weight=3]; 2452[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz203)) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz204)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2452 -> 2534[label="",style="solid", color="black", weight=3]; 2461 -> 681[label="",style="dashed", color="red", weight=0]; 2461[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2461 -> 2535[label="",style="dashed", color="magenta", weight=3]; 2461 -> 2536[label="",style="dashed", color="magenta", weight=3]; 2462 -> 681[label="",style="dashed", color="red", weight=0]; 2462[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2462 -> 2537[label="",style="dashed", color="magenta", weight=3]; 2462 -> 2538[label="",style="dashed", color="magenta", weight=3]; 2460[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz205)) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz206)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2460 -> 2539[label="",style="solid", color="black", weight=3]; 4175[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4175 -> 4194[label="",style="solid", color="black", weight=3]; 4176[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4176 -> 4195[label="",style="solid", color="black", weight=3]; 4177[label="primDivNatS0 (Succ vuz28000) vuz28100 (primGEqNatS (Succ vuz28000) vuz28100)",fontsize=16,color="burlywood",shape="box"];6522[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4177 -> 6522[label="",style="solid", color="burlywood", weight=9]; 6522 -> 4196[label="",style="solid", color="burlywood", weight=3]; 6523[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4177 -> 6523[label="",style="solid", color="burlywood", weight=9]; 6523 -> 4197[label="",style="solid", color="burlywood", weight=3]; 4178[label="primDivNatS0 Zero vuz28100 (primGEqNatS Zero vuz28100)",fontsize=16,color="burlywood",shape="box"];6524[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4178 -> 6524[label="",style="solid", color="burlywood", weight=9]; 6524 -> 4198[label="",style="solid", color="burlywood", weight=3]; 6525[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4178 -> 6525[label="",style="solid", color="burlywood", weight=9]; 6525 -> 4199[label="",style="solid", color="burlywood", weight=3]; 2471 -> 681[label="",style="dashed", color="red", weight=0]; 2471[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2471 -> 2546[label="",style="dashed", color="magenta", weight=3]; 2471 -> 2547[label="",style="dashed", color="magenta", weight=3]; 2472 -> 681[label="",style="dashed", color="red", weight=0]; 2472[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2472 -> 2548[label="",style="dashed", color="magenta", weight=3]; 2472 -> 2549[label="",style="dashed", color="magenta", weight=3]; 2470[label="primQuotInt (primPlusInt (Pos vuz171) (Pos vuz207)) (reduce2D (primPlusInt (Pos vuz172) (Pos vuz208)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2470 -> 2550[label="",style="solid", color="black", weight=3]; 2479 -> 681[label="",style="dashed", color="red", weight=0]; 2479[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2479 -> 2551[label="",style="dashed", color="magenta", weight=3]; 2479 -> 2552[label="",style="dashed", color="magenta", weight=3]; 2480 -> 681[label="",style="dashed", color="red", weight=0]; 2480[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2480 -> 2553[label="",style="dashed", color="magenta", weight=3]; 2480 -> 2554[label="",style="dashed", color="magenta", weight=3]; 2478[label="primQuotInt (primPlusInt (Neg vuz173) (Pos vuz209)) (reduce2D (primPlusInt (Neg vuz174) (Pos vuz210)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2478 -> 2555[label="",style="solid", color="black", weight=3]; 4179[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4179 -> 4200[label="",style="solid", color="black", weight=3]; 4180[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4180 -> 4201[label="",style="solid", color="black", weight=3]; 2489 -> 681[label="",style="dashed", color="red", weight=0]; 2489[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2489 -> 2562[label="",style="dashed", color="magenta", weight=3]; 2489 -> 2563[label="",style="dashed", color="magenta", weight=3]; 2490 -> 681[label="",style="dashed", color="red", weight=0]; 2490[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2490 -> 2564[label="",style="dashed", color="magenta", weight=3]; 2490 -> 2565[label="",style="dashed", color="magenta", weight=3]; 2488[label="primQuotInt (primPlusInt (Neg vuz175) (Pos vuz211)) (reduce2D (primPlusInt (Neg vuz176) (Pos vuz212)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2488 -> 2566[label="",style="solid", color="black", weight=3]; 2497 -> 681[label="",style="dashed", color="red", weight=0]; 2497[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2497 -> 2567[label="",style="dashed", color="magenta", weight=3]; 2497 -> 2568[label="",style="dashed", color="magenta", weight=3]; 2498 -> 681[label="",style="dashed", color="red", weight=0]; 2498[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2498 -> 2569[label="",style="dashed", color="magenta", weight=3]; 2498 -> 2570[label="",style="dashed", color="magenta", weight=3]; 2496[label="primQuotInt (primPlusInt (Pos vuz177) (Pos vuz213)) (reduce2D (primPlusInt (Pos vuz178) (Pos vuz214)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2496 -> 2571[label="",style="solid", color="black", weight=3]; 5786[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5786 -> 5808[label="",style="solid", color="black", weight=3]; 5787[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5787 -> 5809[label="",style="solid", color="black", weight=3]; 2499 -> 681[label="",style="dashed", color="red", weight=0]; 2499[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2499 -> 2578[label="",style="dashed", color="magenta", weight=3]; 2499 -> 2579[label="",style="dashed", color="magenta", weight=3]; 2500[label="vuz179",fontsize=16,color="green",shape="box"];2501[label="vuz77",fontsize=16,color="green",shape="box"];2502[label="vuz180",fontsize=16,color="green",shape="box"];2503 -> 681[label="",style="dashed", color="red", weight=0]; 2503[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2503 -> 2580[label="",style="dashed", color="magenta", weight=3]; 2503 -> 2581[label="",style="dashed", color="magenta", weight=3]; 2491 -> 681[label="",style="dashed", color="red", weight=0]; 2491[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2491 -> 2582[label="",style="dashed", color="magenta", weight=3]; 2491 -> 2583[label="",style="dashed", color="magenta", weight=3]; 2492[label="vuz181",fontsize=16,color="green",shape="box"];2493[label="vuz77",fontsize=16,color="green",shape="box"];2494 -> 681[label="",style="dashed", color="red", weight=0]; 2494[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2494 -> 2584[label="",style="dashed", color="magenta", weight=3]; 2494 -> 2585[label="",style="dashed", color="magenta", weight=3]; 2495[label="vuz182",fontsize=16,color="green",shape="box"];5788[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5788 -> 5810[label="",style="solid", color="black", weight=3]; 5789[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5789 -> 5811[label="",style="solid", color="black", weight=3]; 2481 -> 681[label="",style="dashed", color="red", weight=0]; 2481[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2481 -> 2592[label="",style="dashed", color="magenta", weight=3]; 2481 -> 2593[label="",style="dashed", color="magenta", weight=3]; 2482 -> 681[label="",style="dashed", color="red", weight=0]; 2482[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2482 -> 2594[label="",style="dashed", color="magenta", weight=3]; 2482 -> 2595[label="",style="dashed", color="magenta", weight=3]; 2483[label="vuz92",fontsize=16,color="green",shape="box"];2484[label="vuz184",fontsize=16,color="green",shape="box"];2485[label="vuz183",fontsize=16,color="green",shape="box"];2473 -> 681[label="",style="dashed", color="red", weight=0]; 2473[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2473 -> 2596[label="",style="dashed", color="magenta", weight=3]; 2473 -> 2597[label="",style="dashed", color="magenta", weight=3]; 2474[label="vuz190",fontsize=16,color="green",shape="box"];2475 -> 681[label="",style="dashed", color="red", weight=0]; 2475[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2475 -> 2598[label="",style="dashed", color="magenta", weight=3]; 2475 -> 2599[label="",style="dashed", color="magenta", weight=3]; 2476[label="vuz189",fontsize=16,color="green",shape="box"];2477[label="vuz92",fontsize=16,color="green",shape="box"];4181[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4181 -> 4202[label="",style="solid", color="black", weight=3]; 4182[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4182 -> 4203[label="",style="solid", color="black", weight=3]; 2463[label="vuz107",fontsize=16,color="green",shape="box"];2464[label="vuz192",fontsize=16,color="green",shape="box"];2465[label="vuz191",fontsize=16,color="green",shape="box"];2466 -> 681[label="",style="dashed", color="red", weight=0]; 2466[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2466 -> 2606[label="",style="dashed", color="magenta", weight=3]; 2466 -> 2607[label="",style="dashed", color="magenta", weight=3]; 2467 -> 681[label="",style="dashed", color="red", weight=0]; 2467[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2467 -> 2608[label="",style="dashed", color="magenta", weight=3]; 2467 -> 2609[label="",style="dashed", color="magenta", weight=3]; 2455[label="vuz107",fontsize=16,color="green",shape="box"];2456[label="vuz194",fontsize=16,color="green",shape="box"];2457 -> 681[label="",style="dashed", color="red", weight=0]; 2457[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2457 -> 2610[label="",style="dashed", color="magenta", weight=3]; 2457 -> 2611[label="",style="dashed", color="magenta", weight=3]; 2458[label="vuz193",fontsize=16,color="green",shape="box"];2459 -> 681[label="",style="dashed", color="red", weight=0]; 2459[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2459 -> 2612[label="",style="dashed", color="magenta", weight=3]; 2459 -> 2613[label="",style="dashed", color="magenta", weight=3]; 4183[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4183 -> 4204[label="",style="solid", color="black", weight=3]; 4184[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4184 -> 4205[label="",style="solid", color="black", weight=3]; 2445[label="vuz195",fontsize=16,color="green",shape="box"];2446[label="vuz196",fontsize=16,color="green",shape="box"];2447 -> 681[label="",style="dashed", color="red", weight=0]; 2447[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2447 -> 2620[label="",style="dashed", color="magenta", weight=3]; 2447 -> 2621[label="",style="dashed", color="magenta", weight=3]; 2448 -> 681[label="",style="dashed", color="red", weight=0]; 2448[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2448 -> 2622[label="",style="dashed", color="magenta", weight=3]; 2448 -> 2623[label="",style="dashed", color="magenta", weight=3]; 2449[label="vuz122",fontsize=16,color="green",shape="box"];2437 -> 681[label="",style="dashed", color="red", weight=0]; 2437[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2437 -> 2624[label="",style="dashed", color="magenta", weight=3]; 2437 -> 2625[label="",style="dashed", color="magenta", weight=3]; 2438 -> 681[label="",style="dashed", color="red", weight=0]; 2438[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2438 -> 2626[label="",style="dashed", color="magenta", weight=3]; 2438 -> 2627[label="",style="dashed", color="magenta", weight=3]; 2439[label="vuz197",fontsize=16,color="green",shape="box"];2440[label="vuz198",fontsize=16,color="green",shape="box"];2441[label="vuz122",fontsize=16,color="green",shape="box"];5790[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5790 -> 5812[label="",style="solid", color="black", weight=3]; 5791[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5791 -> 5813[label="",style="solid", color="black", weight=3]; 2514[label="vuz12",fontsize=16,color="green",shape="box"];2515[label="vuz11",fontsize=16,color="green",shape="box"];2516[label="vuz12",fontsize=16,color="green",shape="box"];2517[label="vuz11",fontsize=16,color="green",shape="box"];2518[label="primQuotInt (primMinusNat vuz185 vuz199) (reduce2D (primMinusNat vuz185 vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="triangle"];6526[label="vuz185/Succ vuz1850",fontsize=10,color="white",style="solid",shape="box"];2518 -> 6526[label="",style="solid", color="burlywood", weight=9]; 6526 -> 2634[label="",style="solid", color="burlywood", weight=3]; 6527[label="vuz185/Zero",fontsize=10,color="white",style="solid",shape="box"];2518 -> 6527[label="",style="solid", color="burlywood", weight=9]; 6527 -> 2635[label="",style="solid", color="burlywood", weight=3]; 2519[label="vuz12",fontsize=16,color="green",shape="box"];2520[label="vuz11",fontsize=16,color="green",shape="box"];2521[label="vuz12",fontsize=16,color="green",shape="box"];2522[label="vuz11",fontsize=16,color="green",shape="box"];2523 -> 3509[label="",style="dashed", color="red", weight=0]; 2523[label="primQuotInt (Neg (primPlusNat vuz187 vuz201)) (reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144))",fontsize=16,color="magenta"];2523 -> 3582[label="",style="dashed", color="magenta", weight=3]; 2523 -> 3583[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5826[label="",style="dashed", color="red", weight=0]; 5806[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5806 -> 5827[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5828[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5829[label="",style="dashed", color="red", weight=0]; 5807[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5807 -> 5830[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5831[label="",style="dashed", color="magenta", weight=3]; 2530[label="vuz23",fontsize=16,color="green",shape="box"];2531[label="vuz22",fontsize=16,color="green",shape="box"];2532[label="vuz23",fontsize=16,color="green",shape="box"];2533[label="vuz22",fontsize=16,color="green",shape="box"];2534 -> 3509[label="",style="dashed", color="red", weight=0]; 2534[label="primQuotInt (Neg (primPlusNat vuz167 vuz203)) (reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68))",fontsize=16,color="magenta"];2534 -> 3584[label="",style="dashed", color="magenta", weight=3]; 2534 -> 3585[label="",style="dashed", color="magenta", weight=3]; 2535[label="vuz23",fontsize=16,color="green",shape="box"];2536[label="vuz22",fontsize=16,color="green",shape="box"];2537[label="vuz23",fontsize=16,color="green",shape="box"];2538[label="vuz22",fontsize=16,color="green",shape="box"];2539[label="primQuotInt (primMinusNat vuz169 vuz205) (reduce2D (primMinusNat vuz169 vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="triangle"];6528[label="vuz169/Succ vuz1690",fontsize=10,color="white",style="solid",shape="box"];2539 -> 6528[label="",style="solid", color="burlywood", weight=9]; 6528 -> 2652[label="",style="solid", color="burlywood", weight=3]; 6529[label="vuz169/Zero",fontsize=10,color="white",style="solid",shape="box"];2539 -> 6529[label="",style="solid", color="burlywood", weight=9]; 6529 -> 2653[label="",style="solid", color="burlywood", weight=3]; 4194 -> 4216[label="",style="dashed", color="red", weight=0]; 4194[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4194 -> 4217[label="",style="dashed", color="magenta", weight=3]; 4194 -> 4218[label="",style="dashed", color="magenta", weight=3]; 4195 -> 4219[label="",style="dashed", color="red", weight=0]; 4195[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4195 -> 4220[label="",style="dashed", color="magenta", weight=3]; 4195 -> 4221[label="",style="dashed", color="magenta", weight=3]; 4196[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS (Succ vuz28000) (Succ vuz281000))",fontsize=16,color="black",shape="box"];4196 -> 4222[label="",style="solid", color="black", weight=3]; 4197[label="primDivNatS0 (Succ vuz28000) Zero (primGEqNatS (Succ vuz28000) Zero)",fontsize=16,color="black",shape="box"];4197 -> 4223[label="",style="solid", color="black", weight=3]; 4198[label="primDivNatS0 Zero (Succ vuz281000) (primGEqNatS Zero (Succ vuz281000))",fontsize=16,color="black",shape="box"];4198 -> 4224[label="",style="solid", color="black", weight=3]; 4199[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4199 -> 4225[label="",style="solid", color="black", weight=3]; 2546[label="vuz28",fontsize=16,color="green",shape="box"];2547[label="vuz27",fontsize=16,color="green",shape="box"];2548[label="vuz28",fontsize=16,color="green",shape="box"];2549[label="vuz27",fontsize=16,color="green",shape="box"];2550 -> 5046[label="",style="dashed", color="red", weight=0]; 2550[label="primQuotInt (Pos (primPlusNat vuz171 vuz207)) (reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71))",fontsize=16,color="magenta"];2550 -> 5114[label="",style="dashed", color="magenta", weight=3]; 2550 -> 5115[label="",style="dashed", color="magenta", weight=3]; 2551[label="vuz28",fontsize=16,color="green",shape="box"];2552[label="vuz27",fontsize=16,color="green",shape="box"];2553[label="vuz28",fontsize=16,color="green",shape="box"];2554[label="vuz27",fontsize=16,color="green",shape="box"];2555 -> 2539[label="",style="dashed", color="red", weight=0]; 2555[label="primQuotInt (primMinusNat vuz209 vuz173) (reduce2D (primMinusNat vuz209 vuz173) (Neg vuz71))",fontsize=16,color="magenta"];2555 -> 2667[label="",style="dashed", color="magenta", weight=3]; 2555 -> 2668[label="",style="dashed", color="magenta", weight=3]; 2555 -> 2669[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4226[label="",style="dashed", color="red", weight=0]; 4200[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4200 -> 4227[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4228[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4229[label="",style="dashed", color="red", weight=0]; 4201[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4201 -> 4230[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4231[label="",style="dashed", color="magenta", weight=3]; 2562[label="vuz33",fontsize=16,color="green",shape="box"];2563[label="vuz32",fontsize=16,color="green",shape="box"];2564[label="vuz33",fontsize=16,color="green",shape="box"];2565[label="vuz32",fontsize=16,color="green",shape="box"];2566 -> 2518[label="",style="dashed", color="red", weight=0]; 2566[label="primQuotInt (primMinusNat vuz211 vuz175) (reduce2D (primMinusNat vuz211 vuz175) (Pos vuz74))",fontsize=16,color="magenta"];2566 -> 2680[label="",style="dashed", color="magenta", weight=3]; 2566 -> 2681[label="",style="dashed", color="magenta", weight=3]; 2566 -> 2682[label="",style="dashed", color="magenta", weight=3]; 2567[label="vuz33",fontsize=16,color="green",shape="box"];2568[label="vuz32",fontsize=16,color="green",shape="box"];2569[label="vuz33",fontsize=16,color="green",shape="box"];2570[label="vuz32",fontsize=16,color="green",shape="box"];2571 -> 5046[label="",style="dashed", color="red", weight=0]; 2571[label="primQuotInt (Pos (primPlusNat vuz177 vuz213)) (reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74))",fontsize=16,color="magenta"];2571 -> 5116[label="",style="dashed", color="magenta", weight=3]; 2571 -> 5117[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5832[label="",style="dashed", color="red", weight=0]; 5808[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5808 -> 5833[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5834[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5835[label="",style="dashed", color="red", weight=0]; 5809[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5809 -> 5836[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5837[label="",style="dashed", color="magenta", weight=3]; 2578[label="vuz38",fontsize=16,color="green",shape="box"];2579[label="vuz37",fontsize=16,color="green",shape="box"];2580[label="vuz38",fontsize=16,color="green",shape="box"];2581[label="vuz37",fontsize=16,color="green",shape="box"];2582[label="vuz38",fontsize=16,color="green",shape="box"];2583[label="vuz37",fontsize=16,color="green",shape="box"];2584[label="vuz38",fontsize=16,color="green",shape="box"];2585[label="vuz37",fontsize=16,color="green",shape="box"];5810 -> 5838[label="",style="dashed", color="red", weight=0]; 5810[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5810 -> 5839[label="",style="dashed", color="magenta", weight=3]; 5810 -> 5840[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5841[label="",style="dashed", color="red", weight=0]; 5811[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5811 -> 5842[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5843[label="",style="dashed", color="magenta", weight=3]; 2592[label="vuz43",fontsize=16,color="green",shape="box"];2593[label="vuz42",fontsize=16,color="green",shape="box"];2594[label="vuz43",fontsize=16,color="green",shape="box"];2595[label="vuz42",fontsize=16,color="green",shape="box"];2596[label="vuz43",fontsize=16,color="green",shape="box"];2597[label="vuz42",fontsize=16,color="green",shape="box"];2598[label="vuz43",fontsize=16,color="green",shape="box"];2599[label="vuz42",fontsize=16,color="green",shape="box"];4202 -> 4232[label="",style="dashed", color="red", weight=0]; 4202[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4202 -> 4233[label="",style="dashed", color="magenta", weight=3]; 4202 -> 4234[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4235[label="",style="dashed", color="red", weight=0]; 4203[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4203 -> 4236[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4237[label="",style="dashed", color="magenta", weight=3]; 2606[label="vuz48",fontsize=16,color="green",shape="box"];2607[label="vuz47",fontsize=16,color="green",shape="box"];2608[label="vuz48",fontsize=16,color="green",shape="box"];2609[label="vuz47",fontsize=16,color="green",shape="box"];2610[label="vuz48",fontsize=16,color="green",shape="box"];2611[label="vuz47",fontsize=16,color="green",shape="box"];2612[label="vuz48",fontsize=16,color="green",shape="box"];2613[label="vuz47",fontsize=16,color="green",shape="box"];4204 -> 4238[label="",style="dashed", color="red", weight=0]; 4204[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4204 -> 4239[label="",style="dashed", color="magenta", weight=3]; 4204 -> 4240[label="",style="dashed", color="magenta", weight=3]; 4205 -> 4241[label="",style="dashed", color="red", weight=0]; 4205[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4205 -> 4242[label="",style="dashed", color="magenta", weight=3]; 4205 -> 4243[label="",style="dashed", color="magenta", weight=3]; 2620[label="vuz53",fontsize=16,color="green",shape="box"];2621[label="vuz52",fontsize=16,color="green",shape="box"];2622[label="vuz53",fontsize=16,color="green",shape="box"];2623[label="vuz52",fontsize=16,color="green",shape="box"];2624[label="vuz53",fontsize=16,color="green",shape="box"];2625[label="vuz52",fontsize=16,color="green",shape="box"];2626[label="vuz53",fontsize=16,color="green",shape="box"];2627[label="vuz52",fontsize=16,color="green",shape="box"];5812 -> 5844[label="",style="dashed", color="red", weight=0]; 5812[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5812 -> 5845[label="",style="dashed", color="magenta", weight=3]; 5812 -> 5846[label="",style="dashed", color="magenta", weight=3]; 5813 -> 5847[label="",style="dashed", color="red", weight=0]; 5813[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5813 -> 5848[label="",style="dashed", color="magenta", weight=3]; 5813 -> 5849[label="",style="dashed", color="magenta", weight=3]; 2634[label="primQuotInt (primMinusNat (Succ vuz1850) vuz199) (reduce2D (primMinusNat (Succ vuz1850) vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6530[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2634 -> 6530[label="",style="solid", color="burlywood", weight=9]; 6530 -> 2736[label="",style="solid", color="burlywood", weight=3]; 6531[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2634 -> 6531[label="",style="solid", color="burlywood", weight=9]; 6531 -> 2737[label="",style="solid", color="burlywood", weight=3]; 2635[label="primQuotInt (primMinusNat Zero vuz199) (reduce2D (primMinusNat Zero vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6532[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2635 -> 6532[label="",style="solid", color="burlywood", weight=9]; 6532 -> 2738[label="",style="solid", color="burlywood", weight=3]; 6533[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2635 -> 6533[label="",style="solid", color="burlywood", weight=9]; 6533 -> 2739[label="",style="solid", color="burlywood", weight=3]; 3582 -> 4090[label="",style="dashed", color="red", weight=0]; 3582[label="reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144)",fontsize=16,color="magenta"];3582 -> 4091[label="",style="dashed", color="magenta", weight=3]; 3583 -> 1354[label="",style="dashed", color="red", weight=0]; 3583[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];3583 -> 4101[label="",style="dashed", color="magenta", weight=3]; 3583 -> 4102[label="",style="dashed", color="magenta", weight=3]; 5827 -> 681[label="",style="dashed", color="red", weight=0]; 5827[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5827 -> 5850[label="",style="dashed", color="magenta", weight=3]; 5827 -> 5851[label="",style="dashed", color="magenta", weight=3]; 5828 -> 681[label="",style="dashed", color="red", weight=0]; 5828[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5828 -> 5852[label="",style="dashed", color="magenta", weight=3]; 5828 -> 5853[label="",style="dashed", color="magenta", weight=3]; 5826[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5826 -> 5854[label="",style="solid", color="black", weight=3]; 5830 -> 681[label="",style="dashed", color="red", weight=0]; 5830[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5830 -> 5855[label="",style="dashed", color="magenta", weight=3]; 5830 -> 5856[label="",style="dashed", color="magenta", weight=3]; 5831 -> 681[label="",style="dashed", color="red", weight=0]; 5831[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5831 -> 5857[label="",style="dashed", color="magenta", weight=3]; 5831 -> 5858[label="",style="dashed", color="magenta", weight=3]; 5829[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5829 -> 5859[label="",style="solid", color="black", weight=3]; 3584 -> 4103[label="",style="dashed", color="red", weight=0]; 3584[label="reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68)",fontsize=16,color="magenta"];3584 -> 4104[label="",style="dashed", color="magenta", weight=3]; 3585 -> 1354[label="",style="dashed", color="red", weight=0]; 3585[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];3585 -> 4114[label="",style="dashed", color="magenta", weight=3]; 3585 -> 4115[label="",style="dashed", color="magenta", weight=3]; 2652[label="primQuotInt (primMinusNat (Succ vuz1690) vuz205) (reduce2D (primMinusNat (Succ vuz1690) vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6534[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2652 -> 6534[label="",style="solid", color="burlywood", weight=9]; 6534 -> 2752[label="",style="solid", color="burlywood", weight=3]; 6535[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2652 -> 6535[label="",style="solid", color="burlywood", weight=9]; 6535 -> 2753[label="",style="solid", color="burlywood", weight=3]; 2653[label="primQuotInt (primMinusNat Zero vuz205) (reduce2D (primMinusNat Zero vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6536[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2653 -> 6536[label="",style="solid", color="burlywood", weight=9]; 6536 -> 2754[label="",style="solid", color="burlywood", weight=3]; 6537[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2653 -> 6537[label="",style="solid", color="burlywood", weight=9]; 6537 -> 2755[label="",style="solid", color="burlywood", weight=3]; 4217 -> 681[label="",style="dashed", color="red", weight=0]; 4217[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4217 -> 4244[label="",style="dashed", color="magenta", weight=3]; 4217 -> 4245[label="",style="dashed", color="magenta", weight=3]; 4218 -> 681[label="",style="dashed", color="red", weight=0]; 4218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4218 -> 4246[label="",style="dashed", color="magenta", weight=3]; 4218 -> 4247[label="",style="dashed", color="magenta", weight=3]; 4216[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4216 -> 4248[label="",style="solid", color="black", weight=3]; 4220 -> 681[label="",style="dashed", color="red", weight=0]; 4220[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4220 -> 4249[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4250[label="",style="dashed", color="magenta", weight=3]; 4221 -> 681[label="",style="dashed", color="red", weight=0]; 4221[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4221 -> 4251[label="",style="dashed", color="magenta", weight=3]; 4221 -> 4252[label="",style="dashed", color="magenta", weight=3]; 4219[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4219 -> 4253[label="",style="solid", color="black", weight=3]; 4222 -> 4927[label="",style="dashed", color="red", weight=0]; 4222[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS vuz28000 vuz281000)",fontsize=16,color="magenta"];4222 -> 4928[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4929[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4930[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4931[label="",style="dashed", color="magenta", weight=3]; 4223[label="primDivNatS0 (Succ vuz28000) Zero True",fontsize=16,color="black",shape="box"];4223 -> 4256[label="",style="solid", color="black", weight=3]; 4224[label="primDivNatS0 Zero (Succ vuz281000) False",fontsize=16,color="black",shape="box"];4224 -> 4257[label="",style="solid", color="black", weight=3]; 4225[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];4225 -> 4258[label="",style="solid", color="black", weight=3]; 5114 -> 5689[label="",style="dashed", color="red", weight=0]; 5114[label="reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71)",fontsize=16,color="magenta"];5114 -> 5690[label="",style="dashed", color="magenta", weight=3]; 5115 -> 1354[label="",style="dashed", color="red", weight=0]; 5115[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5115 -> 5703[label="",style="dashed", color="magenta", weight=3]; 5115 -> 5704[label="",style="dashed", color="magenta", weight=3]; 2667[label="vuz71",fontsize=16,color="green",shape="box"];2668[label="vuz209",fontsize=16,color="green",shape="box"];2669[label="vuz173",fontsize=16,color="green",shape="box"];4227 -> 681[label="",style="dashed", color="red", weight=0]; 4227[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4227 -> 4259[label="",style="dashed", color="magenta", weight=3]; 4227 -> 4260[label="",style="dashed", color="magenta", weight=3]; 4228 -> 681[label="",style="dashed", color="red", weight=0]; 4228[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4228 -> 4261[label="",style="dashed", color="magenta", weight=3]; 4228 -> 4262[label="",style="dashed", color="magenta", weight=3]; 4226[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4226 -> 4263[label="",style="solid", color="black", weight=3]; 4230 -> 681[label="",style="dashed", color="red", weight=0]; 4230[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4230 -> 4264[label="",style="dashed", color="magenta", weight=3]; 4230 -> 4265[label="",style="dashed", color="magenta", weight=3]; 4231 -> 681[label="",style="dashed", color="red", weight=0]; 4231[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4231 -> 4266[label="",style="dashed", color="magenta", weight=3]; 4231 -> 4267[label="",style="dashed", color="magenta", weight=3]; 4229[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4229 -> 4268[label="",style="solid", color="black", weight=3]; 2680[label="vuz175",fontsize=16,color="green",shape="box"];2681[label="vuz211",fontsize=16,color="green",shape="box"];2682[label="vuz74",fontsize=16,color="green",shape="box"];5116 -> 5705[label="",style="dashed", color="red", weight=0]; 5116[label="reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74)",fontsize=16,color="magenta"];5116 -> 5706[label="",style="dashed", color="magenta", weight=3]; 5117 -> 1354[label="",style="dashed", color="red", weight=0]; 5117[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5117 -> 5719[label="",style="dashed", color="magenta", weight=3]; 5117 -> 5720[label="",style="dashed", color="magenta", weight=3]; 5833 -> 681[label="",style="dashed", color="red", weight=0]; 5833[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5833 -> 5860[label="",style="dashed", color="magenta", weight=3]; 5833 -> 5861[label="",style="dashed", color="magenta", weight=3]; 5834 -> 681[label="",style="dashed", color="red", weight=0]; 5834[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5834 -> 5862[label="",style="dashed", color="magenta", weight=3]; 5834 -> 5863[label="",style="dashed", color="magenta", weight=3]; 5832[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5832 -> 5864[label="",style="solid", color="black", weight=3]; 5836 -> 681[label="",style="dashed", color="red", weight=0]; 5836[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5836 -> 5865[label="",style="dashed", color="magenta", weight=3]; 5836 -> 5866[label="",style="dashed", color="magenta", weight=3]; 5837 -> 681[label="",style="dashed", color="red", weight=0]; 5837[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5837 -> 5867[label="",style="dashed", color="magenta", weight=3]; 5837 -> 5868[label="",style="dashed", color="magenta", weight=3]; 5835[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5835 -> 5869[label="",style="solid", color="black", weight=3]; 5839 -> 681[label="",style="dashed", color="red", weight=0]; 5839[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5839 -> 5870[label="",style="dashed", color="magenta", weight=3]; 5839 -> 5871[label="",style="dashed", color="magenta", weight=3]; 5840 -> 681[label="",style="dashed", color="red", weight=0]; 5840[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5840 -> 5872[label="",style="dashed", color="magenta", weight=3]; 5840 -> 5873[label="",style="dashed", color="magenta", weight=3]; 5838[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5838 -> 5874[label="",style="solid", color="black", weight=3]; 5842 -> 681[label="",style="dashed", color="red", weight=0]; 5842[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5842 -> 5875[label="",style="dashed", color="magenta", weight=3]; 5842 -> 5876[label="",style="dashed", color="magenta", weight=3]; 5843 -> 681[label="",style="dashed", color="red", weight=0]; 5843[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5843 -> 5877[label="",style="dashed", color="magenta", weight=3]; 5843 -> 5878[label="",style="dashed", color="magenta", weight=3]; 5841[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5841 -> 5879[label="",style="solid", color="black", weight=3]; 4233 -> 681[label="",style="dashed", color="red", weight=0]; 4233[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4233 -> 4269[label="",style="dashed", color="magenta", weight=3]; 4233 -> 4270[label="",style="dashed", color="magenta", weight=3]; 4234 -> 681[label="",style="dashed", color="red", weight=0]; 4234[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4234 -> 4271[label="",style="dashed", color="magenta", weight=3]; 4234 -> 4272[label="",style="dashed", color="magenta", weight=3]; 4232[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4232 -> 4273[label="",style="solid", color="black", weight=3]; 4236 -> 681[label="",style="dashed", color="red", weight=0]; 4236[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4236 -> 4274[label="",style="dashed", color="magenta", weight=3]; 4236 -> 4275[label="",style="dashed", color="magenta", weight=3]; 4237 -> 681[label="",style="dashed", color="red", weight=0]; 4237[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4237 -> 4276[label="",style="dashed", color="magenta", weight=3]; 4237 -> 4277[label="",style="dashed", color="magenta", weight=3]; 4235[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4235 -> 4278[label="",style="solid", color="black", weight=3]; 4239 -> 681[label="",style="dashed", color="red", weight=0]; 4239[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4239 -> 4279[label="",style="dashed", color="magenta", weight=3]; 4239 -> 4280[label="",style="dashed", color="magenta", weight=3]; 4240 -> 681[label="",style="dashed", color="red", weight=0]; 4240[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4240 -> 4281[label="",style="dashed", color="magenta", weight=3]; 4240 -> 4282[label="",style="dashed", color="magenta", weight=3]; 4238[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4238 -> 4283[label="",style="solid", color="black", weight=3]; 4242 -> 681[label="",style="dashed", color="red", weight=0]; 4242[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4242 -> 4284[label="",style="dashed", color="magenta", weight=3]; 4242 -> 4285[label="",style="dashed", color="magenta", weight=3]; 4243 -> 681[label="",style="dashed", color="red", weight=0]; 4243[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4243 -> 4286[label="",style="dashed", color="magenta", weight=3]; 4243 -> 4287[label="",style="dashed", color="magenta", weight=3]; 4241[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4241 -> 4288[label="",style="solid", color="black", weight=3]; 5845 -> 681[label="",style="dashed", color="red", weight=0]; 5845[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5845 -> 5880[label="",style="dashed", color="magenta", weight=3]; 5845 -> 5881[label="",style="dashed", color="magenta", weight=3]; 5846 -> 681[label="",style="dashed", color="red", weight=0]; 5846[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5846 -> 5882[label="",style="dashed", color="magenta", weight=3]; 5846 -> 5883[label="",style="dashed", color="magenta", weight=3]; 5844[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5844 -> 5884[label="",style="solid", color="black", weight=3]; 5848 -> 681[label="",style="dashed", color="red", weight=0]; 5848[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5848 -> 5885[label="",style="dashed", color="magenta", weight=3]; 5848 -> 5886[label="",style="dashed", color="magenta", weight=3]; 5849 -> 681[label="",style="dashed", color="red", weight=0]; 5849[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5849 -> 5887[label="",style="dashed", color="magenta", weight=3]; 5849 -> 5888[label="",style="dashed", color="magenta", weight=3]; 5847[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5847 -> 5889[label="",style="solid", color="black", weight=3]; 2736[label="primQuotInt (primMinusNat (Succ vuz1850) (Succ vuz1990)) (reduce2D (primMinusNat (Succ vuz1850) (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2736 -> 2780[label="",style="solid", color="black", weight=3]; 2737[label="primQuotInt (primMinusNat (Succ vuz1850) Zero) (reduce2D (primMinusNat (Succ vuz1850) Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2737 -> 2781[label="",style="solid", color="black", weight=3]; 2738[label="primQuotInt (primMinusNat Zero (Succ vuz1990)) (reduce2D (primMinusNat Zero (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2738 -> 2782[label="",style="solid", color="black", weight=3]; 2739[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2739 -> 2783[label="",style="solid", color="black", weight=3]; 4091 -> 1354[label="",style="dashed", color="red", weight=0]; 4091[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];4091 -> 4116[label="",style="dashed", color="magenta", weight=3]; 4091 -> 4117[label="",style="dashed", color="magenta", weight=3]; 4090[label="reduce2D (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];4090 -> 4118[label="",style="solid", color="black", weight=3]; 4101[label="vuz201",fontsize=16,color="green",shape="box"];4102[label="vuz187",fontsize=16,color="green",shape="box"];5850[label="vuz10",fontsize=16,color="green",shape="box"];5851[label="vuz90",fontsize=16,color="green",shape="box"];5852[label="vuz10",fontsize=16,color="green",shape="box"];5853[label="vuz90",fontsize=16,color="green",shape="box"];5854[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5854 -> 5900[label="",style="solid", color="black", weight=3]; 5855[label="vuz10",fontsize=16,color="green",shape="box"];5856[label="vuz90",fontsize=16,color="green",shape="box"];5857[label="vuz10",fontsize=16,color="green",shape="box"];5858[label="vuz90",fontsize=16,color="green",shape="box"];5859[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5859 -> 5901[label="",style="solid", color="black", weight=3]; 4104 -> 1354[label="",style="dashed", color="red", weight=0]; 4104[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];4104 -> 4119[label="",style="dashed", color="magenta", weight=3]; 4104 -> 4120[label="",style="dashed", color="magenta", weight=3]; 4103[label="reduce2D (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4103 -> 4121[label="",style="solid", color="black", weight=3]; 4114[label="vuz203",fontsize=16,color="green",shape="box"];4115[label="vuz167",fontsize=16,color="green",shape="box"];2752[label="primQuotInt (primMinusNat (Succ vuz1690) (Succ vuz2050)) (reduce2D (primMinusNat (Succ vuz1690) (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2752 -> 2804[label="",style="solid", color="black", weight=3]; 2753[label="primQuotInt (primMinusNat (Succ vuz1690) Zero) (reduce2D (primMinusNat (Succ vuz1690) Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2753 -> 2805[label="",style="solid", color="black", weight=3]; 2754[label="primQuotInt (primMinusNat Zero (Succ vuz2050)) (reduce2D (primMinusNat Zero (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2754 -> 2806[label="",style="solid", color="black", weight=3]; 2755[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2755 -> 2807[label="",style="solid", color="black", weight=3]; 4244[label="vuz21",fontsize=16,color="green",shape="box"];4245[label="vuz200",fontsize=16,color="green",shape="box"];4246[label="vuz21",fontsize=16,color="green",shape="box"];4247[label="vuz200",fontsize=16,color="green",shape="box"];4248[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4248 -> 4297[label="",style="solid", color="black", weight=3]; 4249[label="vuz21",fontsize=16,color="green",shape="box"];4250[label="vuz200",fontsize=16,color="green",shape="box"];4251[label="vuz21",fontsize=16,color="green",shape="box"];4252[label="vuz200",fontsize=16,color="green",shape="box"];4253[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4253 -> 4298[label="",style="solid", color="black", weight=3]; 4928[label="vuz28000",fontsize=16,color="green",shape="box"];4929[label="vuz281000",fontsize=16,color="green",shape="box"];4930[label="vuz281000",fontsize=16,color="green",shape="box"];4931[label="vuz28000",fontsize=16,color="green",shape="box"];4927[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz340 vuz341)",fontsize=16,color="burlywood",shape="triangle"];6538[label="vuz340/Succ vuz3400",fontsize=10,color="white",style="solid",shape="box"];4927 -> 6538[label="",style="solid", color="burlywood", weight=9]; 6538 -> 4968[label="",style="solid", color="burlywood", weight=3]; 6539[label="vuz340/Zero",fontsize=10,color="white",style="solid",shape="box"];4927 -> 6539[label="",style="solid", color="burlywood", weight=9]; 6539 -> 4969[label="",style="solid", color="burlywood", weight=3]; 4256[label="Succ (primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4256 -> 4303[label="",style="dashed", color="green", weight=3]; 4257[label="Zero",fontsize=16,color="green",shape="box"];4258[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4258 -> 4304[label="",style="dashed", color="green", weight=3]; 5690 -> 1354[label="",style="dashed", color="red", weight=0]; 5690[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5690 -> 5721[label="",style="dashed", color="magenta", weight=3]; 5690 -> 5722[label="",style="dashed", color="magenta", weight=3]; 5689[label="reduce2D (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];5689 -> 5723[label="",style="solid", color="black", weight=3]; 5703[label="vuz207",fontsize=16,color="green",shape="box"];5704[label="vuz171",fontsize=16,color="green",shape="box"];4259[label="vuz26",fontsize=16,color="green",shape="box"];4260[label="vuz250",fontsize=16,color="green",shape="box"];4261[label="vuz26",fontsize=16,color="green",shape="box"];4262[label="vuz250",fontsize=16,color="green",shape="box"];4263[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4263 -> 4305[label="",style="solid", color="black", weight=3]; 4264[label="vuz26",fontsize=16,color="green",shape="box"];4265[label="vuz250",fontsize=16,color="green",shape="box"];4266[label="vuz26",fontsize=16,color="green",shape="box"];4267[label="vuz250",fontsize=16,color="green",shape="box"];4268[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4268 -> 4306[label="",style="solid", color="black", weight=3]; 5706 -> 1354[label="",style="dashed", color="red", weight=0]; 5706[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5706 -> 5724[label="",style="dashed", color="magenta", weight=3]; 5706 -> 5725[label="",style="dashed", color="magenta", weight=3]; 5705[label="reduce2D (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5705 -> 5726[label="",style="solid", color="black", weight=3]; 5719[label="vuz213",fontsize=16,color="green",shape="box"];5720[label="vuz177",fontsize=16,color="green",shape="box"];5860[label="vuz31",fontsize=16,color="green",shape="box"];5861[label="vuz300",fontsize=16,color="green",shape="box"];5862[label="vuz31",fontsize=16,color="green",shape="box"];5863[label="vuz300",fontsize=16,color="green",shape="box"];5864[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5864 -> 5902[label="",style="solid", color="black", weight=3]; 5865[label="vuz31",fontsize=16,color="green",shape="box"];5866[label="vuz300",fontsize=16,color="green",shape="box"];5867[label="vuz31",fontsize=16,color="green",shape="box"];5868[label="vuz300",fontsize=16,color="green",shape="box"];5869[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5869 -> 5903[label="",style="solid", color="black", weight=3]; 5870[label="vuz36",fontsize=16,color="green",shape="box"];5871[label="vuz350",fontsize=16,color="green",shape="box"];5872[label="vuz36",fontsize=16,color="green",shape="box"];5873[label="vuz350",fontsize=16,color="green",shape="box"];5874[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5874 -> 5904[label="",style="solid", color="black", weight=3]; 5875[label="vuz36",fontsize=16,color="green",shape="box"];5876[label="vuz350",fontsize=16,color="green",shape="box"];5877[label="vuz36",fontsize=16,color="green",shape="box"];5878[label="vuz350",fontsize=16,color="green",shape="box"];5879[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5879 -> 5905[label="",style="solid", color="black", weight=3]; 4269[label="vuz41",fontsize=16,color="green",shape="box"];4270[label="vuz400",fontsize=16,color="green",shape="box"];4271[label="vuz41",fontsize=16,color="green",shape="box"];4272[label="vuz400",fontsize=16,color="green",shape="box"];4273[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4273 -> 4307[label="",style="solid", color="black", weight=3]; 4274[label="vuz41",fontsize=16,color="green",shape="box"];4275[label="vuz400",fontsize=16,color="green",shape="box"];4276[label="vuz41",fontsize=16,color="green",shape="box"];4277[label="vuz400",fontsize=16,color="green",shape="box"];4278[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4278 -> 4308[label="",style="solid", color="black", weight=3]; 4279[label="vuz46",fontsize=16,color="green",shape="box"];4280[label="vuz450",fontsize=16,color="green",shape="box"];4281[label="vuz46",fontsize=16,color="green",shape="box"];4282[label="vuz450",fontsize=16,color="green",shape="box"];4283[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4283 -> 4309[label="",style="solid", color="black", weight=3]; 4284[label="vuz46",fontsize=16,color="green",shape="box"];4285[label="vuz450",fontsize=16,color="green",shape="box"];4286[label="vuz46",fontsize=16,color="green",shape="box"];4287[label="vuz450",fontsize=16,color="green",shape="box"];4288[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4288 -> 4310[label="",style="solid", color="black", weight=3]; 5880[label="vuz51",fontsize=16,color="green",shape="box"];5881[label="vuz500",fontsize=16,color="green",shape="box"];5882[label="vuz51",fontsize=16,color="green",shape="box"];5883[label="vuz500",fontsize=16,color="green",shape="box"];5884[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5884 -> 5906[label="",style="solid", color="black", weight=3]; 5885[label="vuz51",fontsize=16,color="green",shape="box"];5886[label="vuz500",fontsize=16,color="green",shape="box"];5887[label="vuz51",fontsize=16,color="green",shape="box"];5888[label="vuz500",fontsize=16,color="green",shape="box"];5889[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5889 -> 5907[label="",style="solid", color="black", weight=3]; 2780 -> 2518[label="",style="dashed", color="red", weight=0]; 2780[label="primQuotInt (primMinusNat vuz1850 vuz1990) (reduce2D (primMinusNat vuz1850 vuz1990) (Pos vuz144))",fontsize=16,color="magenta"];2780 -> 2864[label="",style="dashed", color="magenta", weight=3]; 2780 -> 2865[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5046[label="",style="dashed", color="red", weight=0]; 2781[label="primQuotInt (Pos (Succ vuz1850)) (reduce2D (Pos (Succ vuz1850)) (Pos vuz144))",fontsize=16,color="magenta"];2781 -> 5164[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5165[label="",style="dashed", color="magenta", weight=3]; 2782 -> 3509[label="",style="dashed", color="red", weight=0]; 2782[label="primQuotInt (Neg (Succ vuz1990)) (reduce2D (Neg (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="magenta"];2782 -> 3642[label="",style="dashed", color="magenta", weight=3]; 2782 -> 3643[label="",style="dashed", color="magenta", weight=3]; 2783 -> 5046[label="",style="dashed", color="red", weight=0]; 2783[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz144))",fontsize=16,color="magenta"];2783 -> 5166[label="",style="dashed", color="magenta", weight=3]; 2783 -> 5167[label="",style="dashed", color="magenta", weight=3]; 4116[label="vuz201",fontsize=16,color="green",shape="box"];4117[label="vuz187",fontsize=16,color="green",shape="box"];4118[label="gcd (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4118 -> 4135[label="",style="solid", color="black", weight=3]; 5900 -> 5920[label="",style="dashed", color="red", weight=0]; 5900[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5900 -> 5921[label="",style="dashed", color="magenta", weight=3]; 5900 -> 5922[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5928[label="",style="dashed", color="red", weight=0]; 5901[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5901 -> 5929[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5930[label="",style="dashed", color="magenta", weight=3]; 4119[label="vuz203",fontsize=16,color="green",shape="box"];4120[label="vuz167",fontsize=16,color="green",shape="box"];4121[label="gcd (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4121 -> 4136[label="",style="solid", color="black", weight=3]; 2804 -> 2539[label="",style="dashed", color="red", weight=0]; 2804[label="primQuotInt (primMinusNat vuz1690 vuz2050) (reduce2D (primMinusNat vuz1690 vuz2050) (Neg vuz68))",fontsize=16,color="magenta"];2804 -> 2886[label="",style="dashed", color="magenta", weight=3]; 2804 -> 2887[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5046[label="",style="dashed", color="red", weight=0]; 2805[label="primQuotInt (Pos (Succ vuz1690)) (reduce2D (Pos (Succ vuz1690)) (Neg vuz68))",fontsize=16,color="magenta"];2805 -> 5172[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5173[label="",style="dashed", color="magenta", weight=3]; 2806 -> 3509[label="",style="dashed", color="red", weight=0]; 2806[label="primQuotInt (Neg (Succ vuz2050)) (reduce2D (Neg (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="magenta"];2806 -> 3648[label="",style="dashed", color="magenta", weight=3]; 2806 -> 3649[label="",style="dashed", color="magenta", weight=3]; 2807 -> 5046[label="",style="dashed", color="red", weight=0]; 2807[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz68))",fontsize=16,color="magenta"];2807 -> 5174[label="",style="dashed", color="magenta", weight=3]; 2807 -> 5175[label="",style="dashed", color="magenta", weight=3]; 4297 -> 4319[label="",style="dashed", color="red", weight=0]; 4297[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4297 -> 4320[label="",style="dashed", color="magenta", weight=3]; 4297 -> 4321[label="",style="dashed", color="magenta", weight=3]; 4298 -> 4327[label="",style="dashed", color="red", weight=0]; 4298[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4298 -> 4328[label="",style="dashed", color="magenta", weight=3]; 4298 -> 4329[label="",style="dashed", color="magenta", weight=3]; 4968[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) vuz341)",fontsize=16,color="burlywood",shape="box"];6540[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4968 -> 6540[label="",style="solid", color="burlywood", weight=9]; 6540 -> 4992[label="",style="solid", color="burlywood", weight=3]; 6541[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4968 -> 6541[label="",style="solid", color="burlywood", weight=9]; 6541 -> 4993[label="",style="solid", color="burlywood", weight=3]; 4969[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero vuz341)",fontsize=16,color="burlywood",shape="box"];6542[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4969 -> 6542[label="",style="solid", color="burlywood", weight=9]; 6542 -> 4994[label="",style="solid", color="burlywood", weight=3]; 6543[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4969 -> 6543[label="",style="solid", color="burlywood", weight=9]; 6543 -> 4995[label="",style="solid", color="burlywood", weight=3]; 4303 -> 4129[label="",style="dashed", color="red", weight=0]; 4303[label="primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero)",fontsize=16,color="magenta"];4303 -> 4339[label="",style="dashed", color="magenta", weight=3]; 4303 -> 4340[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4129[label="",style="dashed", color="red", weight=0]; 4304[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];4304 -> 4341[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4342[label="",style="dashed", color="magenta", weight=3]; 5721[label="vuz207",fontsize=16,color="green",shape="box"];5722[label="vuz171",fontsize=16,color="green",shape="box"];5723[label="gcd (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5723 -> 5741[label="",style="solid", color="black", weight=3]; 4305 -> 4343[label="",style="dashed", color="red", weight=0]; 4305[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4305 -> 4344[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4345[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4351[label="",style="dashed", color="red", weight=0]; 4306[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4306 -> 4352[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4353[label="",style="dashed", color="magenta", weight=3]; 5724[label="vuz213",fontsize=16,color="green",shape="box"];5725[label="vuz177",fontsize=16,color="green",shape="box"];5726[label="gcd (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5726 -> 5742[label="",style="solid", color="black", weight=3]; 5902 -> 5936[label="",style="dashed", color="red", weight=0]; 5902[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5902 -> 5937[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5938[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5944[label="",style="dashed", color="red", weight=0]; 5903[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5903 -> 5945[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5946[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5944[label="",style="dashed", color="red", weight=0]; 5904[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5904 -> 5947[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5948[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5949[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5950[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5951[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5936[label="",style="dashed", color="red", weight=0]; 5905[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5905 -> 5939[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5940[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5941[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5942[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5943[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4351[label="",style="dashed", color="red", weight=0]; 4307[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4307 -> 4354[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4355[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4356[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4357[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4358[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4343[label="",style="dashed", color="red", weight=0]; 4308[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4308 -> 4346[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4347[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4348[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4349[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4350[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4327[label="",style="dashed", color="red", weight=0]; 4309[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4309 -> 4330[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4331[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4332[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4333[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4334[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4319[label="",style="dashed", color="red", weight=0]; 4310[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4310 -> 4322[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4323[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4324[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4325[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4326[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5928[label="",style="dashed", color="red", weight=0]; 5906[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5906 -> 5931[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5932[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5933[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5934[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5935[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5920[label="",style="dashed", color="red", weight=0]; 5907[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5907 -> 5923[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5924[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5925[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5926[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5927[label="",style="dashed", color="magenta", weight=3]; 2864[label="vuz1990",fontsize=16,color="green",shape="box"];2865[label="vuz1850",fontsize=16,color="green",shape="box"];5164 -> 5705[label="",style="dashed", color="red", weight=0]; 5164[label="reduce2D (Pos (Succ vuz1850)) (Pos vuz144)",fontsize=16,color="magenta"];5164 -> 5707[label="",style="dashed", color="magenta", weight=3]; 5164 -> 5708[label="",style="dashed", color="magenta", weight=3]; 5165[label="Succ vuz1850",fontsize=16,color="green",shape="box"];3642 -> 4090[label="",style="dashed", color="red", weight=0]; 3642[label="reduce2D (Neg (Succ vuz1990)) (Pos vuz144)",fontsize=16,color="magenta"];3642 -> 4092[label="",style="dashed", color="magenta", weight=3]; 3643[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5166 -> 5705[label="",style="dashed", color="red", weight=0]; 5166[label="reduce2D (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];5166 -> 5709[label="",style="dashed", color="magenta", weight=3]; 5166 -> 5710[label="",style="dashed", color="magenta", weight=3]; 5167[label="Zero",fontsize=16,color="green",shape="box"];4135[label="gcd3 (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4135 -> 4151[label="",style="solid", color="black", weight=3]; 5921 -> 681[label="",style="dashed", color="red", weight=0]; 5921[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5921 -> 5952[label="",style="dashed", color="magenta", weight=3]; 5921 -> 5953[label="",style="dashed", color="magenta", weight=3]; 5922 -> 681[label="",style="dashed", color="red", weight=0]; 5922[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5922 -> 5954[label="",style="dashed", color="magenta", weight=3]; 5922 -> 5955[label="",style="dashed", color="magenta", weight=3]; 5920[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz366)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz365)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5920 -> 5956[label="",style="solid", color="black", weight=3]; 5929 -> 681[label="",style="dashed", color="red", weight=0]; 5929[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5929 -> 5957[label="",style="dashed", color="magenta", weight=3]; 5929 -> 5958[label="",style="dashed", color="magenta", weight=3]; 5930 -> 681[label="",style="dashed", color="red", weight=0]; 5930[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5930 -> 5959[label="",style="dashed", color="magenta", weight=3]; 5930 -> 5960[label="",style="dashed", color="magenta", weight=3]; 5928[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz368)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz367)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5928 -> 5961[label="",style="solid", color="black", weight=3]; 4136[label="gcd3 (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4136 -> 4152[label="",style="solid", color="black", weight=3]; 2886[label="vuz1690",fontsize=16,color="green",shape="box"];2887[label="vuz2050",fontsize=16,color="green",shape="box"];5172 -> 5689[label="",style="dashed", color="red", weight=0]; 5172[label="reduce2D (Pos (Succ vuz1690)) (Neg vuz68)",fontsize=16,color="magenta"];5172 -> 5691[label="",style="dashed", color="magenta", weight=3]; 5172 -> 5692[label="",style="dashed", color="magenta", weight=3]; 5173[label="Succ vuz1690",fontsize=16,color="green",shape="box"];3648 -> 4103[label="",style="dashed", color="red", weight=0]; 3648[label="reduce2D (Neg (Succ vuz2050)) (Neg vuz68)",fontsize=16,color="magenta"];3648 -> 4105[label="",style="dashed", color="magenta", weight=3]; 3649[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5174 -> 5689[label="",style="dashed", color="red", weight=0]; 5174[label="reduce2D (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];5174 -> 5693[label="",style="dashed", color="magenta", weight=3]; 5174 -> 5694[label="",style="dashed", color="magenta", weight=3]; 5175[label="Zero",fontsize=16,color="green",shape="box"];4320 -> 681[label="",style="dashed", color="red", weight=0]; 4320[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4320 -> 4359[label="",style="dashed", color="magenta", weight=3]; 4320 -> 4360[label="",style="dashed", color="magenta", weight=3]; 4321 -> 681[label="",style="dashed", color="red", weight=0]; 4321[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4321 -> 4361[label="",style="dashed", color="magenta", weight=3]; 4321 -> 4362[label="",style="dashed", color="magenta", weight=3]; 4319[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz301)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz300)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4319 -> 4363[label="",style="solid", color="black", weight=3]; 4328 -> 681[label="",style="dashed", color="red", weight=0]; 4328[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4328 -> 4364[label="",style="dashed", color="magenta", weight=3]; 4328 -> 4365[label="",style="dashed", color="magenta", weight=3]; 4329 -> 681[label="",style="dashed", color="red", weight=0]; 4329[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4329 -> 4366[label="",style="dashed", color="magenta", weight=3]; 4329 -> 4367[label="",style="dashed", color="magenta", weight=3]; 4327[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz303)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz302)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4327 -> 4368[label="",style="solid", color="black", weight=3]; 4992[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) (Succ vuz3410))",fontsize=16,color="black",shape="box"];4992 -> 5003[label="",style="solid", color="black", weight=3]; 4993[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) Zero)",fontsize=16,color="black",shape="box"];4993 -> 5004[label="",style="solid", color="black", weight=3]; 4994[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero (Succ vuz3410))",fontsize=16,color="black",shape="box"];4994 -> 5005[label="",style="solid", color="black", weight=3]; 4995[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4995 -> 5006[label="",style="solid", color="black", weight=3]; 4339[label="Zero",fontsize=16,color="green",shape="box"];4340[label="primMinusNatS (Succ vuz28000) Zero",fontsize=16,color="black",shape="triangle"];4340 -> 4374[label="",style="solid", color="black", weight=3]; 4341[label="Zero",fontsize=16,color="green",shape="box"];4342[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];4342 -> 4375[label="",style="solid", color="black", weight=3]; 5741[label="gcd3 (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5741 -> 5758[label="",style="solid", color="black", weight=3]; 4344 -> 681[label="",style="dashed", color="red", weight=0]; 4344[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4344 -> 4376[label="",style="dashed", color="magenta", weight=3]; 4344 -> 4377[label="",style="dashed", color="magenta", weight=3]; 4345 -> 681[label="",style="dashed", color="red", weight=0]; 4345[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4345 -> 4378[label="",style="dashed", color="magenta", weight=3]; 4345 -> 4379[label="",style="dashed", color="magenta", weight=3]; 4343[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos vuz305)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos vuz304)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4343 -> 4380[label="",style="solid", color="black", weight=3]; 4352 -> 681[label="",style="dashed", color="red", weight=0]; 4352[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4352 -> 4381[label="",style="dashed", color="magenta", weight=3]; 4352 -> 4382[label="",style="dashed", color="magenta", weight=3]; 4353 -> 681[label="",style="dashed", color="red", weight=0]; 4353[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4353 -> 4383[label="",style="dashed", color="magenta", weight=3]; 4353 -> 4384[label="",style="dashed", color="magenta", weight=3]; 4351[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos vuz307)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos vuz306)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4351 -> 4385[label="",style="solid", color="black", weight=3]; 5742[label="gcd3 (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5742 -> 5759[label="",style="solid", color="black", weight=3]; 5937 -> 681[label="",style="dashed", color="red", weight=0]; 5937[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5937 -> 5962[label="",style="dashed", color="magenta", weight=3]; 5937 -> 5963[label="",style="dashed", color="magenta", weight=3]; 5938 -> 681[label="",style="dashed", color="red", weight=0]; 5938[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5938 -> 5964[label="",style="dashed", color="magenta", weight=3]; 5938 -> 5965[label="",style="dashed", color="magenta", weight=3]; 5936[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos vuz370)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos vuz369)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5936 -> 5966[label="",style="solid", color="black", weight=3]; 5945 -> 681[label="",style="dashed", color="red", weight=0]; 5945[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5945 -> 5967[label="",style="dashed", color="magenta", weight=3]; 5945 -> 5968[label="",style="dashed", color="magenta", weight=3]; 5946 -> 681[label="",style="dashed", color="red", weight=0]; 5946[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5946 -> 5969[label="",style="dashed", color="magenta", weight=3]; 5946 -> 5970[label="",style="dashed", color="magenta", weight=3]; 5944[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos vuz372)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos vuz371)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5944 -> 5971[label="",style="solid", color="black", weight=3]; 5947 -> 681[label="",style="dashed", color="red", weight=0]; 5947[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5947 -> 5972[label="",style="dashed", color="magenta", weight=3]; 5947 -> 5973[label="",style="dashed", color="magenta", weight=3]; 5948[label="vuz77",fontsize=16,color="green",shape="box"];5949 -> 681[label="",style="dashed", color="red", weight=0]; 5949[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5949 -> 5974[label="",style="dashed", color="magenta", weight=3]; 5949 -> 5975[label="",style="dashed", color="magenta", weight=3]; 5950[label="vuz358",fontsize=16,color="green",shape="box"];5951[label="vuz357",fontsize=16,color="green",shape="box"];5939 -> 681[label="",style="dashed", color="red", weight=0]; 5939[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5939 -> 5976[label="",style="dashed", color="magenta", weight=3]; 5939 -> 5977[label="",style="dashed", color="magenta", weight=3]; 5940[label="vuz77",fontsize=16,color="green",shape="box"];5941[label="vuz360",fontsize=16,color="green",shape="box"];5942[label="vuz359",fontsize=16,color="green",shape="box"];5943 -> 681[label="",style="dashed", color="red", weight=0]; 5943[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5943 -> 5978[label="",style="dashed", color="magenta", weight=3]; 5943 -> 5979[label="",style="dashed", color="magenta", weight=3]; 4354 -> 681[label="",style="dashed", color="red", weight=0]; 4354[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4354 -> 4386[label="",style="dashed", color="magenta", weight=3]; 4354 -> 4387[label="",style="dashed", color="magenta", weight=3]; 4355[label="vuz293",fontsize=16,color="green",shape="box"];4356 -> 681[label="",style="dashed", color="red", weight=0]; 4356[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4356 -> 4388[label="",style="dashed", color="magenta", weight=3]; 4356 -> 4389[label="",style="dashed", color="magenta", weight=3]; 4357[label="vuz292",fontsize=16,color="green",shape="box"];4358[label="vuz92",fontsize=16,color="green",shape="box"];4346[label="vuz294",fontsize=16,color="green",shape="box"];4347[label="vuz92",fontsize=16,color="green",shape="box"];4348 -> 681[label="",style="dashed", color="red", weight=0]; 4348[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4348 -> 4390[label="",style="dashed", color="magenta", weight=3]; 4348 -> 4391[label="",style="dashed", color="magenta", weight=3]; 4349 -> 681[label="",style="dashed", color="red", weight=0]; 4349[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4349 -> 4392[label="",style="dashed", color="magenta", weight=3]; 4349 -> 4393[label="",style="dashed", color="magenta", weight=3]; 4350[label="vuz295",fontsize=16,color="green",shape="box"];4330[label="vuz107",fontsize=16,color="green",shape="box"];4331[label="vuz297",fontsize=16,color="green",shape="box"];4332[label="vuz296",fontsize=16,color="green",shape="box"];4333 -> 681[label="",style="dashed", color="red", weight=0]; 4333[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4333 -> 4394[label="",style="dashed", color="magenta", weight=3]; 4333 -> 4395[label="",style="dashed", color="magenta", weight=3]; 4334 -> 681[label="",style="dashed", color="red", weight=0]; 4334[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4334 -> 4396[label="",style="dashed", color="magenta", weight=3]; 4334 -> 4397[label="",style="dashed", color="magenta", weight=3]; 4322 -> 681[label="",style="dashed", color="red", weight=0]; 4322[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4322 -> 4398[label="",style="dashed", color="magenta", weight=3]; 4322 -> 4399[label="",style="dashed", color="magenta", weight=3]; 4323[label="vuz107",fontsize=16,color="green",shape="box"];4324[label="vuz299",fontsize=16,color="green",shape="box"];4325[label="vuz298",fontsize=16,color="green",shape="box"];4326 -> 681[label="",style="dashed", color="red", weight=0]; 4326[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4326 -> 4400[label="",style="dashed", color="magenta", weight=3]; 4326 -> 4401[label="",style="dashed", color="magenta", weight=3]; 5931[label="vuz361",fontsize=16,color="green",shape="box"];5932 -> 681[label="",style="dashed", color="red", weight=0]; 5932[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5932 -> 5980[label="",style="dashed", color="magenta", weight=3]; 5932 -> 5981[label="",style="dashed", color="magenta", weight=3]; 5933[label="vuz362",fontsize=16,color="green",shape="box"];5934 -> 681[label="",style="dashed", color="red", weight=0]; 5934[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5934 -> 5982[label="",style="dashed", color="magenta", weight=3]; 5934 -> 5983[label="",style="dashed", color="magenta", weight=3]; 5935[label="vuz122",fontsize=16,color="green",shape="box"];5923 -> 681[label="",style="dashed", color="red", weight=0]; 5923[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5923 -> 5984[label="",style="dashed", color="magenta", weight=3]; 5923 -> 5985[label="",style="dashed", color="magenta", weight=3]; 5924[label="vuz364",fontsize=16,color="green",shape="box"];5925 -> 681[label="",style="dashed", color="red", weight=0]; 5925[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5925 -> 5986[label="",style="dashed", color="magenta", weight=3]; 5925 -> 5987[label="",style="dashed", color="magenta", weight=3]; 5926[label="vuz363",fontsize=16,color="green",shape="box"];5927[label="vuz122",fontsize=16,color="green",shape="box"];5707[label="Succ vuz1850",fontsize=16,color="green",shape="box"];5708[label="vuz144",fontsize=16,color="green",shape="box"];4092[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5709[label="Zero",fontsize=16,color="green",shape="box"];5710[label="vuz144",fontsize=16,color="green",shape="box"];4151[label="gcd2 (Neg vuz282 == fromInt (Pos Zero)) (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4151 -> 4166[label="",style="solid", color="black", weight=3]; 5952[label="vuz12",fontsize=16,color="green",shape="box"];5953[label="vuz11",fontsize=16,color="green",shape="box"];5954[label="vuz12",fontsize=16,color="green",shape="box"];5955[label="vuz11",fontsize=16,color="green",shape="box"];5956[label="gcd2 (primEqInt (primMinusNat vuz350 vuz366) (fromInt (Pos Zero))) (primMinusNat vuz350 vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6544[label="vuz350/Succ vuz3500",fontsize=10,color="white",style="solid",shape="box"];5956 -> 6544[label="",style="solid", color="burlywood", weight=9]; 6544 -> 6004[label="",style="solid", color="burlywood", weight=3]; 6545[label="vuz350/Zero",fontsize=10,color="white",style="solid",shape="box"];5956 -> 6545[label="",style="solid", color="burlywood", weight=9]; 6545 -> 6005[label="",style="solid", color="burlywood", weight=3]; 5957[label="vuz12",fontsize=16,color="green",shape="box"];5958[label="vuz11",fontsize=16,color="green",shape="box"];5959[label="vuz12",fontsize=16,color="green",shape="box"];5960[label="vuz11",fontsize=16,color="green",shape="box"];5961 -> 4166[label="",style="dashed", color="red", weight=0]; 5961[label="gcd2 (primEqInt (Neg (primPlusNat vuz352 vuz368)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz352 vuz368)) (Pos vuz144)",fontsize=16,color="magenta"];5961 -> 6006[label="",style="dashed", color="magenta", weight=3]; 4152[label="gcd2 (Neg vuz283 == fromInt (Pos Zero)) (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4152 -> 4167[label="",style="solid", color="black", weight=3]; 5691[label="Succ vuz1690",fontsize=16,color="green",shape="box"];5692[label="vuz68",fontsize=16,color="green",shape="box"];4105[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5693[label="Zero",fontsize=16,color="green",shape="box"];5694[label="vuz68",fontsize=16,color="green",shape="box"];4359[label="vuz23",fontsize=16,color="green",shape="box"];4360[label="vuz22",fontsize=16,color="green",shape="box"];4361[label="vuz23",fontsize=16,color="green",shape="box"];4362[label="vuz22",fontsize=16,color="green",shape="box"];4363 -> 4167[label="",style="dashed", color="red", weight=0]; 4363[label="gcd2 (primEqInt (Neg (primPlusNat vuz285 vuz301)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz285 vuz301)) (Neg vuz68)",fontsize=16,color="magenta"];4363 -> 4410[label="",style="dashed", color="magenta", weight=3]; 4364[label="vuz23",fontsize=16,color="green",shape="box"];4365[label="vuz22",fontsize=16,color="green",shape="box"];4366[label="vuz23",fontsize=16,color="green",shape="box"];4367[label="vuz22",fontsize=16,color="green",shape="box"];4368[label="gcd2 (primEqInt (primMinusNat vuz287 vuz303) (fromInt (Pos Zero))) (primMinusNat vuz287 vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6546[label="vuz287/Succ vuz2870",fontsize=10,color="white",style="solid",shape="box"];4368 -> 6546[label="",style="solid", color="burlywood", weight=9]; 6546 -> 4411[label="",style="solid", color="burlywood", weight=3]; 6547[label="vuz287/Zero",fontsize=10,color="white",style="solid",shape="box"];4368 -> 6547[label="",style="solid", color="burlywood", weight=9]; 6547 -> 4412[label="",style="solid", color="burlywood", weight=3]; 5003 -> 4927[label="",style="dashed", color="red", weight=0]; 5003[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz3400 vuz3410)",fontsize=16,color="magenta"];5003 -> 5013[label="",style="dashed", color="magenta", weight=3]; 5003 -> 5014[label="",style="dashed", color="magenta", weight=3]; 5004[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="black",shape="triangle"];5004 -> 5015[label="",style="solid", color="black", weight=3]; 5005[label="primDivNatS0 (Succ vuz338) (Succ vuz339) False",fontsize=16,color="black",shape="box"];5005 -> 5016[label="",style="solid", color="black", weight=3]; 5006 -> 5004[label="",style="dashed", color="red", weight=0]; 5006[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="magenta"];4374[label="Succ vuz28000",fontsize=16,color="green",shape="box"];4375[label="Zero",fontsize=16,color="green",shape="box"];5758[label="gcd2 (Pos vuz347 == fromInt (Pos Zero)) (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5758 -> 5773[label="",style="solid", color="black", weight=3]; 4376[label="vuz28",fontsize=16,color="green",shape="box"];4377[label="vuz27",fontsize=16,color="green",shape="box"];4378[label="vuz28",fontsize=16,color="green",shape="box"];4379[label="vuz27",fontsize=16,color="green",shape="box"];4380 -> 4419[label="",style="dashed", color="red", weight=0]; 4380[label="gcd2 (primEqInt (Pos (primPlusNat vuz289 vuz305)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz289 vuz305)) (Neg vuz71)",fontsize=16,color="magenta"];4380 -> 4420[label="",style="dashed", color="magenta", weight=3]; 4380 -> 4421[label="",style="dashed", color="magenta", weight=3]; 4381[label="vuz28",fontsize=16,color="green",shape="box"];4382[label="vuz27",fontsize=16,color="green",shape="box"];4383[label="vuz28",fontsize=16,color="green",shape="box"];4384[label="vuz27",fontsize=16,color="green",shape="box"];4385 -> 4368[label="",style="dashed", color="red", weight=0]; 4385[label="gcd2 (primEqInt (primMinusNat vuz307 vuz291) (fromInt (Pos Zero))) (primMinusNat vuz307 vuz291) (Neg vuz71)",fontsize=16,color="magenta"];4385 -> 4422[label="",style="dashed", color="magenta", weight=3]; 4385 -> 4423[label="",style="dashed", color="magenta", weight=3]; 4385 -> 4424[label="",style="dashed", color="magenta", weight=3]; 5759[label="gcd2 (Pos vuz348 == fromInt (Pos Zero)) (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5759 -> 5774[label="",style="solid", color="black", weight=3]; 5962[label="vuz33",fontsize=16,color="green",shape="box"];5963[label="vuz32",fontsize=16,color="green",shape="box"];5964[label="vuz33",fontsize=16,color="green",shape="box"];5965[label="vuz32",fontsize=16,color="green",shape="box"];5966 -> 5956[label="",style="dashed", color="red", weight=0]; 5966[label="gcd2 (primEqInt (primMinusNat vuz370 vuz354) (fromInt (Pos Zero))) (primMinusNat vuz370 vuz354) (Pos vuz74)",fontsize=16,color="magenta"];5966 -> 6007[label="",style="dashed", color="magenta", weight=3]; 5966 -> 6008[label="",style="dashed", color="magenta", weight=3]; 5966 -> 6009[label="",style="dashed", color="magenta", weight=3]; 5967[label="vuz33",fontsize=16,color="green",shape="box"];5968[label="vuz32",fontsize=16,color="green",shape="box"];5969[label="vuz33",fontsize=16,color="green",shape="box"];5970[label="vuz32",fontsize=16,color="green",shape="box"];5971 -> 5774[label="",style="dashed", color="red", weight=0]; 5971[label="gcd2 (primEqInt (Pos (primPlusNat vuz356 vuz372)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz356 vuz372)) (Pos vuz74)",fontsize=16,color="magenta"];5971 -> 6010[label="",style="dashed", color="magenta", weight=3]; 5972[label="vuz38",fontsize=16,color="green",shape="box"];5973[label="vuz37",fontsize=16,color="green",shape="box"];5974[label="vuz38",fontsize=16,color="green",shape="box"];5975[label="vuz37",fontsize=16,color="green",shape="box"];5976[label="vuz38",fontsize=16,color="green",shape="box"];5977[label="vuz37",fontsize=16,color="green",shape="box"];5978[label="vuz38",fontsize=16,color="green",shape="box"];5979[label="vuz37",fontsize=16,color="green",shape="box"];4386[label="vuz43",fontsize=16,color="green",shape="box"];4387[label="vuz42",fontsize=16,color="green",shape="box"];4388[label="vuz43",fontsize=16,color="green",shape="box"];4389[label="vuz42",fontsize=16,color="green",shape="box"];4390[label="vuz43",fontsize=16,color="green",shape="box"];4391[label="vuz42",fontsize=16,color="green",shape="box"];4392[label="vuz43",fontsize=16,color="green",shape="box"];4393[label="vuz42",fontsize=16,color="green",shape="box"];4394[label="vuz48",fontsize=16,color="green",shape="box"];4395[label="vuz47",fontsize=16,color="green",shape="box"];4396[label="vuz48",fontsize=16,color="green",shape="box"];4397[label="vuz47",fontsize=16,color="green",shape="box"];4398[label="vuz48",fontsize=16,color="green",shape="box"];4399[label="vuz47",fontsize=16,color="green",shape="box"];4400[label="vuz48",fontsize=16,color="green",shape="box"];4401[label="vuz47",fontsize=16,color="green",shape="box"];5980[label="vuz53",fontsize=16,color="green",shape="box"];5981[label="vuz52",fontsize=16,color="green",shape="box"];5982[label="vuz53",fontsize=16,color="green",shape="box"];5983[label="vuz52",fontsize=16,color="green",shape="box"];5984[label="vuz53",fontsize=16,color="green",shape="box"];5985[label="vuz52",fontsize=16,color="green",shape="box"];5986[label="vuz53",fontsize=16,color="green",shape="box"];5987[label="vuz52",fontsize=16,color="green",shape="box"];4166[label="gcd2 (primEqInt (Neg vuz282) (fromInt (Pos Zero))) (Neg vuz282) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6548[label="vuz282/Succ vuz2820",fontsize=10,color="white",style="solid",shape="box"];4166 -> 6548[label="",style="solid", color="burlywood", weight=9]; 6548 -> 4185[label="",style="solid", color="burlywood", weight=3]; 6549[label="vuz282/Zero",fontsize=10,color="white",style="solid",shape="box"];4166 -> 6549[label="",style="solid", color="burlywood", weight=9]; 6549 -> 4186[label="",style="solid", color="burlywood", weight=3]; 6004[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) vuz366) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6550[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6004 -> 6550[label="",style="solid", color="burlywood", weight=9]; 6550 -> 6026[label="",style="solid", color="burlywood", weight=3]; 6551[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6004 -> 6551[label="",style="solid", color="burlywood", weight=9]; 6551 -> 6027[label="",style="solid", color="burlywood", weight=3]; 6005[label="gcd2 (primEqInt (primMinusNat Zero vuz366) (fromInt (Pos Zero))) (primMinusNat Zero vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6552[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6005 -> 6552[label="",style="solid", color="burlywood", weight=9]; 6552 -> 6028[label="",style="solid", color="burlywood", weight=3]; 6553[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6005 -> 6553[label="",style="solid", color="burlywood", weight=9]; 6553 -> 6029[label="",style="solid", color="burlywood", weight=3]; 6006 -> 1354[label="",style="dashed", color="red", weight=0]; 6006[label="primPlusNat vuz352 vuz368",fontsize=16,color="magenta"];6006 -> 6030[label="",style="dashed", color="magenta", weight=3]; 6006 -> 6031[label="",style="dashed", color="magenta", weight=3]; 4167[label="gcd2 (primEqInt (Neg vuz283) (fromInt (Pos Zero))) (Neg vuz283) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6554[label="vuz283/Succ vuz2830",fontsize=10,color="white",style="solid",shape="box"];4167 -> 6554[label="",style="solid", color="burlywood", weight=9]; 6554 -> 4187[label="",style="solid", color="burlywood", weight=3]; 6555[label="vuz283/Zero",fontsize=10,color="white",style="solid",shape="box"];4167 -> 6555[label="",style="solid", color="burlywood", weight=9]; 6555 -> 4188[label="",style="solid", color="burlywood", weight=3]; 4410 -> 1354[label="",style="dashed", color="red", weight=0]; 4410[label="primPlusNat vuz285 vuz301",fontsize=16,color="magenta"];4410 -> 4425[label="",style="dashed", color="magenta", weight=3]; 4410 -> 4426[label="",style="dashed", color="magenta", weight=3]; 4411[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) vuz303) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6556[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4411 -> 6556[label="",style="solid", color="burlywood", weight=9]; 6556 -> 4427[label="",style="solid", color="burlywood", weight=3]; 6557[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4411 -> 6557[label="",style="solid", color="burlywood", weight=9]; 6557 -> 4428[label="",style="solid", color="burlywood", weight=3]; 4412[label="gcd2 (primEqInt (primMinusNat Zero vuz303) (fromInt (Pos Zero))) (primMinusNat Zero vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6558[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4412 -> 6558[label="",style="solid", color="burlywood", weight=9]; 6558 -> 4429[label="",style="solid", color="burlywood", weight=3]; 6559[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4412 -> 6559[label="",style="solid", color="burlywood", weight=9]; 6559 -> 4430[label="",style="solid", color="burlywood", weight=3]; 5013[label="vuz3400",fontsize=16,color="green",shape="box"];5014[label="vuz3410",fontsize=16,color="green",shape="box"];5015[label="Succ (primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339)))",fontsize=16,color="green",shape="box"];5015 -> 5039[label="",style="dashed", color="green", weight=3]; 5016[label="Zero",fontsize=16,color="green",shape="box"];5773 -> 4419[label="",style="dashed", color="red", weight=0]; 5773[label="gcd2 (primEqInt (Pos vuz347) (fromInt (Pos Zero))) (Pos vuz347) (Neg vuz71)",fontsize=16,color="magenta"];5773 -> 5792[label="",style="dashed", color="magenta", weight=3]; 5773 -> 5793[label="",style="dashed", color="magenta", weight=3]; 4420 -> 1354[label="",style="dashed", color="red", weight=0]; 4420[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4420 -> 4439[label="",style="dashed", color="magenta", weight=3]; 4420 -> 4440[label="",style="dashed", color="magenta", weight=3]; 4421 -> 1354[label="",style="dashed", color="red", weight=0]; 4421[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4421 -> 4441[label="",style="dashed", color="magenta", weight=3]; 4421 -> 4442[label="",style="dashed", color="magenta", weight=3]; 4419[label="gcd2 (primEqInt (Pos vuz309) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="triangle"];6560[label="vuz309/Succ vuz3090",fontsize=10,color="white",style="solid",shape="box"];4419 -> 6560[label="",style="solid", color="burlywood", weight=9]; 6560 -> 4443[label="",style="solid", color="burlywood", weight=3]; 6561[label="vuz309/Zero",fontsize=10,color="white",style="solid",shape="box"];4419 -> 6561[label="",style="solid", color="burlywood", weight=9]; 6561 -> 4444[label="",style="solid", color="burlywood", weight=3]; 4422[label="vuz71",fontsize=16,color="green",shape="box"];4423[label="vuz307",fontsize=16,color="green",shape="box"];4424[label="vuz291",fontsize=16,color="green",shape="box"];5774[label="gcd2 (primEqInt (Pos vuz348) (fromInt (Pos Zero))) (Pos vuz348) (Pos vuz74)",fontsize=16,color="burlywood",shape="triangle"];6562[label="vuz348/Succ vuz3480",fontsize=10,color="white",style="solid",shape="box"];5774 -> 6562[label="",style="solid", color="burlywood", weight=9]; 6562 -> 5794[label="",style="solid", color="burlywood", weight=3]; 6563[label="vuz348/Zero",fontsize=10,color="white",style="solid",shape="box"];5774 -> 6563[label="",style="solid", color="burlywood", weight=9]; 6563 -> 5795[label="",style="solid", color="burlywood", weight=3]; 6007[label="vuz370",fontsize=16,color="green",shape="box"];6008[label="vuz354",fontsize=16,color="green",shape="box"];6009[label="vuz74",fontsize=16,color="green",shape="box"];6010 -> 1354[label="",style="dashed", color="red", weight=0]; 6010[label="primPlusNat vuz356 vuz372",fontsize=16,color="magenta"];6010 -> 6032[label="",style="dashed", color="magenta", weight=3]; 6010 -> 6033[label="",style="dashed", color="magenta", weight=3]; 4185[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (fromInt (Pos Zero))) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4185 -> 4206[label="",style="solid", color="black", weight=3]; 4186[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4186 -> 4207[label="",style="solid", color="black", weight=3]; 6026[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6026 -> 6049[label="",style="solid", color="black", weight=3]; 6027[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6027 -> 6050[label="",style="solid", color="black", weight=3]; 6028[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6028 -> 6051[label="",style="solid", color="black", weight=3]; 6029[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6029 -> 6052[label="",style="solid", color="black", weight=3]; 6030[label="vuz368",fontsize=16,color="green",shape="box"];6031[label="vuz352",fontsize=16,color="green",shape="box"];4187[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (fromInt (Pos Zero))) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4187 -> 4208[label="",style="solid", color="black", weight=3]; 4188[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4188 -> 4209[label="",style="solid", color="black", weight=3]; 4425[label="vuz301",fontsize=16,color="green",shape="box"];4426[label="vuz285",fontsize=16,color="green",shape="box"];4427[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4427 -> 4455[label="",style="solid", color="black", weight=3]; 4428[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4428 -> 4456[label="",style="solid", color="black", weight=3]; 4429[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4429 -> 4457[label="",style="solid", color="black", weight=3]; 4430[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4430 -> 4458[label="",style="solid", color="black", weight=3]; 5039 -> 4129[label="",style="dashed", color="red", weight=0]; 5039[label="primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339))",fontsize=16,color="magenta"];5039 -> 5727[label="",style="dashed", color="magenta", weight=3]; 5039 -> 5728[label="",style="dashed", color="magenta", weight=3]; 5792[label="vuz347",fontsize=16,color="green",shape="box"];5793[label="vuz347",fontsize=16,color="green",shape="box"];4439[label="vuz305",fontsize=16,color="green",shape="box"];4440[label="vuz289",fontsize=16,color="green",shape="box"];4441[label="vuz305",fontsize=16,color="green",shape="box"];4442[label="vuz289",fontsize=16,color="green",shape="box"];4443[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4443 -> 4466[label="",style="solid", color="black", weight=3]; 4444[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4444 -> 4467[label="",style="solid", color="black", weight=3]; 5794[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (fromInt (Pos Zero))) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5794 -> 5814[label="",style="solid", color="black", weight=3]; 5795[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5795 -> 5815[label="",style="solid", color="black", weight=3]; 6032[label="vuz372",fontsize=16,color="green",shape="box"];6033[label="vuz356",fontsize=16,color="green",shape="box"];4206[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (Pos Zero)) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4206 -> 4289[label="",style="solid", color="black", weight=3]; 4207[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4207 -> 4290[label="",style="solid", color="black", weight=3]; 6049 -> 5956[label="",style="dashed", color="red", weight=0]; 6049[label="gcd2 (primEqInt (primMinusNat vuz3500 vuz3660) (fromInt (Pos Zero))) (primMinusNat vuz3500 vuz3660) (Pos vuz144)",fontsize=16,color="magenta"];6049 -> 6059[label="",style="dashed", color="magenta", weight=3]; 6049 -> 6060[label="",style="dashed", color="magenta", weight=3]; 6050 -> 5774[label="",style="dashed", color="red", weight=0]; 6050[label="gcd2 (primEqInt (Pos (Succ vuz3500)) (fromInt (Pos Zero))) (Pos (Succ vuz3500)) (Pos vuz144)",fontsize=16,color="magenta"];6050 -> 6061[label="",style="dashed", color="magenta", weight=3]; 6050 -> 6062[label="",style="dashed", color="magenta", weight=3]; 6051 -> 4166[label="",style="dashed", color="red", weight=0]; 6051[label="gcd2 (primEqInt (Neg (Succ vuz3660)) (fromInt (Pos Zero))) (Neg (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="magenta"];6051 -> 6063[label="",style="dashed", color="magenta", weight=3]; 6052 -> 5774[label="",style="dashed", color="red", weight=0]; 6052[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];6052 -> 6064[label="",style="dashed", color="magenta", weight=3]; 6052 -> 6065[label="",style="dashed", color="magenta", weight=3]; 4208[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (Pos Zero)) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4208 -> 4291[label="",style="solid", color="black", weight=3]; 4209[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4209 -> 4292[label="",style="solid", color="black", weight=3]; 4455 -> 4368[label="",style="dashed", color="red", weight=0]; 4455[label="gcd2 (primEqInt (primMinusNat vuz2870 vuz3030) (fromInt (Pos Zero))) (primMinusNat vuz2870 vuz3030) (Neg vuz68)",fontsize=16,color="magenta"];4455 -> 4478[label="",style="dashed", color="magenta", weight=3]; 4455 -> 4479[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4419[label="",style="dashed", color="red", weight=0]; 4456[label="gcd2 (primEqInt (Pos (Succ vuz2870)) (fromInt (Pos Zero))) (Pos (Succ vuz2870)) (Neg vuz68)",fontsize=16,color="magenta"];4456 -> 4480[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4481[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4482[label="",style="dashed", color="magenta", weight=3]; 4457 -> 4167[label="",style="dashed", color="red", weight=0]; 4457[label="gcd2 (primEqInt (Neg (Succ vuz3030)) (fromInt (Pos Zero))) (Neg (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="magenta"];4457 -> 4483[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4419[label="",style="dashed", color="red", weight=0]; 4458[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];4458 -> 4484[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4485[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4486[label="",style="dashed", color="magenta", weight=3]; 5727[label="Succ vuz339",fontsize=16,color="green",shape="box"];5728[label="primMinusNatS (Succ vuz338) (Succ vuz339)",fontsize=16,color="black",shape="box"];5728 -> 5743[label="",style="solid", color="black", weight=3]; 4466[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4466 -> 4494[label="",style="solid", color="black", weight=3]; 4467[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4467 -> 4495[label="",style="solid", color="black", weight=3]; 5814[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (Pos Zero)) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5814 -> 5890[label="",style="solid", color="black", weight=3]; 5815[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5815 -> 5891[label="",style="solid", color="black", weight=3]; 4289[label="gcd2 False (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4289 -> 4311[label="",style="solid", color="black", weight=3]; 4290[label="gcd2 True (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4290 -> 4312[label="",style="solid", color="black", weight=3]; 6059[label="vuz3500",fontsize=16,color="green",shape="box"];6060[label="vuz3660",fontsize=16,color="green",shape="box"];6061[label="Succ vuz3500",fontsize=16,color="green",shape="box"];6062[label="vuz144",fontsize=16,color="green",shape="box"];6063[label="Succ vuz3660",fontsize=16,color="green",shape="box"];6064[label="Zero",fontsize=16,color="green",shape="box"];6065[label="vuz144",fontsize=16,color="green",shape="box"];4291[label="gcd2 False (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4291 -> 4313[label="",style="solid", color="black", weight=3]; 4292[label="gcd2 True (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4292 -> 4314[label="",style="solid", color="black", weight=3]; 4478[label="vuz2870",fontsize=16,color="green",shape="box"];4479[label="vuz3030",fontsize=16,color="green",shape="box"];4480[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4481[label="vuz68",fontsize=16,color="green",shape="box"];4482[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4483[label="Succ vuz3030",fontsize=16,color="green",shape="box"];4484[label="Zero",fontsize=16,color="green",shape="box"];4485[label="vuz68",fontsize=16,color="green",shape="box"];4486[label="Zero",fontsize=16,color="green",shape="box"];5743[label="primMinusNatS vuz338 vuz339",fontsize=16,color="burlywood",shape="triangle"];6564[label="vuz338/Succ vuz3380",fontsize=10,color="white",style="solid",shape="box"];5743 -> 6564[label="",style="solid", color="burlywood", weight=9]; 6564 -> 5760[label="",style="solid", color="burlywood", weight=3]; 6565[label="vuz338/Zero",fontsize=10,color="white",style="solid",shape="box"];5743 -> 6565[label="",style="solid", color="burlywood", weight=9]; 6565 -> 5761[label="",style="solid", color="burlywood", weight=3]; 4494[label="gcd2 False (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4494 -> 4517[label="",style="solid", color="black", weight=3]; 4495[label="gcd2 True (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4495 -> 4518[label="",style="solid", color="black", weight=3]; 5890[label="gcd2 False (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5890 -> 5908[label="",style="solid", color="black", weight=3]; 5891[label="gcd2 True (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5891 -> 5909[label="",style="solid", color="black", weight=3]; 4311[label="gcd0 (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4311 -> 4402[label="",style="solid", color="black", weight=3]; 4312[label="gcd1 (Pos vuz144 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4312 -> 4403[label="",style="solid", color="black", weight=3]; 4313[label="gcd0 (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4313 -> 4404[label="",style="solid", color="black", weight=3]; 4314[label="gcd1 (Neg vuz68 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4314 -> 4405[label="",style="solid", color="black", weight=3]; 5760[label="primMinusNatS (Succ vuz3380) vuz339",fontsize=16,color="burlywood",shape="box"];6566[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5760 -> 6566[label="",style="solid", color="burlywood", weight=9]; 6566 -> 5775[label="",style="solid", color="burlywood", weight=3]; 6567[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5760 -> 6567[label="",style="solid", color="burlywood", weight=9]; 6567 -> 5776[label="",style="solid", color="burlywood", weight=3]; 5761[label="primMinusNatS Zero vuz339",fontsize=16,color="burlywood",shape="box"];6568[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5761 -> 6568[label="",style="solid", color="burlywood", weight=9]; 6568 -> 5777[label="",style="solid", color="burlywood", weight=3]; 6569[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5761 -> 6569[label="",style="solid", color="burlywood", weight=9]; 6569 -> 5778[label="",style="solid", color="burlywood", weight=3]; 4517[label="gcd0 (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4517 -> 4539[label="",style="solid", color="black", weight=3]; 4518[label="gcd1 (Neg vuz71 == fromInt (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4518 -> 4540[label="",style="solid", color="black", weight=3]; 5908[label="gcd0 (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5908 -> 5988[label="",style="solid", color="black", weight=3]; 5909[label="gcd1 (Pos vuz74 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5909 -> 5989[label="",style="solid", color="black", weight=3]; 4402 -> 6011[label="",style="dashed", color="red", weight=0]; 4402[label="gcd0Gcd' (abs (Neg (Succ vuz2820))) (abs (Pos vuz144))",fontsize=16,color="magenta"];4402 -> 6012[label="",style="dashed", color="magenta", weight=3]; 4402 -> 6013[label="",style="dashed", color="magenta", weight=3]; 4403[label="gcd1 (primEqInt (Pos vuz144) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6570[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6570[label="",style="solid", color="burlywood", weight=9]; 6570 -> 4446[label="",style="solid", color="burlywood", weight=3]; 6571[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6571[label="",style="solid", color="burlywood", weight=9]; 6571 -> 4447[label="",style="solid", color="burlywood", weight=3]; 4404 -> 6011[label="",style="dashed", color="red", weight=0]; 4404[label="gcd0Gcd' (abs (Neg (Succ vuz2830))) (abs (Neg vuz68))",fontsize=16,color="magenta"];4404 -> 6014[label="",style="dashed", color="magenta", weight=3]; 4404 -> 6015[label="",style="dashed", color="magenta", weight=3]; 4405[label="gcd1 (primEqInt (Neg vuz68) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6572[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];4405 -> 6572[label="",style="solid", color="burlywood", weight=9]; 6572 -> 4449[label="",style="solid", color="burlywood", weight=3]; 6573[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];4405 -> 6573[label="",style="solid", color="burlywood", weight=9]; 6573 -> 4450[label="",style="solid", color="burlywood", weight=3]; 5775[label="primMinusNatS (Succ vuz3380) (Succ vuz3390)",fontsize=16,color="black",shape="box"];5775 -> 5796[label="",style="solid", color="black", weight=3]; 5776[label="primMinusNatS (Succ vuz3380) Zero",fontsize=16,color="black",shape="box"];5776 -> 5797[label="",style="solid", color="black", weight=3]; 5777[label="primMinusNatS Zero (Succ vuz3390)",fontsize=16,color="black",shape="box"];5777 -> 5798[label="",style="solid", color="black", weight=3]; 5778[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];5778 -> 5799[label="",style="solid", color="black", weight=3]; 4539 -> 6011[label="",style="dashed", color="red", weight=0]; 4539[label="gcd0Gcd' (abs (Pos vuz308)) (abs (Neg vuz71))",fontsize=16,color="magenta"];4539 -> 6016[label="",style="dashed", color="magenta", weight=3]; 4539 -> 6017[label="",style="dashed", color="magenta", weight=3]; 4540[label="gcd1 (primEqInt (Neg vuz71) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6574[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];4540 -> 6574[label="",style="solid", color="burlywood", weight=9]; 6574 -> 4559[label="",style="solid", color="burlywood", weight=3]; 6575[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];4540 -> 6575[label="",style="solid", color="burlywood", weight=9]; 6575 -> 4560[label="",style="solid", color="burlywood", weight=3]; 5988 -> 6011[label="",style="dashed", color="red", weight=0]; 5988[label="gcd0Gcd' (abs (Pos (Succ vuz3480))) (abs (Pos vuz74))",fontsize=16,color="magenta"];5988 -> 6018[label="",style="dashed", color="magenta", weight=3]; 5988 -> 6019[label="",style="dashed", color="magenta", weight=3]; 5989[label="gcd1 (primEqInt (Pos vuz74) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6576[label="vuz74/Succ vuz740",fontsize=10,color="white",style="solid",shape="box"];5989 -> 6576[label="",style="solid", color="burlywood", weight=9]; 6576 -> 6034[label="",style="solid", color="burlywood", weight=3]; 6577[label="vuz74/Zero",fontsize=10,color="white",style="solid",shape="box"];5989 -> 6577[label="",style="solid", color="burlywood", weight=9]; 6577 -> 6035[label="",style="solid", color="burlywood", weight=3]; 6012[label="abs (Pos vuz144)",fontsize=16,color="black",shape="triangle"];6012 -> 6036[label="",style="solid", color="black", weight=3]; 6013[label="abs (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6013 -> 6037[label="",style="solid", color="black", weight=3]; 6011[label="gcd0Gcd' vuz374 vuz373",fontsize=16,color="black",shape="triangle"];6011 -> 6038[label="",style="solid", color="black", weight=3]; 4446[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4446 -> 4469[label="",style="solid", color="black", weight=3]; 4447[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4447 -> 4470[label="",style="solid", color="black", weight=3]; 6014[label="abs (Neg vuz68)",fontsize=16,color="black",shape="triangle"];6014 -> 6039[label="",style="solid", color="black", weight=3]; 6015 -> 6014[label="",style="dashed", color="red", weight=0]; 6015[label="abs (Neg (Succ vuz2830))",fontsize=16,color="magenta"];6015 -> 6040[label="",style="dashed", color="magenta", weight=3]; 4449[label="gcd1 (primEqInt (Neg (Succ vuz680)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4449 -> 4472[label="",style="solid", color="black", weight=3]; 4450[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4450 -> 4473[label="",style="solid", color="black", weight=3]; 5796 -> 5743[label="",style="dashed", color="red", weight=0]; 5796[label="primMinusNatS vuz3380 vuz3390",fontsize=16,color="magenta"];5796 -> 5816[label="",style="dashed", color="magenta", weight=3]; 5796 -> 5817[label="",style="dashed", color="magenta", weight=3]; 5797[label="Succ vuz3380",fontsize=16,color="green",shape="box"];5798[label="Zero",fontsize=16,color="green",shape="box"];5799[label="Zero",fontsize=16,color="green",shape="box"];6016 -> 6014[label="",style="dashed", color="red", weight=0]; 6016[label="abs (Neg vuz71)",fontsize=16,color="magenta"];6016 -> 6041[label="",style="dashed", color="magenta", weight=3]; 6017 -> 6012[label="",style="dashed", color="red", weight=0]; 6017[label="abs (Pos vuz308)",fontsize=16,color="magenta"];6017 -> 6042[label="",style="dashed", color="magenta", weight=3]; 4559[label="gcd1 (primEqInt (Neg (Succ vuz710)) (fromInt (Pos Zero))) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4559 -> 4579[label="",style="solid", color="black", weight=3]; 4560[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4560 -> 4580[label="",style="solid", color="black", weight=3]; 6018 -> 6012[label="",style="dashed", color="red", weight=0]; 6018[label="abs (Pos vuz74)",fontsize=16,color="magenta"];6018 -> 6043[label="",style="dashed", color="magenta", weight=3]; 6019 -> 6012[label="",style="dashed", color="red", weight=0]; 6019[label="abs (Pos (Succ vuz3480))",fontsize=16,color="magenta"];6019 -> 6044[label="",style="dashed", color="magenta", weight=3]; 6034[label="gcd1 (primEqInt (Pos (Succ vuz740)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6034 -> 6053[label="",style="solid", color="black", weight=3]; 6035[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6035 -> 6054[label="",style="solid", color="black", weight=3]; 6036[label="absReal (Pos vuz144)",fontsize=16,color="black",shape="box"];6036 -> 6055[label="",style="solid", color="black", weight=3]; 6037[label="absReal (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6037 -> 6056[label="",style="solid", color="black", weight=3]; 6038[label="gcd0Gcd'2 vuz374 vuz373",fontsize=16,color="black",shape="box"];6038 -> 6057[label="",style="solid", color="black", weight=3]; 4469[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4469 -> 4497[label="",style="solid", color="black", weight=3]; 4470[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4470 -> 4498[label="",style="solid", color="black", weight=3]; 6039[label="absReal (Neg vuz68)",fontsize=16,color="black",shape="box"];6039 -> 6058[label="",style="solid", color="black", weight=3]; 6040[label="Succ vuz2830",fontsize=16,color="green",shape="box"];4472[label="gcd1 (primEqInt (Neg (Succ vuz680)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4472 -> 4500[label="",style="solid", color="black", weight=3]; 4473[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4473 -> 4501[label="",style="solid", color="black", weight=3]; 5816[label="vuz3390",fontsize=16,color="green",shape="box"];5817[label="vuz3380",fontsize=16,color="green",shape="box"];6041[label="vuz71",fontsize=16,color="green",shape="box"];6042[label="vuz308",fontsize=16,color="green",shape="box"];4579[label="gcd1 (primEqInt (Neg (Succ vuz710)) (Pos Zero)) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4579 -> 4602[label="",style="solid", color="black", weight=3]; 4580[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4580 -> 4603[label="",style="solid", color="black", weight=3]; 6043[label="vuz74",fontsize=16,color="green",shape="box"];6044[label="Succ vuz3480",fontsize=16,color="green",shape="box"];6053[label="gcd1 (primEqInt (Pos (Succ vuz740)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6053 -> 6066[label="",style="solid", color="black", weight=3]; 6054[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6054 -> 6067[label="",style="solid", color="black", weight=3]; 6055[label="absReal2 (Pos vuz144)",fontsize=16,color="black",shape="box"];6055 -> 6068[label="",style="solid", color="black", weight=3]; 6056[label="absReal2 (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6056 -> 6069[label="",style="solid", color="black", weight=3]; 6057[label="gcd0Gcd'1 (vuz373 == fromInt (Pos Zero)) vuz374 vuz373",fontsize=16,color="black",shape="box"];6057 -> 6070[label="",style="solid", color="black", weight=3]; 4497[label="gcd1 False (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4497 -> 4520[label="",style="solid", color="black", weight=3]; 4498[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4498 -> 4521[label="",style="solid", color="black", weight=3]; 6058[label="absReal2 (Neg vuz68)",fontsize=16,color="black",shape="box"];6058 -> 6071[label="",style="solid", color="black", weight=3]; 4500[label="gcd1 False (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4500 -> 4523[label="",style="solid", color="black", weight=3]; 4501[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4501 -> 4524[label="",style="solid", color="black", weight=3]; 4602[label="gcd1 False (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4602 -> 4625[label="",style="solid", color="black", weight=3]; 4603[label="gcd1 True (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4603 -> 4626[label="",style="solid", color="black", weight=3]; 6066[label="gcd1 False (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6066 -> 6072[label="",style="solid", color="black", weight=3]; 6067[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6067 -> 6073[label="",style="solid", color="black", weight=3]; 6068[label="absReal1 (Pos vuz144) (Pos vuz144 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6068 -> 6074[label="",style="solid", color="black", weight=3]; 6069[label="absReal1 (Neg (Succ vuz2820)) (Neg (Succ vuz2820) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6069 -> 6075[label="",style="solid", color="black", weight=3]; 6070[label="gcd0Gcd'1 (primEqInt vuz373 (fromInt (Pos Zero))) vuz374 vuz373",fontsize=16,color="burlywood",shape="box"];6578[label="vuz373/Pos vuz3730",fontsize=10,color="white",style="solid",shape="box"];6070 -> 6578[label="",style="solid", color="burlywood", weight=9]; 6578 -> 6076[label="",style="solid", color="burlywood", weight=3]; 6579[label="vuz373/Neg vuz3730",fontsize=10,color="white",style="solid",shape="box"];6070 -> 6579[label="",style="solid", color="burlywood", weight=9]; 6579 -> 6077[label="",style="solid", color="burlywood", weight=3]; 4520[label="gcd0 (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4520 -> 4542[label="",style="solid", color="black", weight=3]; 4521 -> 4108[label="",style="dashed", color="red", weight=0]; 4521[label="error []",fontsize=16,color="magenta"];6071[label="absReal1 (Neg vuz68) (Neg vuz68 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6071 -> 6078[label="",style="solid", color="black", weight=3]; 4523[label="gcd0 (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4523 -> 4544[label="",style="solid", color="black", weight=3]; 4524 -> 4108[label="",style="dashed", color="red", weight=0]; 4524[label="error []",fontsize=16,color="magenta"];4625 -> 4517[label="",style="dashed", color="red", weight=0]; 4625[label="gcd0 (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="magenta"];4625 -> 4648[label="",style="dashed", color="magenta", weight=3]; 4626 -> 4108[label="",style="dashed", color="red", weight=0]; 4626[label="error []",fontsize=16,color="magenta"];6072[label="gcd0 (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6072 -> 6079[label="",style="solid", color="black", weight=3]; 6073 -> 4108[label="",style="dashed", color="red", weight=0]; 6073[label="error []",fontsize=16,color="magenta"];6074[label="absReal1 (Pos vuz144) (compare (Pos vuz144) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6074 -> 6080[label="",style="solid", color="black", weight=3]; 6075[label="absReal1 (Neg (Succ vuz2820)) (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6075 -> 6081[label="",style="solid", color="black", weight=3]; 6076[label="gcd0Gcd'1 (primEqInt (Pos vuz3730) (fromInt (Pos Zero))) vuz374 (Pos vuz3730)",fontsize=16,color="burlywood",shape="box"];6580[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6076 -> 6580[label="",style="solid", color="burlywood", weight=9]; 6580 -> 6082[label="",style="solid", color="burlywood", weight=3]; 6581[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6076 -> 6581[label="",style="solid", color="burlywood", weight=9]; 6581 -> 6083[label="",style="solid", color="burlywood", weight=3]; 6077[label="gcd0Gcd'1 (primEqInt (Neg vuz3730) (fromInt (Pos Zero))) vuz374 (Neg vuz3730)",fontsize=16,color="burlywood",shape="box"];6582[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6077 -> 6582[label="",style="solid", color="burlywood", weight=9]; 6582 -> 6084[label="",style="solid", color="burlywood", weight=3]; 6583[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6077 -> 6583[label="",style="solid", color="burlywood", weight=9]; 6583 -> 6085[label="",style="solid", color="burlywood", weight=3]; 4542 -> 6011[label="",style="dashed", color="red", weight=0]; 4542[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz1440)))",fontsize=16,color="magenta"];4542 -> 6020[label="",style="dashed", color="magenta", weight=3]; 4542 -> 6021[label="",style="dashed", color="magenta", weight=3]; 6078[label="absReal1 (Neg vuz68) (compare (Neg vuz68) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6078 -> 6086[label="",style="solid", color="black", weight=3]; 4544 -> 6011[label="",style="dashed", color="red", weight=0]; 4544[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz680)))",fontsize=16,color="magenta"];4544 -> 6022[label="",style="dashed", color="magenta", weight=3]; 4544 -> 6023[label="",style="dashed", color="magenta", weight=3]; 4648[label="Succ vuz710",fontsize=16,color="green",shape="box"];6079 -> 6011[label="",style="dashed", color="red", weight=0]; 6079[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz740)))",fontsize=16,color="magenta"];6079 -> 6087[label="",style="dashed", color="magenta", weight=3]; 6079 -> 6088[label="",style="dashed", color="magenta", weight=3]; 6080[label="absReal1 (Pos vuz144) (not (compare (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6080 -> 6089[label="",style="solid", color="black", weight=3]; 6081[label="absReal1 (Neg (Succ vuz2820)) (not (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6081 -> 6090[label="",style="solid", color="black", weight=3]; 6082[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6082 -> 6091[label="",style="solid", color="black", weight=3]; 6083[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6083 -> 6092[label="",style="solid", color="black", weight=3]; 6084[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6084 -> 6093[label="",style="solid", color="black", weight=3]; 6085[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6085 -> 6094[label="",style="solid", color="black", weight=3]; 6020 -> 6012[label="",style="dashed", color="red", weight=0]; 6020[label="abs (Pos (Succ vuz1440))",fontsize=16,color="magenta"];6020 -> 6045[label="",style="dashed", color="magenta", weight=3]; 6021 -> 6014[label="",style="dashed", color="red", weight=0]; 6021[label="abs (Neg Zero)",fontsize=16,color="magenta"];6021 -> 6046[label="",style="dashed", color="magenta", weight=3]; 6086[label="absReal1 (Neg vuz68) (not (compare (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6086 -> 6095[label="",style="solid", color="black", weight=3]; 6022 -> 6014[label="",style="dashed", color="red", weight=0]; 6022[label="abs (Neg (Succ vuz680))",fontsize=16,color="magenta"];6022 -> 6047[label="",style="dashed", color="magenta", weight=3]; 6023 -> 6014[label="",style="dashed", color="red", weight=0]; 6023[label="abs (Neg Zero)",fontsize=16,color="magenta"];6023 -> 6048[label="",style="dashed", color="magenta", weight=3]; 6087 -> 6012[label="",style="dashed", color="red", weight=0]; 6087[label="abs (Pos (Succ vuz740))",fontsize=16,color="magenta"];6087 -> 6096[label="",style="dashed", color="magenta", weight=3]; 6088 -> 6012[label="",style="dashed", color="red", weight=0]; 6088[label="abs (Pos Zero)",fontsize=16,color="magenta"];6088 -> 6097[label="",style="dashed", color="magenta", weight=3]; 6089[label="absReal1 (Pos vuz144) (not (primCmpInt (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6584[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];6089 -> 6584[label="",style="solid", color="burlywood", weight=9]; 6584 -> 6098[label="",style="solid", color="burlywood", weight=3]; 6585[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];6089 -> 6585[label="",style="solid", color="burlywood", weight=9]; 6585 -> 6099[label="",style="solid", color="burlywood", weight=3]; 6090[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6090 -> 6100[label="",style="solid", color="black", weight=3]; 6091[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (Pos Zero)) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6091 -> 6101[label="",style="solid", color="black", weight=3]; 6092[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6092 -> 6102[label="",style="solid", color="black", weight=3]; 6093[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (Pos Zero)) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6093 -> 6103[label="",style="solid", color="black", weight=3]; 6094[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6094 -> 6104[label="",style="solid", color="black", weight=3]; 6045[label="Succ vuz1440",fontsize=16,color="green",shape="box"];6046[label="Zero",fontsize=16,color="green",shape="box"];6095[label="absReal1 (Neg vuz68) (not (primCmpInt (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6586[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];6095 -> 6586[label="",style="solid", color="burlywood", weight=9]; 6586 -> 6105[label="",style="solid", color="burlywood", weight=3]; 6587[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];6095 -> 6587[label="",style="solid", color="burlywood", weight=9]; 6587 -> 6106[label="",style="solid", color="burlywood", weight=3]; 6047[label="Succ vuz680",fontsize=16,color="green",shape="box"];6048[label="Zero",fontsize=16,color="green",shape="box"];6096[label="Succ vuz740",fontsize=16,color="green",shape="box"];6097[label="Zero",fontsize=16,color="green",shape="box"];6098[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6098 -> 6107[label="",style="solid", color="black", weight=3]; 6099[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6099 -> 6108[label="",style="solid", color="black", weight=3]; 6100[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];6100 -> 6109[label="",style="solid", color="black", weight=3]; 6101[label="gcd0Gcd'1 False vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6101 -> 6110[label="",style="solid", color="black", weight=3]; 6102[label="gcd0Gcd'1 True vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6102 -> 6111[label="",style="solid", color="black", weight=3]; 6103[label="gcd0Gcd'1 False vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6103 -> 6112[label="",style="solid", color="black", weight=3]; 6104[label="gcd0Gcd'1 True vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6104 -> 6113[label="",style="solid", color="black", weight=3]; 6105[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6105 -> 6114[label="",style="solid", color="black", weight=3]; 6106[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6106 -> 6115[label="",style="solid", color="black", weight=3]; 6107[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6107 -> 6116[label="",style="solid", color="black", weight=3]; 6108[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6108 -> 6117[label="",style="solid", color="black", weight=3]; 6109[label="absReal1 (Neg (Succ vuz2820)) (not (LT == LT))",fontsize=16,color="black",shape="box"];6109 -> 6118[label="",style="solid", color="black", weight=3]; 6110[label="gcd0Gcd'0 vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6110 -> 6119[label="",style="solid", color="black", weight=3]; 6111[label="vuz374",fontsize=16,color="green",shape="box"];6112[label="gcd0Gcd'0 vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6112 -> 6120[label="",style="solid", color="black", weight=3]; 6113[label="vuz374",fontsize=16,color="green",shape="box"];6114 -> 6100[label="",style="dashed", color="red", weight=0]; 6114[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (Pos Zero) == LT))",fontsize=16,color="magenta"];6114 -> 6121[label="",style="dashed", color="magenta", weight=3]; 6115[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6115 -> 6122[label="",style="solid", color="black", weight=3]; 6116[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpNat (Succ vuz1440) Zero == LT))",fontsize=16,color="black",shape="box"];6116 -> 6123[label="",style="solid", color="black", weight=3]; 6117[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6117 -> 6124[label="",style="solid", color="black", weight=3]; 6118[label="absReal1 (Neg (Succ vuz2820)) (not True)",fontsize=16,color="black",shape="box"];6118 -> 6125[label="",style="solid", color="black", weight=3]; 6119 -> 6011[label="",style="dashed", color="red", weight=0]; 6119[label="gcd0Gcd' (Pos (Succ vuz37300)) (vuz374 `rem` Pos (Succ vuz37300))",fontsize=16,color="magenta"];6119 -> 6126[label="",style="dashed", color="magenta", weight=3]; 6119 -> 6127[label="",style="dashed", color="magenta", weight=3]; 6120 -> 6011[label="",style="dashed", color="red", weight=0]; 6120[label="gcd0Gcd' (Neg (Succ vuz37300)) (vuz374 `rem` Neg (Succ vuz37300))",fontsize=16,color="magenta"];6120 -> 6128[label="",style="dashed", color="magenta", weight=3]; 6120 -> 6129[label="",style="dashed", color="magenta", weight=3]; 6121[label="vuz680",fontsize=16,color="green",shape="box"];6122[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6122 -> 6130[label="",style="solid", color="black", weight=3]; 6123[label="absReal1 (Pos (Succ vuz1440)) (not (GT == LT))",fontsize=16,color="black",shape="box"];6123 -> 6131[label="",style="solid", color="black", weight=3]; 6124[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];6124 -> 6132[label="",style="solid", color="black", weight=3]; 6125[label="absReal1 (Neg (Succ vuz2820)) False",fontsize=16,color="black",shape="box"];6125 -> 6133[label="",style="solid", color="black", weight=3]; 6126[label="vuz374 `rem` Pos (Succ vuz37300)",fontsize=16,color="black",shape="box"];6126 -> 6134[label="",style="solid", color="black", weight=3]; 6127[label="Pos (Succ vuz37300)",fontsize=16,color="green",shape="box"];6128[label="vuz374 `rem` Neg (Succ vuz37300)",fontsize=16,color="black",shape="box"];6128 -> 6135[label="",style="solid", color="black", weight=3]; 6129[label="Neg (Succ vuz37300)",fontsize=16,color="green",shape="box"];6130[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];6130 -> 6136[label="",style="solid", color="black", weight=3]; 6131[label="absReal1 (Pos (Succ vuz1440)) (not False)",fontsize=16,color="black",shape="box"];6131 -> 6137[label="",style="solid", color="black", weight=3]; 6132[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];6132 -> 6138[label="",style="solid", color="black", weight=3]; 6133[label="absReal0 (Neg (Succ vuz2820)) otherwise",fontsize=16,color="black",shape="box"];6133 -> 6139[label="",style="solid", color="black", weight=3]; 6134[label="primRemInt vuz374 (Pos (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6588[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6134 -> 6588[label="",style="solid", color="burlywood", weight=9]; 6588 -> 6140[label="",style="solid", color="burlywood", weight=3]; 6589[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6134 -> 6589[label="",style="solid", color="burlywood", weight=9]; 6589 -> 6141[label="",style="solid", color="burlywood", weight=3]; 6135[label="primRemInt vuz374 (Neg (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6590[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6135 -> 6590[label="",style="solid", color="burlywood", weight=9]; 6590 -> 6142[label="",style="solid", color="burlywood", weight=3]; 6591[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6135 -> 6591[label="",style="solid", color="burlywood", weight=9]; 6591 -> 6143[label="",style="solid", color="burlywood", weight=3]; 6136[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];6136 -> 6144[label="",style="solid", color="black", weight=3]; 6137[label="absReal1 (Pos (Succ vuz1440)) True",fontsize=16,color="black",shape="box"];6137 -> 6145[label="",style="solid", color="black", weight=3]; 6138[label="Pos Zero",fontsize=16,color="green",shape="box"];6139[label="absReal0 (Neg (Succ vuz2820)) True",fontsize=16,color="black",shape="box"];6139 -> 6146[label="",style="solid", color="black", weight=3]; 6140[label="primRemInt (Pos vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6140 -> 6147[label="",style="solid", color="black", weight=3]; 6141[label="primRemInt (Neg vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6141 -> 6148[label="",style="solid", color="black", weight=3]; 6142[label="primRemInt (Pos vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6142 -> 6149[label="",style="solid", color="black", weight=3]; 6143[label="primRemInt (Neg vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6143 -> 6150[label="",style="solid", color="black", weight=3]; 6144[label="Neg Zero",fontsize=16,color="green",shape="box"];6145[label="Pos (Succ vuz1440)",fontsize=16,color="green",shape="box"];6146[label="`negate` Neg (Succ vuz2820)",fontsize=16,color="black",shape="box"];6146 -> 6151[label="",style="solid", color="black", weight=3]; 6147[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6147 -> 6152[label="",style="dashed", color="green", weight=3]; 6148[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6148 -> 6153[label="",style="dashed", color="green", weight=3]; 6149[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6149 -> 6154[label="",style="dashed", color="green", weight=3]; 6150[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6150 -> 6155[label="",style="dashed", color="green", weight=3]; 6151[label="primNegInt (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6151 -> 6156[label="",style="solid", color="black", weight=3]; 6152[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="burlywood",shape="triangle"];6592[label="vuz3740/Succ vuz37400",fontsize=10,color="white",style="solid",shape="box"];6152 -> 6592[label="",style="solid", color="burlywood", weight=9]; 6592 -> 6157[label="",style="solid", color="burlywood", weight=3]; 6593[label="vuz3740/Zero",fontsize=10,color="white",style="solid",shape="box"];6152 -> 6593[label="",style="solid", color="burlywood", weight=9]; 6593 -> 6158[label="",style="solid", color="burlywood", weight=3]; 6153 -> 6152[label="",style="dashed", color="red", weight=0]; 6153[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6153 -> 6159[label="",style="dashed", color="magenta", weight=3]; 6154 -> 6152[label="",style="dashed", color="red", weight=0]; 6154[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6154 -> 6160[label="",style="dashed", color="magenta", weight=3]; 6155 -> 6152[label="",style="dashed", color="red", weight=0]; 6155[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6155 -> 6161[label="",style="dashed", color="magenta", weight=3]; 6155 -> 6162[label="",style="dashed", color="magenta", weight=3]; 6156[label="Pos (Succ vuz2820)",fontsize=16,color="green",shape="box"];6157[label="primModNatS (Succ vuz37400) (Succ vuz37300)",fontsize=16,color="black",shape="box"];6157 -> 6163[label="",style="solid", color="black", weight=3]; 6158[label="primModNatS Zero (Succ vuz37300)",fontsize=16,color="black",shape="box"];6158 -> 6164[label="",style="solid", color="black", weight=3]; 6159[label="vuz3740",fontsize=16,color="green",shape="box"];6160[label="vuz37300",fontsize=16,color="green",shape="box"];6161[label="vuz37300",fontsize=16,color="green",shape="box"];6162[label="vuz3740",fontsize=16,color="green",shape="box"];6163[label="primModNatS0 vuz37400 vuz37300 (primGEqNatS vuz37400 vuz37300)",fontsize=16,color="burlywood",shape="box"];6594[label="vuz37400/Succ vuz374000",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6594[label="",style="solid", color="burlywood", weight=9]; 6594 -> 6165[label="",style="solid", color="burlywood", weight=3]; 6595[label="vuz37400/Zero",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6595[label="",style="solid", color="burlywood", weight=9]; 6595 -> 6166[label="",style="solid", color="burlywood", weight=3]; 6164[label="Zero",fontsize=16,color="green",shape="box"];6165[label="primModNatS0 (Succ vuz374000) vuz37300 (primGEqNatS (Succ vuz374000) vuz37300)",fontsize=16,color="burlywood",shape="box"];6596[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6165 -> 6596[label="",style="solid", color="burlywood", weight=9]; 6596 -> 6167[label="",style="solid", color="burlywood", weight=3]; 6597[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6165 -> 6597[label="",style="solid", color="burlywood", weight=9]; 6597 -> 6168[label="",style="solid", color="burlywood", weight=3]; 6166[label="primModNatS0 Zero vuz37300 (primGEqNatS Zero vuz37300)",fontsize=16,color="burlywood",shape="box"];6598[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6166 -> 6598[label="",style="solid", color="burlywood", weight=9]; 6598 -> 6169[label="",style="solid", color="burlywood", weight=3]; 6599[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6166 -> 6599[label="",style="solid", color="burlywood", weight=9]; 6599 -> 6170[label="",style="solid", color="burlywood", weight=3]; 6167[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS (Succ vuz374000) (Succ vuz373000))",fontsize=16,color="black",shape="box"];6167 -> 6171[label="",style="solid", color="black", weight=3]; 6168[label="primModNatS0 (Succ vuz374000) Zero (primGEqNatS (Succ vuz374000) Zero)",fontsize=16,color="black",shape="box"];6168 -> 6172[label="",style="solid", color="black", weight=3]; 6169[label="primModNatS0 Zero (Succ vuz373000) (primGEqNatS Zero (Succ vuz373000))",fontsize=16,color="black",shape="box"];6169 -> 6173[label="",style="solid", color="black", weight=3]; 6170[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6170 -> 6174[label="",style="solid", color="black", weight=3]; 6171 -> 6333[label="",style="dashed", color="red", weight=0]; 6171[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS vuz374000 vuz373000)",fontsize=16,color="magenta"];6171 -> 6334[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6335[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6336[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6337[label="",style="dashed", color="magenta", weight=3]; 6172[label="primModNatS0 (Succ vuz374000) Zero True",fontsize=16,color="black",shape="box"];6172 -> 6177[label="",style="solid", color="black", weight=3]; 6173[label="primModNatS0 Zero (Succ vuz373000) False",fontsize=16,color="black",shape="box"];6173 -> 6178[label="",style="solid", color="black", weight=3]; 6174[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];6174 -> 6179[label="",style="solid", color="black", weight=3]; 6334[label="vuz373000",fontsize=16,color="green",shape="box"];6335[label="vuz373000",fontsize=16,color="green",shape="box"];6336[label="vuz374000",fontsize=16,color="green",shape="box"];6337[label="vuz374000",fontsize=16,color="green",shape="box"];6333[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz393 vuz394)",fontsize=16,color="burlywood",shape="triangle"];6600[label="vuz393/Succ vuz3930",fontsize=10,color="white",style="solid",shape="box"];6333 -> 6600[label="",style="solid", color="burlywood", weight=9]; 6600 -> 6366[label="",style="solid", color="burlywood", weight=3]; 6601[label="vuz393/Zero",fontsize=10,color="white",style="solid",shape="box"];6333 -> 6601[label="",style="solid", color="burlywood", weight=9]; 6601 -> 6367[label="",style="solid", color="burlywood", weight=3]; 6177 -> 6152[label="",style="dashed", color="red", weight=0]; 6177[label="primModNatS (primMinusNatS (Succ vuz374000) Zero) (Succ Zero)",fontsize=16,color="magenta"];6177 -> 6184[label="",style="dashed", color="magenta", weight=3]; 6177 -> 6185[label="",style="dashed", color="magenta", weight=3]; 6178[label="Succ Zero",fontsize=16,color="green",shape="box"];6179 -> 6152[label="",style="dashed", color="red", weight=0]; 6179[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];6179 -> 6186[label="",style="dashed", color="magenta", weight=3]; 6179 -> 6187[label="",style="dashed", color="magenta", weight=3]; 6366[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) vuz394)",fontsize=16,color="burlywood",shape="box"];6602[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6366 -> 6602[label="",style="solid", color="burlywood", weight=9]; 6602 -> 6368[label="",style="solid", color="burlywood", weight=3]; 6603[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6366 -> 6603[label="",style="solid", color="burlywood", weight=9]; 6603 -> 6369[label="",style="solid", color="burlywood", weight=3]; 6367[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero vuz394)",fontsize=16,color="burlywood",shape="box"];6604[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6367 -> 6604[label="",style="solid", color="burlywood", weight=9]; 6604 -> 6370[label="",style="solid", color="burlywood", weight=3]; 6605[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6367 -> 6605[label="",style="solid", color="burlywood", weight=9]; 6605 -> 6371[label="",style="solid", color="burlywood", weight=3]; 6184[label="Zero",fontsize=16,color="green",shape="box"];6185 -> 5743[label="",style="dashed", color="red", weight=0]; 6185[label="primMinusNatS (Succ vuz374000) Zero",fontsize=16,color="magenta"];6185 -> 6192[label="",style="dashed", color="magenta", weight=3]; 6185 -> 6193[label="",style="dashed", color="magenta", weight=3]; 6186[label="Zero",fontsize=16,color="green",shape="box"];6187 -> 5743[label="",style="dashed", color="red", weight=0]; 6187[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];6187 -> 6194[label="",style="dashed", color="magenta", weight=3]; 6187 -> 6195[label="",style="dashed", color="magenta", weight=3]; 6368[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) (Succ vuz3940))",fontsize=16,color="black",shape="box"];6368 -> 6372[label="",style="solid", color="black", weight=3]; 6369[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) Zero)",fontsize=16,color="black",shape="box"];6369 -> 6373[label="",style="solid", color="black", weight=3]; 6370[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero (Succ vuz3940))",fontsize=16,color="black",shape="box"];6370 -> 6374[label="",style="solid", color="black", weight=3]; 6371[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6371 -> 6375[label="",style="solid", color="black", weight=3]; 6192[label="Zero",fontsize=16,color="green",shape="box"];6193[label="Succ vuz374000",fontsize=16,color="green",shape="box"];6194[label="Zero",fontsize=16,color="green",shape="box"];6195[label="Zero",fontsize=16,color="green",shape="box"];6372 -> 6333[label="",style="dashed", color="red", weight=0]; 6372[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz3930 vuz3940)",fontsize=16,color="magenta"];6372 -> 6376[label="",style="dashed", color="magenta", weight=3]; 6372 -> 6377[label="",style="dashed", color="magenta", weight=3]; 6373[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="black",shape="triangle"];6373 -> 6378[label="",style="solid", color="black", weight=3]; 6374[label="primModNatS0 (Succ vuz391) (Succ vuz392) False",fontsize=16,color="black",shape="box"];6374 -> 6379[label="",style="solid", color="black", weight=3]; 6375 -> 6373[label="",style="dashed", color="red", weight=0]; 6375[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="magenta"];6376[label="vuz3940",fontsize=16,color="green",shape="box"];6377[label="vuz3930",fontsize=16,color="green",shape="box"];6378 -> 6152[label="",style="dashed", color="red", weight=0]; 6378[label="primModNatS (primMinusNatS (Succ vuz391) (Succ vuz392)) (Succ (Succ vuz392))",fontsize=16,color="magenta"];6378 -> 6380[label="",style="dashed", color="magenta", weight=3]; 6378 -> 6381[label="",style="dashed", color="magenta", weight=3]; 6379[label="Succ (Succ vuz391)",fontsize=16,color="green",shape="box"];6380[label="Succ vuz392",fontsize=16,color="green",shape="box"];6381 -> 5743[label="",style="dashed", color="red", weight=0]; 6381[label="primMinusNatS (Succ vuz391) (Succ vuz392)",fontsize=16,color="magenta"];6381 -> 6382[label="",style="dashed", color="magenta", weight=3]; 6381 -> 6383[label="",style="dashed", color="magenta", weight=3]; 6382[label="Succ vuz392",fontsize=16,color="green",shape="box"];6383[label="Succ vuz391",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vuz410000), vuz3100) -> new_primMulNat(vuz410000, vuz3100) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primMulNat(Succ(vuz410000), vuz3100) -> new_primMulNat(vuz410000, vuz3100) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (19) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) the following chains were created: *We consider the chain new_gcd0Gcd'(x0, Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1)), new_gcd0Gcd'(x2, Pos(Succ(x3))) -> new_gcd0Gcd'(Pos(Succ(x3)), new_primRemInt(x2, x3)) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))=new_gcd0Gcd'(x2, Pos(Succ(x3))) ==> new_gcd0Gcd'(x0, Pos(Succ(x1)))_>=_new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt(x0, x1)=Pos(Succ(x3)) ==> new_gcd0Gcd'(x0, Pos(Succ(x1)))_>=_new_gcd0Gcd'(Pos(Succ(x1)), new_primRemInt(x0, x1))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt(x0, x1)=Pos(Succ(x3)) which results in the following new constraint: (3) (Pos(new_primModNatS1(x17, x16))=Pos(Succ(x3)) ==> new_gcd0Gcd'(Pos(x17), Pos(Succ(x16)))_>=_new_gcd0Gcd'(Pos(Succ(x16)), new_primRemInt(Pos(x17), x16))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x17, x16)=Succ(x3) ==> new_gcd0Gcd'(Pos(x17), Pos(Succ(x16)))_>=_new_gcd0Gcd'(Pos(Succ(x16)), new_primRemInt(Pos(x17), x16))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x17, x16)=Succ(x3) which results in the following new constraints: (5) (Succ(Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x21), Zero), Zero)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) (8) (new_primModNatS02(x24, x23, x24, x23)=Succ(x3) ==> new_gcd0Gcd'(Pos(Succ(Succ(x24))), Pos(Succ(Succ(x23))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x23))), new_primRemInt(Pos(Succ(Succ(x24))), Succ(x23)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Pos(Succ(Succ(x33))), Pos(Succ(Succ(x34))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x34))), new_primRemInt(Pos(Succ(Succ(x33))), Succ(x34)))) *We consider the chain new_gcd0Gcd'(x4, Pos(Succ(x5))) -> new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5)), new_gcd0Gcd'(x6, Neg(Succ(x7))) -> new_gcd0Gcd'(Neg(Succ(x7)), new_primRemInt0(x6, x7)) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))=new_gcd0Gcd'(x6, Neg(Succ(x7))) ==> new_gcd0Gcd'(x4, Pos(Succ(x5)))_>=_new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt(x4, x5)=Neg(Succ(x7)) ==> new_gcd0Gcd'(x4, Pos(Succ(x5)))_>=_new_gcd0Gcd'(Pos(Succ(x5)), new_primRemInt(x4, x5))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt(x4, x5)=Neg(Succ(x7)) which results in the following new constraint: (3) (Neg(new_primModNatS1(x38, x37))=Neg(Succ(x7)) ==> new_gcd0Gcd'(Neg(x38), Pos(Succ(x37)))_>=_new_gcd0Gcd'(Pos(Succ(x37)), new_primRemInt(Neg(x38), x37))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x38, x37)=Succ(x7) ==> new_gcd0Gcd'(Neg(x38), Pos(Succ(x37)))_>=_new_gcd0Gcd'(Pos(Succ(x37)), new_primRemInt(Neg(x38), x37))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x38, x37)=Succ(x7) which results in the following new constraints: (5) (Succ(Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x40), Zero), Zero)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) (8) (new_primModNatS02(x43, x42, x43, x42)=Succ(x7) ==> new_gcd0Gcd'(Neg(Succ(Succ(x43))), Pos(Succ(Succ(x42))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x42))), new_primRemInt(Neg(Succ(Succ(x43))), Succ(x42)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Succ(x53))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x53))), new_primRemInt(Neg(Succ(Succ(x52))), Succ(x53)))) For Pair new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) the following chains were created: *We consider the chain new_gcd0Gcd'(x8, Neg(Succ(x9))) -> new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9)), new_gcd0Gcd'(x10, Pos(Succ(x11))) -> new_gcd0Gcd'(Pos(Succ(x11)), new_primRemInt(x10, x11)) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))=new_gcd0Gcd'(x10, Pos(Succ(x11))) ==> new_gcd0Gcd'(x8, Neg(Succ(x9)))_>=_new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt0(x8, x9)=Pos(Succ(x11)) ==> new_gcd0Gcd'(x8, Neg(Succ(x9)))_>=_new_gcd0Gcd'(Neg(Succ(x9)), new_primRemInt0(x8, x9))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt0(x8, x9)=Pos(Succ(x11)) which results in the following new constraint: (3) (Pos(new_primModNatS1(x57, x56))=Pos(Succ(x11)) ==> new_gcd0Gcd'(Pos(x57), Neg(Succ(x56)))_>=_new_gcd0Gcd'(Neg(Succ(x56)), new_primRemInt0(Pos(x57), x56))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x57, x56)=Succ(x11) ==> new_gcd0Gcd'(Pos(x57), Neg(Succ(x56)))_>=_new_gcd0Gcd'(Neg(Succ(x56)), new_primRemInt0(Pos(x57), x56))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x57, x56)=Succ(x11) which results in the following new constraints: (5) (Succ(Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x59), Zero), Zero)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) (8) (new_primModNatS02(x62, x61, x62, x61)=Succ(x11) ==> new_gcd0Gcd'(Pos(Succ(Succ(x62))), Neg(Succ(Succ(x61))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x61))), new_primRemInt0(Pos(Succ(Succ(x62))), Succ(x61)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Pos(Succ(Succ(x71))), Neg(Succ(Succ(x72))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x72))), new_primRemInt0(Pos(Succ(Succ(x71))), Succ(x72)))) *We consider the chain new_gcd0Gcd'(x12, Neg(Succ(x13))) -> new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13)), new_gcd0Gcd'(x14, Neg(Succ(x15))) -> new_gcd0Gcd'(Neg(Succ(x15)), new_primRemInt0(x14, x15)) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))=new_gcd0Gcd'(x14, Neg(Succ(x15))) ==> new_gcd0Gcd'(x12, Neg(Succ(x13)))_>=_new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))) We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint: (2) (new_primRemInt0(x12, x13)=Neg(Succ(x15)) ==> new_gcd0Gcd'(x12, Neg(Succ(x13)))_>=_new_gcd0Gcd'(Neg(Succ(x13)), new_primRemInt0(x12, x13))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primRemInt0(x12, x13)=Neg(Succ(x15)) which results in the following new constraint: (3) (Neg(new_primModNatS1(x74, x73))=Neg(Succ(x15)) ==> new_gcd0Gcd'(Neg(x74), Neg(Succ(x73)))_>=_new_gcd0Gcd'(Neg(Succ(x73)), new_primRemInt0(Neg(x74), x73))) We simplified constraint (3) using rules (I), (II) which results in the following new constraint: (4) (new_primModNatS1(x74, x73)=Succ(x15) ==> new_gcd0Gcd'(Neg(x74), Neg(Succ(x73)))_>=_new_gcd0Gcd'(Neg(Succ(x73)), new_primRemInt0(Neg(x74), x73))) We simplified constraint (4) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x74, x73)=Succ(x15) which results in the following new constraints: (5) (Succ(Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) (6) (new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) (7) (new_primModNatS1(new_primMinusNatS0(Succ(x78), Zero), Zero)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) (8) (new_primModNatS02(x81, x80, x81, x80)=Succ(x15) ==> new_gcd0Gcd'(Neg(Succ(Succ(x81))), Neg(Succ(Succ(x80))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x80))), new_primRemInt0(Neg(Succ(Succ(x81))), Succ(x80)))) We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (9) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) We simplified constraint (6) using rules (III), (IV), (VII) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) We simplified constraint (8) using rules (III), (IV), (VII) which results in the following new constraint: (12) (new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Succ(x91))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x91))), new_primRemInt0(Neg(Succ(Succ(x90))), Succ(x91)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) *(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x20))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x20))), new_primRemInt(Pos(Succ(Zero)), Succ(x20)))) *(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x21))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Pos(Succ(Succ(x21))), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x33))), Pos(Succ(Succ(x34))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x34))), new_primRemInt(Pos(Succ(Succ(x33))), Succ(x34)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x39))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x39))), new_primRemInt(Neg(Succ(Zero)), Succ(x39)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x40))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'(Pos(Succ(Zero)), new_primRemInt(Neg(Succ(Succ(x40))), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Succ(x53))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x53))), new_primRemInt(Neg(Succ(Succ(x52))), Succ(x53)))) *new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) *(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x58))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x58))), new_primRemInt0(Pos(Succ(Zero)), Succ(x58)))) *(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x59))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Pos(Succ(Succ(x59))), Zero))) *(new_gcd0Gcd'(Pos(Succ(Succ(x71))), Neg(Succ(Succ(x72))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x72))), new_primRemInt0(Pos(Succ(Succ(x71))), Succ(x72)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x77))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x77))), new_primRemInt0(Neg(Succ(Zero)), Succ(x77)))) *(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Zero)), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x78))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'(Neg(Succ(Zero)), new_primRemInt0(Neg(Succ(Succ(x78))), Zero))) *(new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Succ(x91))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x91))), new_primRemInt0(Neg(Succ(Succ(x90))), Succ(x91)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(vuz374, Pos(Succ(vuz37300))) -> new_gcd0Gcd'(Pos(Succ(vuz37300)), new_primRemInt(vuz374, vuz37300)) at position [1] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))) (new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))) ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (24) Complex Obligation (AND) ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt(Pos(x0), x1) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1)))) ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (33) Complex Obligation (AND) ---------------------------------------- (34) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (35) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1) ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (42) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (43) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (47) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (49) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (52) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (53) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) ---------------------------------------- (54) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (55) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (56) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (57) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (58) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (59) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (60) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (61) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Pos(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 *new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (62) YES ---------------------------------------- (63) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (65) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (66) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))) ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (69) Complex Obligation (AND) ---------------------------------------- (70) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (71) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (72) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (73) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (75) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (78) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (79) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (80) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (81) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (84) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (85) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero)))) ---------------------------------------- (86) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (87) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (89) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Pos(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 1 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (90) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (91) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (92) TRUE ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (97) Complex Obligation (AND) ---------------------------------------- (98) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (99) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (100) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (101) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (102) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (103) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (104) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (105) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (106) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (107) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (110) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (111) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (112) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (113) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (114) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (115) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (116) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (117) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Pos(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 3 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 3 + x_1 POL(new_primModNatS1(x_1, x_2)) = 2 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (118) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (119) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (120) TRUE ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1))), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x0))=x4 & Succ(Succ(x1))=x5 & new_primModNatS02(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1))))), Pos(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (3) (new_primModNatS01(x8, x7)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x6)))=x8 & Succ(Succ(Zero))=x7 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) (4) (new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x10)))=x12 & Succ(Succ(Succ(x9)))=x11 & (\/x13:new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x13)))) & Succ(Succ(x10))=x12 & Succ(Succ(x9))=x11 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x10))))), Pos(Succ(Succ(Succ(Succ(x9))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x9))))), Pos(new_primModNatS02(Succ(Succ(x10)), Succ(Succ(x9)), x10, x9)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x10)))))), Pos(Succ(Succ(Succ(Succ(Succ(x9)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x9)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x10))), Succ(Succ(Succ(x9))), Succ(x10), Succ(x9))))) (5) (new_primModNatS01(x15, x14)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x15 & Succ(Succ(Zero))=x14 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (6) (Succ(Succ(x18))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x18 & Succ(Succ(Succ(x16)))=x17 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x8, x7)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x20), Succ(x19)), Succ(x19))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x6)))=x20 & Succ(Succ(Zero))=x19 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x10)))=x12 & Succ(Succ(Succ(x9)))=x11 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x10)))))), Pos(Succ(Succ(Succ(Succ(Succ(x9)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x9)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x10))), Succ(Succ(Succ(x9))), Succ(x10), Succ(x9))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x15, x14)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x39), Succ(x38)), Succ(x38))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x39 & Succ(Succ(Zero))=x38 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (12) (new_primModNatS01(x27, x26)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x25))))=x27 & Succ(Succ(Succ(Zero)))=x26 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) (13) (new_primModNatS02(x31, x30, x29, x28)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x29))))=x31 & Succ(Succ(Succ(Succ(x28))))=x30 & (\/x32:new_primModNatS02(x31, x30, x29, x28)=Succ(Succ(Succ(Succ(x32)))) & Succ(Succ(Succ(x29)))=x31 & Succ(Succ(Succ(x28)))=x30 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x29)))))), Pos(Succ(Succ(Succ(Succ(Succ(x28)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x28)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x29))), Succ(Succ(Succ(x28))), Succ(x29), Succ(x28))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) (14) (new_primModNatS01(x34, x33)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x34 & Succ(Succ(Succ(Zero)))=x33 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (15) (Succ(Succ(x37))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x37 & Succ(Succ(Succ(Succ(x35))))=x36 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x16)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primRemInt(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primRemInt(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (125) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (126) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primRemInt(Pos(x0), x1) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primRemInt(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (127) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt(Pos(x0), x1) new_primRemInt(Neg(x0), x1) ---------------------------------------- (128) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (129) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(vuz374, Neg(Succ(vuz37300))) -> new_gcd0Gcd'(Neg(Succ(vuz37300)), new_primRemInt0(vuz374, vuz37300)) at position [1] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))) (new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))),new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))) ---------------------------------------- (130) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (131) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (132) Complex Obligation (AND) ---------------------------------------- (133) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (135) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (136) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt0(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (137) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (138) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero)))) (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1)))) ---------------------------------------- (139) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (140) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (141) Complex Obligation (AND) ---------------------------------------- (142) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (143) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (144) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (145) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1) ---------------------------------------- (146) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (147) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (148) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (149) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (150) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (151) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (152) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (153) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (154) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (155) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (156) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (157) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (158) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (159) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (160) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (161) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (162) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (163) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (164) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (165) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (166) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (167) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (168) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Zero) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (169) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (170) YES ---------------------------------------- (171) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (172) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (173) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (174) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))) ---------------------------------------- (175) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (176) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (177) Complex Obligation (AND) ---------------------------------------- (178) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (179) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (180) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (181) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (182) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (183) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (184) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (185) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (186) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (187) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (188) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (189) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (190) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (191) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (192) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (193) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero)))) ---------------------------------------- (194) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (195) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (196) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (197) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 1 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (198) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (199) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (200) TRUE ---------------------------------------- (201) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (202) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (203) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (204) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (205) Complex Obligation (AND) ---------------------------------------- (206) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (207) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (208) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (209) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (210) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (211) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (212) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (213) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (214) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (215) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (216) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (217) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (218) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (219) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (220) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (221) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (222) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (223) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (224) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (225) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 3 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 3 + x_1 POL(new_primModNatS1(x_1, x_2)) = 2 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (226) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (227) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (228) TRUE ---------------------------------------- (229) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (230) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1))), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x0))=x4 & Succ(Succ(x1))=x5 & new_primModNatS02(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Succ(Succ(x1))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1))))), Neg(new_primModNatS02(Succ(Succ(x0)), Succ(Succ(x1)), x0, x1)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x4, x5, x0, x1)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (3) (new_primModNatS01(x8, x7)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x6)))=x8 & Succ(Succ(Zero))=x7 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x6)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) (4) (new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x10)))=x12 & Succ(Succ(Succ(x9)))=x11 & (\/x13:new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x13)))) & Succ(Succ(x10))=x12 & Succ(Succ(x9))=x11 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x10))))), Neg(Succ(Succ(Succ(Succ(x9))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x9))))), Neg(new_primModNatS02(Succ(Succ(x10)), Succ(Succ(x9)), x10, x9)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x10)))))), Neg(Succ(Succ(Succ(Succ(Succ(x9)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x10))), Succ(Succ(Succ(x9))), Succ(x10), Succ(x9))))) (5) (new_primModNatS01(x15, x14)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x15 & Succ(Succ(Zero))=x14 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (6) (Succ(Succ(x18))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x18 & Succ(Succ(Succ(x16)))=x17 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x8, x7)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x20), Succ(x19)), Succ(x19))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x6)))=x20 & Succ(Succ(Zero))=x19 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x6)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(x10)))=x12 & Succ(Succ(Succ(x9)))=x11 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x10)))))), Neg(Succ(Succ(Succ(Succ(Succ(x9)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x9)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x10))), Succ(Succ(Succ(x9))), Succ(x10), Succ(x9))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x15, x14)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x39), Succ(x38)), Succ(x38))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Zero))=x39 & Succ(Succ(Zero))=x38 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x6)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x12, x11, x10, x9)=Succ(Succ(Succ(Succ(x3)))) which results in the following new constraints: (12) (new_primModNatS01(x27, x26)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x25))))=x27 & Succ(Succ(Succ(Zero)))=x26 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) (13) (new_primModNatS02(x31, x30, x29, x28)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Succ(x29))))=x31 & Succ(Succ(Succ(Succ(x28))))=x30 & (\/x32:new_primModNatS02(x31, x30, x29, x28)=Succ(Succ(Succ(Succ(x32)))) & Succ(Succ(Succ(x29)))=x31 & Succ(Succ(Succ(x28)))=x30 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x29)))))), Neg(Succ(Succ(Succ(Succ(Succ(x28)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x28)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x29))), Succ(Succ(Succ(x28))), Succ(x29), Succ(x28))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) (14) (new_primModNatS01(x34, x33)=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x34 & Succ(Succ(Succ(Zero)))=x33 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (15) (Succ(Succ(x37))=Succ(Succ(Succ(Succ(x3)))) & Succ(Succ(Succ(Zero)))=x37 & Succ(Succ(Succ(Succ(x35))))=x36 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x35))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x35)))), Succ(Zero), Succ(Succ(x35)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x16)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x16)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x16))), Zero, Succ(x16))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x6)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Zero)), Succ(x6), Zero)))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x25))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x25)))), Succ(Succ(Succ(Zero))), Succ(Succ(x25)), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x29))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x28))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x29)))), Succ(Succ(Succ(Succ(x28)))), Succ(Succ(x29)), Succ(Succ(x28)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (231) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (232) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primRemInt0(Neg(vuz3740), vuz37300) -> Neg(new_primModNatS1(vuz3740, vuz37300)) new_primRemInt0(Pos(vuz3740), vuz37300) -> Pos(new_primModNatS1(vuz3740, vuz37300)) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (233) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (234) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primRemInt0(Neg(x0), x1) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primRemInt0(Pos(x0), x1) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (235) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primRemInt0(Neg(x0), x1) new_primRemInt0(Pos(x0), x1) ---------------------------------------- (236) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (237) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) -> new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero)))) (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero))) (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1)))) ---------------------------------------- (238) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Zero), Neg(Succ(x0))) -> new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (239) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (240) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (241) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (242) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (243) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (244) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (245) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (246) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (247) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) -> new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero)))) (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero))) (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1)))) ---------------------------------------- (248) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Zero), Pos(Succ(x0))) -> new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (249) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 2 less nodes. ---------------------------------------- (250) Complex Obligation (AND) ---------------------------------------- (251) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (252) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (253) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (254) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1) ---------------------------------------- (255) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (256) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (257) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (258) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (259) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (260) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (261) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (262) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (263) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (264) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (265) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (266) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x0)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (267) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (268) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (269) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (270) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (271) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (272) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (273) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (274) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = x_1 POL(Pos(x_1)) = 1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Zero))) -> new_gcd0Gcd'(Pos(Succ(Zero)), Neg(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (275) YES ---------------------------------------- (276) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (277) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (278) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (279) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primModNatS01(x0, x1) ---------------------------------------- (280) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (281) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (282) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (283) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (284) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (285) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (286) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (287) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (288) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (289) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x0)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)))) ---------------------------------------- (290) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (291) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x0), Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero)))) ---------------------------------------- (292) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (293) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero)))) ---------------------------------------- (294) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Zero, Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (295) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (296) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (297) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Neg(x_1)) = 1 POL(Pos(x_1)) = x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 >= 2 *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Zero))) -> new_gcd0Gcd'(Neg(Succ(Zero)), Pos(new_primModNatS1(Succ(x0), Zero))) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 2 >= 1, 1 > 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (298) YES ---------------------------------------- (299) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS1(Succ(Succ(vuz374000)), Zero) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (300) UsableRulesProof (EQUIVALENT) 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. ---------------------------------------- (301) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (302) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Succ(x1)))) -> new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(new_primModNatS02(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))) ---------------------------------------- (303) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (304) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (305) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (306) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS01(Zero, Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (307) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (308) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (309) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (310) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero))))) ---------------------------------------- (311) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (312) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (313) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (314) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero))))) ---------------------------------------- (315) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Zero, Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (316) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (317) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (318) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (319) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (320) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (321) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (322) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS01(Succ(Zero), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (323) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (324) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (325) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (326) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (327) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (328) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (329) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (330) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero)))))) ---------------------------------------- (331) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (332) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (333) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (334) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(new_primMinusNatS0(Zero, Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero)))))) ---------------------------------------- (335) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (336) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (337) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (338) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Succ(x1)))) -> new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(new_primModNatS02(x0, x1, x0, x1))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))) ---------------------------------------- (339) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Zero, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (340) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 1 less node. ---------------------------------------- (341) Complex Obligation (AND) ---------------------------------------- (342) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (343) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS01(Succ(x2), Zero))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero))))) ---------------------------------------- (344) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (345) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero))))) ---------------------------------------- (346) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (347) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Zero)))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero))))) ---------------------------------------- (348) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (349) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero)))) ---------------------------------------- (350) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (351) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (352) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (353) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x0))))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(new_primModNatS02(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 3 + x_1 POL(Pos(x_1)) = 0 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (354) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (355) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (356) TRUE ---------------------------------------- (357) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (358) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS1(Succ(x2), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero)))) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero)))) ---------------------------------------- (359) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Zero))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (360) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (361) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (362) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x0))))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(new_primModNatS02(x0, Zero, x0, Zero))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 0 POL(Pos(x_1)) = 3 + x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = 2*x_1 + 2*x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 2 + x_1 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 POL(new_primModNatS1(x_1, x_2)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (363) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (364) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (365) TRUE ---------------------------------------- (366) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (367) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Succ(x3))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(new_primModNatS02(Succ(x2), Succ(x3), x2, x3))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero))))) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))) ---------------------------------------- (368) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Zero), Succ(Zero)))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (369) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 1 less node. ---------------------------------------- (370) Complex Obligation (AND) ---------------------------------------- (371) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (372) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Zero)))) at position [1,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero)))))) ---------------------------------------- (373) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (374) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero)))))) ---------------------------------------- (375) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (376) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero)))))) ---------------------------------------- (377) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (378) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(new_primMinusNatS0(Succ(x2), Zero), Succ(Succ(Zero))))) at position [1,0,0] we obtained the following new rules [LPAR04]: (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero)))))) ---------------------------------------- (379) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (380) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 3 + 2*x_1 POL(Pos(x_1)) = 3 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 2 + x_1 + x_2 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 + x_2 POL(new_primModNatS1(x_1, x_2)) = x_1 + x_2 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (381) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (382) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (383) TRUE ---------------------------------------- (384) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (385) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Neg(x_1)) = 3 POL(Pos(x_1)) = 3 + 2*x_1 POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_gcd0Gcd'(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 POL(new_primModNatS01(x_1, x_2)) = 2 + x_1 + x_2 POL(new_primModNatS02(x_1, x_2, x_3, x_4)) = 2 + x_1 + x_2 POL(new_primModNatS1(x_1, x_2)) = x_1 + x_2 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (386) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (387) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (388) TRUE ---------------------------------------- (389) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (390) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x4))))), Neg(Succ(Succ(Succ(Succ(x5)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x5))))), Pos(new_primModNatS02(Succ(Succ(x4)), Succ(Succ(x5)), x4, x5))) which results in the following constraint: (1) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x4))))), Neg(Succ(Succ(Succ(Succ(x5)))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x2))=x12 & Succ(Succ(x3))=x13 & new_primModNatS02(x12, x13, x2, x3)=Succ(Succ(Succ(Succ(x5)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x12, x13, x2, x3)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraints: (3) (new_primModNatS01(x16, x15)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Zero))=x15 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x14)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x14))), Succ(Succ(Zero)), Succ(x14), Zero)))) (4) (new_primModNatS02(x20, x19, x18, x17)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x18)))=x20 & Succ(Succ(Succ(x17)))=x19 & (\/x21:new_primModNatS02(x20, x19, x18, x17)=Succ(Succ(Succ(Succ(x21)))) & Succ(Succ(x18))=x20 & Succ(Succ(x17))=x19 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x18))))), Pos(Succ(Succ(Succ(Succ(x17))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x17))))), Neg(new_primModNatS02(Succ(Succ(x18)), Succ(Succ(x17)), x18, x17)))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x18)))))), Pos(Succ(Succ(Succ(Succ(Succ(x17)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x17)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x18))), Succ(Succ(Succ(x17))), Succ(x18), Succ(x17))))) (5) (new_primModNatS01(x23, x22)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x23 & Succ(Succ(Zero))=x22 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (6) (Succ(Succ(x26))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x26 & Succ(Succ(Succ(x24)))=x25 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x16, x15)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x28), Succ(x27)), Succ(x27))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x14)))=x28 & Succ(Succ(Zero))=x27 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x14)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x14))), Succ(Succ(Zero)), Succ(x14), Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS02(x20, x19, x18, x17)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(x18)))=x20 & Succ(Succ(Succ(x17)))=x19 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x18)))))), Pos(Succ(Succ(Succ(Succ(Succ(x17)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x17)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x18))), Succ(Succ(Succ(x17))), Succ(x18), Succ(x17))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x23, x22)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x47), Succ(x46)), Succ(x46))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Zero))=x47 & Succ(Succ(Zero))=x46 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x14)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x14))), Succ(Succ(Zero)), Succ(x14), Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x20, x19, x18, x17)=Succ(Succ(Succ(Succ(x5)))) which results in the following new constraints: (12) (new_primModNatS01(x35, x34)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Succ(x33))))=x35 & Succ(Succ(Succ(Zero)))=x34 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x33))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x33)))), Succ(Succ(Succ(Zero))), Succ(Succ(x33)), Succ(Zero))))) (13) (new_primModNatS02(x39, x38, x37, x36)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Succ(x37))))=x39 & Succ(Succ(Succ(Succ(x36))))=x38 & (\/x40:new_primModNatS02(x39, x38, x37, x36)=Succ(Succ(Succ(Succ(x40)))) & Succ(Succ(Succ(x37)))=x39 & Succ(Succ(Succ(x36)))=x38 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x37)))))), Pos(Succ(Succ(Succ(Succ(Succ(x36)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x36)))))), Neg(new_primModNatS02(Succ(Succ(Succ(x37))), Succ(Succ(Succ(x36))), Succ(x37), Succ(x36))))) ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x37))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x37)))), Succ(Succ(Succ(Succ(x36)))), Succ(Succ(x37)), Succ(Succ(x36)))))) (14) (new_primModNatS01(x42, x41)=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Zero)))=x42 & Succ(Succ(Succ(Zero)))=x41 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (15) (Succ(Succ(x45))=Succ(Succ(Succ(Succ(x5)))) & Succ(Succ(Succ(Zero)))=x45 & Succ(Succ(Succ(Succ(x43))))=x44 ==> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x33))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x33)))), Succ(Succ(Succ(Zero))), Succ(Succ(x33)), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x37))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x37)))), Succ(Succ(Succ(Succ(x36)))), Succ(Succ(x37)), Succ(Succ(x36)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) the following chains were created: *We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS02(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7))), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x8))))), Pos(Succ(Succ(Succ(Succ(x9)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x9))))), Neg(new_primModNatS02(Succ(Succ(x8)), Succ(Succ(x9)), x8, x9))) which results in the following constraint: (1) (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS02(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x8))))), Pos(Succ(Succ(Succ(Succ(x9)))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS02(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))) We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint: (2) (Succ(Succ(x6))=x52 & Succ(Succ(x7))=x53 & new_primModNatS02(x52, x53, x6, x7)=Succ(Succ(Succ(Succ(x9)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x6))))), Neg(Succ(Succ(Succ(Succ(x7))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x7))))), Pos(new_primModNatS02(Succ(Succ(x6)), Succ(Succ(x7)), x6, x7)))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x52, x53, x6, x7)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraints: (3) (new_primModNatS01(x56, x55)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x54)))=x56 & Succ(Succ(Zero))=x55 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x54)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x54))), Succ(Succ(Zero)), Succ(x54), Zero)))) (4) (new_primModNatS02(x60, x59, x58, x57)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x58)))=x60 & Succ(Succ(Succ(x57)))=x59 & (\/x61:new_primModNatS02(x60, x59, x58, x57)=Succ(Succ(Succ(Succ(x61)))) & Succ(Succ(x58))=x60 & Succ(Succ(x57))=x59 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x58))))), Neg(Succ(Succ(Succ(Succ(x57))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x57))))), Pos(new_primModNatS02(Succ(Succ(x58)), Succ(Succ(x57)), x58, x57)))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x58)))))), Neg(Succ(Succ(Succ(Succ(Succ(x57)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x57)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x58))), Succ(Succ(Succ(x57))), Succ(x58), Succ(x57))))) (5) (new_primModNatS01(x63, x62)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x63 & Succ(Succ(Zero))=x62 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) (6) (Succ(Succ(x66))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x66 & Succ(Succ(Succ(x64)))=x65 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) We simplified constraint (3) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x56, x55)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraint: (7) (new_primModNatS1(new_primMinusNatS0(Succ(x68), Succ(x67)), Succ(x67))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x54)))=x68 & Succ(Succ(Zero))=x67 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x54)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x54))), Succ(Succ(Zero)), Succ(x54), Zero)))) We simplified constraint (4) using rule (IV) which results in the following new constraint: (8) (new_primModNatS02(x60, x59, x58, x57)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(x58)))=x60 & Succ(Succ(Succ(x57)))=x59 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x58)))))), Neg(Succ(Succ(Succ(Succ(Succ(x57)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x57)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x58))), Succ(Succ(Succ(x57))), Succ(x58), Succ(x57))))) We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x63, x62)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraint: (9) (new_primModNatS1(new_primMinusNatS0(Succ(x87), Succ(x86)), Succ(x86))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Zero))=x87 & Succ(Succ(Zero))=x86 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) We simplified constraint (6) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) We simplified constraint (7) using rules (III), (IV), (VII) which results in the following new constraint: (11) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x54)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x54))), Succ(Succ(Zero)), Succ(x54), Zero)))) We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x60, x59, x58, x57)=Succ(Succ(Succ(Succ(x9)))) which results in the following new constraints: (12) (new_primModNatS01(x75, x74)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Succ(x73))))=x75 & Succ(Succ(Succ(Zero)))=x74 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x73))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x73)))), Succ(Succ(Succ(Zero))), Succ(Succ(x73)), Succ(Zero))))) (13) (new_primModNatS02(x79, x78, x77, x76)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Succ(x77))))=x79 & Succ(Succ(Succ(Succ(x76))))=x78 & (\/x80:new_primModNatS02(x79, x78, x77, x76)=Succ(Succ(Succ(Succ(x80)))) & Succ(Succ(Succ(x77)))=x79 & Succ(Succ(Succ(x76)))=x78 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x77)))))), Neg(Succ(Succ(Succ(Succ(Succ(x76)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x76)))))), Pos(new_primModNatS02(Succ(Succ(Succ(x77))), Succ(Succ(Succ(x76))), Succ(x77), Succ(x76))))) ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x77))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x77)))), Succ(Succ(Succ(Succ(x76)))), Succ(Succ(x77)), Succ(Succ(x76)))))) (14) (new_primModNatS01(x82, x81)=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Zero)))=x82 & Succ(Succ(Succ(Zero)))=x81 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) (15) (Succ(Succ(x85))=Succ(Succ(Succ(Succ(x9)))) & Succ(Succ(Succ(Zero)))=x85 & Succ(Succ(Succ(Succ(x83))))=x84 ==> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) We simplified constraint (12) using rules (III), (IV) which results in the following new constraint: (16) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x73))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x73)))), Succ(Succ(Succ(Zero))), Succ(Succ(x73)), Succ(Zero))))) We simplified constraint (13) using rules (III), (IV) which results in the following new constraint: (17) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x77))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x77)))), Succ(Succ(Succ(Succ(x76)))), Succ(Succ(x77)), Succ(Succ(x76)))))) We simplified constraint (14) using rules (III), (IV) which results in the following new constraint: (18) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint: (19) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) We simplified constraint (9) using rules (III), (IV), (VII) which results in the following new constraint: (20) (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x43))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x43)))), Succ(Zero), Succ(Succ(x43)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x24)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x24)))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x24))), Zero, Succ(x24))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x14)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Succ(x14))), Succ(Succ(Zero)), Succ(x14), Zero)))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x33))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x33)))), Succ(Succ(Succ(Zero))), Succ(Succ(x33)), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x37))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x36))))))), Neg(new_primModNatS02(Succ(Succ(Succ(Succ(x37)))), Succ(Succ(Succ(Succ(x36)))), Succ(Succ(x37)), Succ(Succ(x36)))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) *new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x83))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x83)))), Succ(Zero), Succ(Succ(x83)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x64)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x64)))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Succ(x64))), Zero, Succ(x64))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x54)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Succ(x54))), Succ(Succ(Zero)), Succ(x54), Zero)))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x73))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x73)))), Succ(Succ(Succ(Zero))), Succ(Succ(x73)), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x77))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x76))))))), Pos(new_primModNatS02(Succ(Succ(Succ(Succ(x77)))), Succ(Succ(Succ(Succ(x76)))), Succ(Succ(x77)), Succ(Succ(x76)))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(new_primModNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero))))) *(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(new_primModNatS02(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero)))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (391) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Succ(x3)))))) -> new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))) The TRS R consists of the following rules: new_primModNatS1(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS02(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS01(vuz391, vuz392) -> new_primModNatS1(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS02(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS02(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS02(vuz391, vuz392, Zero, Zero) -> new_primModNatS01(vuz391, vuz392) new_primModNatS02(vuz391, vuz392, Zero, Succ(vuz3940)) -> Succ(Succ(vuz391)) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primModNatS1(Succ(Zero), Succ(vuz373000)) -> Succ(Zero) new_primModNatS1(Zero, vuz37300) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primModNatS02(x0, x1, Zero, Zero) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primModNatS1(Succ(Succ(x0)), Succ(x1)) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primMinusNatS0(Zero, Succ(x0)) new_primModNatS1(Succ(Succ(x0)), Zero) new_primModNatS1(Succ(Zero), Succ(x0)) new_primMinusNatS0(Zero, Zero) new_primModNatS1(Zero, x0) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primModNatS1(Succ(Zero), Zero) new_primModNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (392) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd2(Succ(vuz2870), Succ(vuz3030), vuz68) -> new_gcd2(vuz2870, vuz3030, vuz68) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (393) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_gcd2(Succ(vuz2870), Succ(vuz3030), vuz68) -> new_gcd2(vuz2870, vuz3030, vuz68) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (394) YES ---------------------------------------- (395) Obligation: Q DP problem: The TRS P consists of the following rules: new_primQuotInt(Succ(vuz1690), Succ(vuz2050), vuz68) -> new_primQuotInt(vuz1690, vuz2050, vuz68) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (396) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primQuotInt(Succ(vuz1690), Succ(vuz2050), vuz68) -> new_primQuotInt(vuz1690, vuz2050, vuz68) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (397) YES ---------------------------------------- (398) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Zero), Zero) -> new_primModNatS(new_primMinusNatS0(Zero, Zero), Zero) new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (399) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (400) Complex Obligation (AND) ---------------------------------------- (401) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (402) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) at position [0] we obtained the following new rules [LPAR04]: (new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)),new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392))) ---------------------------------------- (403) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (404) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(Succ(vuz391), Succ(vuz392)), Succ(vuz392)) at position [0] we obtained the following new rules [LPAR04]: (new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)),new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392))) ---------------------------------------- (405) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (406) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Zero) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primModNatS00(vuz391, vuz392) -> new_primModNatS(new_primMinusNatS0(vuz391, vuz392), Succ(vuz392)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primModNatS(Succ(Succ(vuz374000)), Succ(vuz373000)) -> new_primModNatS0(vuz374000, vuz373000, vuz374000, vuz373000) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4 *new_primModNatS0(vuz391, vuz392, Succ(vuz3930), Succ(vuz3940)) -> new_primModNatS0(vuz391, vuz392, vuz3930, vuz3940) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 *new_primModNatS0(vuz391, vuz392, Zero, Zero) -> new_primModNatS00(vuz391, vuz392) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) ---------------------------------------- (407) YES ---------------------------------------- (408) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (409) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primModNatS(Succ(Succ(vuz374000)), Zero) -> new_primModNatS(new_primMinusNatS0(Succ(vuz374000), Zero), Zero) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 > 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) ---------------------------------------- (410) YES ---------------------------------------- (411) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) new_primDivNatS(Succ(Zero), Zero) -> new_primDivNatS(new_primMinusNatS2, Zero) new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (412) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (413) Complex Obligation (AND) ---------------------------------------- (414) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (415) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: new_primDivNatS(Succ(Succ(vuz28000)), Zero) -> new_primDivNatS(new_primMinusNatS1(vuz28000), Zero) Strictly oriented rules of the TRS R: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + 2*x_1 POL(Zero) = 1 POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS0(x_1, x_2)) = x_1 + x_2 POL(new_primMinusNatS1(x_1)) = 2 + 2*x_1 POL(new_primMinusNatS2) = 2 ---------------------------------------- (416) Obligation: Q DP problem: P is empty. R is empty. The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (417) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (418) YES ---------------------------------------- (419) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) The TRS R consists of the following rules: new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS1(vuz28000) -> Succ(vuz28000) new_primMinusNatS2 -> Zero new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) The set Q consists of the following terms: new_primMinusNatS0(Succ(x0), Zero) new_primMinusNatS0(Zero, Zero) new_primMinusNatS2 new_primMinusNatS0(Succ(x0), Succ(x1)) new_primMinusNatS0(Zero, Succ(x0)) new_primMinusNatS1(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (420) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 1 POL(new_primMinusNatS0(x_1, x_2)) = x_1 From the DPs we obtained the following set of size-change graphs: *new_primDivNatS(Succ(Succ(vuz28000)), Succ(vuz281000)) -> new_primDivNatS0(vuz28000, vuz281000, vuz28000, vuz281000) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4 *new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Succ(vuz3410)) -> new_primDivNatS0(vuz338, vuz339, vuz3400, vuz3410) (allowed arguments on rhs = {1, 2, 3, 4}) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 *new_primDivNatS0(vuz338, vuz339, Succ(vuz3400), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 *new_primDivNatS0(vuz338, vuz339, Zero, Zero) -> new_primDivNatS00(vuz338, vuz339) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1, 2 >= 2 *new_primDivNatS00(vuz338, vuz339) -> new_primDivNatS(new_primMinusNatS0(vuz338, vuz339), Succ(vuz339)) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 >= 1 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_primMinusNatS0(Zero, Zero) -> Zero new_primMinusNatS0(Zero, Succ(vuz3390)) -> Zero new_primMinusNatS0(Succ(vuz3380), Zero) -> Succ(vuz3380) new_primMinusNatS0(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS0(vuz3380, vuz3390) ---------------------------------------- (421) YES ---------------------------------------- (422) Obligation: Q DP problem: The TRS P consists of the following rules: new_primQuotInt0(Succ(vuz1850), Succ(vuz1990), vuz144) -> new_primQuotInt0(vuz1850, vuz1990, vuz144) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (423) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primQuotInt0(Succ(vuz1850), Succ(vuz1990), vuz144) -> new_primQuotInt0(vuz1850, vuz1990, vuz144) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (424) YES ---------------------------------------- (425) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNatS(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS(vuz3380, vuz3390) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (426) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primMinusNatS(Succ(vuz3380), Succ(vuz3390)) -> new_primMinusNatS(vuz3380, vuz3390) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (427) YES ---------------------------------------- (428) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuz6600), Succ(vuz31000)) -> new_primPlusNat(vuz6600, vuz31000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (429) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat(Succ(vuz6600), Succ(vuz31000)) -> new_primPlusNat(vuz6600, vuz31000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (430) YES ---------------------------------------- (431) Obligation: Q DP problem: The TRS P consists of the following rules: new_gcd20(Succ(vuz3500), Succ(vuz3660), vuz144) -> new_gcd20(vuz3500, vuz3660, vuz144) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (432) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *new_gcd20(Succ(vuz3500), Succ(vuz3660), vuz144) -> new_gcd20(vuz3500, vuz3660, vuz144) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (433) YES ---------------------------------------- (434) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="subtract",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="subtract vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="subtract vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="flip (-) vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="(-) vuz4 vuz3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="vuz4 + (negate vuz3)",fontsize=16,color="burlywood",shape="box"];6384[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];7 -> 6384[label="",style="solid", color="burlywood", weight=9]; 6384 -> 8[label="",style="solid", color="burlywood", weight=3]; 8[label="vuz40 :% vuz41 + (negate vuz3)",fontsize=16,color="burlywood",shape="box"];6385[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];8 -> 6385[label="",style="solid", color="burlywood", weight=9]; 6385 -> 9[label="",style="solid", color="burlywood", weight=3]; 9[label="vuz40 :% vuz41 + (negate vuz30 :% vuz31)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10[label="vuz40 :% vuz41 + (negate vuz30) :% vuz31",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11[label="vuz40 :% vuz41 + primNegInt vuz30 :% vuz31",fontsize=16,color="burlywood",shape="box"];6386[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];11 -> 6386[label="",style="solid", color="burlywood", weight=9]; 6386 -> 12[label="",style="solid", color="burlywood", weight=3]; 6387[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];11 -> 6387[label="",style="solid", color="burlywood", weight=9]; 6387 -> 13[label="",style="solid", color="burlywood", weight=3]; 12[label="vuz40 :% vuz41 + primNegInt (Pos vuz300) :% vuz31",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vuz40 :% vuz41 + primNegInt (Neg vuz300) :% vuz31",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="vuz40 :% vuz41 + Neg vuz300 :% vuz31",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="vuz40 :% vuz41 + Pos vuz300 :% vuz31",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="reduce (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="reduce (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="reduce2 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="reduce2 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31)",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz41 * vuz31 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz41 * vuz31 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (vuz41 * vuz31) (primEqInt (vuz41 * vuz31) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 23[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (vuz40 * vuz31 + Pos vuz300 * vuz41) (vuz41 * vuz31) (primEqInt (vuz41 * vuz31) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 24[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * vuz41) (primMulInt vuz41 vuz31) (vuz40 * vuz31 + Neg vuz300 * vuz41) (primMulInt vuz41 vuz31) (primEqInt (primMulInt vuz41 vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6388[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];24 -> 6388[label="",style="solid", color="burlywood", weight=9]; 6388 -> 26[label="",style="solid", color="burlywood", weight=3]; 6389[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];24 -> 6389[label="",style="solid", color="burlywood", weight=9]; 6389 -> 27[label="",style="solid", color="burlywood", weight=3]; 25[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * vuz41) (primMulInt vuz41 vuz31) (vuz40 * vuz31 + Pos vuz300 * vuz41) (primMulInt vuz41 vuz31) (primEqInt (primMulInt vuz41 vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6390[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6390[label="",style="solid", color="burlywood", weight=9]; 6390 -> 28[label="",style="solid", color="burlywood", weight=3]; 6391[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6391[label="",style="solid", color="burlywood", weight=9]; 6391 -> 29[label="",style="solid", color="burlywood", weight=3]; 26[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (vuz40 * vuz31 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (primEqInt (primMulInt (Pos vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6392[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];26 -> 6392[label="",style="solid", color="burlywood", weight=9]; 6392 -> 30[label="",style="solid", color="burlywood", weight=3]; 6393[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];26 -> 6393[label="",style="solid", color="burlywood", weight=9]; 6393 -> 31[label="",style="solid", color="burlywood", weight=3]; 27[label="reduce2Reduce1 (vuz40 * vuz31 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (vuz40 * vuz31 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (primEqInt (primMulInt (Neg vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6394[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];27 -> 6394[label="",style="solid", color="burlywood", weight=9]; 6394 -> 32[label="",style="solid", color="burlywood", weight=3]; 6395[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];27 -> 6395[label="",style="solid", color="burlywood", weight=9]; 6395 -> 33[label="",style="solid", color="burlywood", weight=3]; 28[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (vuz40 * vuz31 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) vuz31) (primEqInt (primMulInt (Pos vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6396[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];28 -> 6396[label="",style="solid", color="burlywood", weight=9]; 6396 -> 34[label="",style="solid", color="burlywood", weight=3]; 6397[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];28 -> 6397[label="",style="solid", color="burlywood", weight=9]; 6397 -> 35[label="",style="solid", color="burlywood", weight=3]; 29[label="reduce2Reduce1 (vuz40 * vuz31 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (vuz40 * vuz31 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) vuz31) (primEqInt (primMulInt (Neg vuz410) vuz31) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6398[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 6398[label="",style="solid", color="burlywood", weight=9]; 6398 -> 36[label="",style="solid", color="burlywood", weight=3]; 6399[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 6399[label="",style="solid", color="burlywood", weight=9]; 6399 -> 37[label="",style="solid", color="burlywood", weight=3]; 30[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (primEqInt (primMulInt (Pos vuz410) (Pos vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3]; 31[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (primEqInt (primMulInt (Pos vuz410) (Neg vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3]; 32[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Pos vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Pos vuz310)) (primEqInt (primMulInt (Neg vuz410) (Pos vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3]; 33[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (primEqInt (primMulInt (Neg vuz410) (Neg vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3]; 34[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Pos vuz310)) (primEqInt (primMulInt (Pos vuz410) (Pos vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3]; 35[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (primMulInt (Pos vuz410) (Neg vuz310)) (primEqInt (primMulInt (Pos vuz410) (Neg vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3]; 36[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Pos vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Pos vuz310)) (primEqInt (primMulInt (Neg vuz410) (Pos vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3]; 37[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Neg vuz410) (primMulInt (Neg vuz410) (Neg vuz310)) (primEqInt (primMulInt (Neg vuz410) (Neg vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];37 -> 45[label="",style="solid", color="black", weight=3]; 38[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6400[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];38 -> 6400[label="",style="solid", color="burlywood", weight=9]; 6400 -> 46[label="",style="solid", color="burlywood", weight=3]; 6401[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 6401[label="",style="solid", color="burlywood", weight=9]; 6401 -> 47[label="",style="solid", color="burlywood", weight=3]; 39[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Pos vuz410) (Neg (primMulNat vuz410 vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Pos vuz410) (Neg (primMulNat vuz410 vuz310)) (primEqInt (Neg (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6402[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];39 -> 6402[label="",style="solid", color="burlywood", weight=9]; 6402 -> 48[label="",style="solid", color="burlywood", weight=3]; 6403[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 6403[label="",style="solid", color="burlywood", weight=9]; 6403 -> 49[label="",style="solid", color="burlywood", weight=3]; 40[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Neg vuz410) (Neg (primMulNat vuz410 vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Neg vuz410) (Neg (primMulNat vuz410 vuz310)) (primEqInt (Neg (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6404[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];40 -> 6404[label="",style="solid", color="burlywood", weight=9]; 6404 -> 50[label="",style="solid", color="burlywood", weight=3]; 6405[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];40 -> 6405[label="",style="solid", color="burlywood", weight=9]; 6405 -> 51[label="",style="solid", color="burlywood", weight=3]; 41[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6406[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];41 -> 6406[label="",style="solid", color="burlywood", weight=9]; 6406 -> 52[label="",style="solid", color="burlywood", weight=3]; 6407[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 6407[label="",style="solid", color="burlywood", weight=9]; 6407 -> 53[label="",style="solid", color="burlywood", weight=3]; 42[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6408[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];42 -> 6408[label="",style="solid", color="burlywood", weight=9]; 6408 -> 54[label="",style="solid", color="burlywood", weight=3]; 6409[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 6409[label="",style="solid", color="burlywood", weight=9]; 6409 -> 55[label="",style="solid", color="burlywood", weight=3]; 43[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (Neg (primMulNat vuz410 vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos vuz410) (Neg (primMulNat vuz410 vuz310)) (primEqInt (Neg (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6410[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];43 -> 6410[label="",style="solid", color="burlywood", weight=9]; 6410 -> 56[label="",style="solid", color="burlywood", weight=3]; 6411[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 6411[label="",style="solid", color="burlywood", weight=9]; 6411 -> 57[label="",style="solid", color="burlywood", weight=3]; 44[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Neg vuz410) (Neg (primMulNat vuz410 vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Neg vuz410) (Neg (primMulNat vuz410 vuz310)) (primEqInt (Neg (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6412[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];44 -> 6412[label="",style="solid", color="burlywood", weight=9]; 6412 -> 58[label="",style="solid", color="burlywood", weight=3]; 6413[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 6413[label="",style="solid", color="burlywood", weight=9]; 6413 -> 59[label="",style="solid", color="burlywood", weight=3]; 45[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Neg vuz410) (Pos (primMulNat vuz410 vuz310)) (primEqInt (Pos (primMulNat vuz410 vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6414[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];45 -> 6414[label="",style="solid", color="burlywood", weight=9]; 6414 -> 60[label="",style="solid", color="burlywood", weight=3]; 6415[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 6415[label="",style="solid", color="burlywood", weight=9]; 6415 -> 61[label="",style="solid", color="burlywood", weight=3]; 46[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6416[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];46 -> 6416[label="",style="solid", color="burlywood", weight=9]; 6416 -> 62[label="",style="solid", color="burlywood", weight=3]; 6417[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 6417[label="",style="solid", color="burlywood", weight=9]; 6417 -> 63[label="",style="solid", color="burlywood", weight=3]; 47[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero vuz310)) (primEqInt (Pos (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6418[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];47 -> 6418[label="",style="solid", color="burlywood", weight=9]; 6418 -> 64[label="",style="solid", color="burlywood", weight=3]; 6419[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 6419[label="",style="solid", color="burlywood", weight=9]; 6419 -> 65[label="",style="solid", color="burlywood", weight=3]; 48[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6420[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];48 -> 6420[label="",style="solid", color="burlywood", weight=9]; 6420 -> 66[label="",style="solid", color="burlywood", weight=3]; 6421[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 6421[label="",style="solid", color="burlywood", weight=9]; 6421 -> 67[label="",style="solid", color="burlywood", weight=3]; 49[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Pos Zero) (Neg (primMulNat Zero vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Pos Zero) (Neg (primMulNat Zero vuz310)) (primEqInt (Neg (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6422[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];49 -> 6422[label="",style="solid", color="burlywood", weight=9]; 6422 -> 68[label="",style="solid", color="burlywood", weight=3]; 6423[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 6423[label="",style="solid", color="burlywood", weight=9]; 6423 -> 69[label="",style="solid", color="burlywood", weight=3]; 50[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6424[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];50 -> 6424[label="",style="solid", color="burlywood", weight=9]; 6424 -> 70[label="",style="solid", color="burlywood", weight=3]; 6425[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 6425[label="",style="solid", color="burlywood", weight=9]; 6425 -> 71[label="",style="solid", color="burlywood", weight=3]; 51[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero vuz310)) (vuz40 * Pos vuz310 + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero vuz310)) (primEqInt (Neg (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6426[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];51 -> 6426[label="",style="solid", color="burlywood", weight=9]; 6426 -> 72[label="",style="solid", color="burlywood", weight=3]; 6427[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 6427[label="",style="solid", color="burlywood", weight=9]; 6427 -> 73[label="",style="solid", color="burlywood", weight=3]; 52[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6428[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];52 -> 6428[label="",style="solid", color="burlywood", weight=9]; 6428 -> 74[label="",style="solid", color="burlywood", weight=3]; 6429[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 6429[label="",style="solid", color="burlywood", weight=9]; 6429 -> 75[label="",style="solid", color="burlywood", weight=3]; 53[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero vuz310)) (vuz40 * Neg vuz310 + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero vuz310)) (primEqInt (Pos (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6430[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];53 -> 6430[label="",style="solid", color="burlywood", weight=9]; 6430 -> 76[label="",style="solid", color="burlywood", weight=3]; 6431[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 6431[label="",style="solid", color="burlywood", weight=9]; 6431 -> 77[label="",style="solid", color="burlywood", weight=3]; 54[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6432[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];54 -> 6432[label="",style="solid", color="burlywood", weight=9]; 6432 -> 78[label="",style="solid", color="burlywood", weight=3]; 6433[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 6433[label="",style="solid", color="burlywood", weight=9]; 6433 -> 79[label="",style="solid", color="burlywood", weight=3]; 55[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero vuz310)) (primEqInt (Pos (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6434[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];55 -> 6434[label="",style="solid", color="burlywood", weight=9]; 6434 -> 80[label="",style="solid", color="burlywood", weight=3]; 6435[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 6435[label="",style="solid", color="burlywood", weight=9]; 6435 -> 81[label="",style="solid", color="burlywood", weight=3]; 56[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6436[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];56 -> 6436[label="",style="solid", color="burlywood", weight=9]; 6436 -> 82[label="",style="solid", color="burlywood", weight=3]; 6437[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 6437[label="",style="solid", color="burlywood", weight=9]; 6437 -> 83[label="",style="solid", color="burlywood", weight=3]; 57[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero vuz310)) (primEqInt (Neg (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6438[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];57 -> 6438[label="",style="solid", color="burlywood", weight=9]; 6438 -> 84[label="",style="solid", color="burlywood", weight=3]; 6439[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 6439[label="",style="solid", color="burlywood", weight=9]; 6439 -> 85[label="",style="solid", color="burlywood", weight=3]; 58[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Neg (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6440[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];58 -> 6440[label="",style="solid", color="burlywood", weight=9]; 6440 -> 86[label="",style="solid", color="burlywood", weight=3]; 6441[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 6441[label="",style="solid", color="burlywood", weight=9]; 6441 -> 87[label="",style="solid", color="burlywood", weight=3]; 59[label="reduce2Reduce1 (vuz40 * Pos vuz310 + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero vuz310)) (vuz40 * Pos vuz310 + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero vuz310)) (primEqInt (Neg (primMulNat Zero vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6442[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];59 -> 6442[label="",style="solid", color="burlywood", weight=9]; 6442 -> 88[label="",style="solid", color="burlywood", weight=3]; 6443[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 6443[label="",style="solid", color="burlywood", weight=9]; 6443 -> 89[label="",style="solid", color="burlywood", weight=3]; 60[label="reduce2Reduce1 (vuz40 * Neg vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (vuz40 * Neg vuz310 + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) vuz310)) (primEqInt (Pos (primMulNat (Succ vuz4100) vuz310)) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];6444[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];60 -> 6444[label="",style="solid", color="burlywood", weight=9]; 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63[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];63 -> 95[label="",style="solid", color="black", weight=3]; 64[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];64 -> 96[label="",style="solid", color="black", weight=3]; 65[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];65 -> 97[label="",style="solid", color="black", weight=3]; 66[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];66 -> 98[label="",style="solid", color="black", weight=3]; 67[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];67 -> 99[label="",style="solid", color="black", weight=3]; 68[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg (primMulNat Zero (Succ vuz3100))) (primEqInt (Neg (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];68 -> 100[label="",style="solid", color="black", weight=3]; 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72[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero (Succ vuz3100))) (primEqInt (Neg (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];72 -> 104[label="",style="solid", color="black", weight=3]; 73[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];73 -> 105[label="",style="solid", color="black", weight=3]; 74[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];74 -> 106[label="",style="solid", color="black", weight=3]; 75[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];75 -> 107[label="",style="solid", color="black", weight=3]; 76[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];76 -> 108[label="",style="solid", color="black", weight=3]; 77[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];77 -> 109[label="",style="solid", color="black", weight=3]; 78[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];78 -> 110[label="",style="solid", color="black", weight=3]; 79[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];79 -> 111[label="",style="solid", color="black", weight=3]; 80[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];80 -> 112[label="",style="solid", color="black", weight=3]; 81[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];81 -> 113[label="",style="solid", color="black", weight=3]; 82[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];82 -> 114[label="",style="solid", color="black", weight=3]; 83[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];83 -> 115[label="",style="solid", color="black", weight=3]; 84[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero (Succ vuz3100))) (primEqInt (Neg (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];84 -> 116[label="",style="solid", color="black", weight=3]; 85[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero Zero)) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];85 -> 117[label="",style="solid", color="black", weight=3]; 86[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Neg (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];86 -> 118[label="",style="solid", color="black", weight=3]; 87[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primMulNat (Succ vuz4100) Zero)) (primEqInt (Neg (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];87 -> 119[label="",style="solid", color="black", weight=3]; 88[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero (Succ vuz3100))) (primEqInt (Neg (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];88 -> 120[label="",style="solid", color="black", weight=3]; 89[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg (primMulNat Zero Zero)) (primEqInt (Neg (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];89 -> 121[label="",style="solid", color="black", weight=3]; 90[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (primEqInt (Pos (primMulNat (Succ vuz4100) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];90 -> 122[label="",style="solid", color="black", weight=3]; 91[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primMulNat (Succ vuz4100) Zero)) (primEqInt (Pos (primMulNat (Succ vuz4100) Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];91 -> 123[label="",style="solid", color="black", weight=3]; 92[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero (Succ vuz3100))) (primEqInt (Pos (primMulNat Zero (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];92 -> 124[label="",style="solid", color="black", weight=3]; 93[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos (primMulNat Zero Zero)) (primEqInt (Pos (primMulNat Zero Zero)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];93 -> 125[label="",style="solid", color="black", weight=3]; 94 -> 1965[label="",style="dashed", color="red", weight=0]; 94[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];94 -> 1966[label="",style="dashed", color="magenta", weight=3]; 94 -> 1967[label="",style="dashed", color="magenta", weight=3]; 94 -> 1968[label="",style="dashed", color="magenta", weight=3]; 94 -> 1969[label="",style="dashed", color="magenta", weight=3]; 94 -> 1970[label="",style="dashed", color="magenta", weight=3]; 94 -> 1971[label="",style="dashed", color="magenta", weight=3]; 94 -> 1972[label="",style="dashed", color="magenta", weight=3]; 95[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];95 -> 128[label="",style="solid", color="black", weight=3]; 96[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];96 -> 129[label="",style="solid", color="black", weight=3]; 97[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];97 -> 130[label="",style="solid", color="black", weight=3]; 98 -> 1032[label="",style="dashed", color="red", weight=0]; 98[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];98 -> 1033[label="",style="dashed", color="magenta", weight=3]; 98 -> 1034[label="",style="dashed", color="magenta", weight=3]; 98 -> 1035[label="",style="dashed", color="magenta", weight=3]; 98 -> 1036[label="",style="dashed", color="magenta", weight=3]; 98 -> 1037[label="",style="dashed", color="magenta", weight=3]; 98 -> 1038[label="",style="dashed", color="magenta", weight=3]; 98 -> 1039[label="",style="dashed", color="magenta", weight=3]; 99[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];99 -> 133[label="",style="solid", color="black", weight=3]; 100[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];100 -> 134[label="",style="solid", color="black", weight=3]; 101[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];101 -> 135[label="",style="solid", color="black", weight=3]; 102 -> 1075[label="",style="dashed", color="red", weight=0]; 102[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];102 -> 1076[label="",style="dashed", color="magenta", weight=3]; 102 -> 1077[label="",style="dashed", color="magenta", weight=3]; 102 -> 1078[label="",style="dashed", color="magenta", weight=3]; 102 -> 1079[label="",style="dashed", color="magenta", weight=3]; 102 -> 1080[label="",style="dashed", color="magenta", weight=3]; 102 -> 1081[label="",style="dashed", color="magenta", weight=3]; 102 -> 1082[label="",style="dashed", color="magenta", weight=3]; 103[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];103 -> 138[label="",style="solid", color="black", weight=3]; 104[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];104 -> 139[label="",style="solid", color="black", weight=3]; 105[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];105 -> 140[label="",style="solid", color="black", weight=3]; 106 -> 1128[label="",style="dashed", color="red", weight=0]; 106[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];106 -> 1129[label="",style="dashed", color="magenta", weight=3]; 106 -> 1130[label="",style="dashed", color="magenta", weight=3]; 106 -> 1131[label="",style="dashed", color="magenta", weight=3]; 106 -> 1132[label="",style="dashed", color="magenta", weight=3]; 106 -> 1133[label="",style="dashed", color="magenta", weight=3]; 106 -> 1134[label="",style="dashed", color="magenta", weight=3]; 106 -> 1135[label="",style="dashed", color="magenta", weight=3]; 107[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];107 -> 143[label="",style="solid", color="black", weight=3]; 108[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];108 -> 144[label="",style="solid", color="black", weight=3]; 109[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];109 -> 145[label="",style="solid", color="black", weight=3]; 110 -> 1188[label="",style="dashed", color="red", weight=0]; 110[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];110 -> 1189[label="",style="dashed", color="magenta", weight=3]; 110 -> 1190[label="",style="dashed", color="magenta", weight=3]; 110 -> 1191[label="",style="dashed", color="magenta", weight=3]; 110 -> 1192[label="",style="dashed", color="magenta", weight=3]; 110 -> 1193[label="",style="dashed", color="magenta", weight=3]; 110 -> 1194[label="",style="dashed", color="magenta", weight=3]; 110 -> 1195[label="",style="dashed", color="magenta", weight=3]; 111[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];111 -> 148[label="",style="solid", color="black", weight=3]; 112[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];112 -> 149[label="",style="solid", color="black", weight=3]; 113[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];113 -> 150[label="",style="solid", color="black", weight=3]; 114 -> 1361[label="",style="dashed", color="red", weight=0]; 114[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];114 -> 1362[label="",style="dashed", color="magenta", weight=3]; 114 -> 1363[label="",style="dashed", color="magenta", weight=3]; 114 -> 1364[label="",style="dashed", color="magenta", weight=3]; 114 -> 1365[label="",style="dashed", color="magenta", weight=3]; 114 -> 1366[label="",style="dashed", color="magenta", weight=3]; 114 -> 1367[label="",style="dashed", color="magenta", weight=3]; 114 -> 1368[label="",style="dashed", color="magenta", weight=3]; 115[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];115 -> 153[label="",style="solid", color="black", weight=3]; 116[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];116 -> 154[label="",style="solid", color="black", weight=3]; 117[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];117 -> 155[label="",style="solid", color="black", weight=3]; 118 -> 1541[label="",style="dashed", color="red", weight=0]; 118[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Neg (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];118 -> 1542[label="",style="dashed", color="magenta", weight=3]; 118 -> 1543[label="",style="dashed", color="magenta", weight=3]; 118 -> 1544[label="",style="dashed", color="magenta", weight=3]; 118 -> 1545[label="",style="dashed", color="magenta", weight=3]; 118 -> 1546[label="",style="dashed", color="magenta", weight=3]; 118 -> 1547[label="",style="dashed", color="magenta", weight=3]; 118 -> 1548[label="",style="dashed", color="magenta", weight=3]; 119[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];119 -> 158[label="",style="solid", color="black", weight=3]; 120[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];120 -> 159[label="",style="solid", color="black", weight=3]; 121[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];121 -> 160[label="",style="solid", color="black", weight=3]; 122 -> 1724[label="",style="dashed", color="red", weight=0]; 122[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg (Succ vuz4100)) (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (primEqInt (Pos (primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100))) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];122 -> 1725[label="",style="dashed", color="magenta", weight=3]; 122 -> 1726[label="",style="dashed", color="magenta", weight=3]; 122 -> 1727[label="",style="dashed", color="magenta", weight=3]; 122 -> 1728[label="",style="dashed", color="magenta", weight=3]; 122 -> 1729[label="",style="dashed", color="magenta", weight=3]; 122 -> 1730[label="",style="dashed", color="magenta", weight=3]; 122 -> 1731[label="",style="dashed", color="magenta", weight=3]; 123[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];123 -> 163[label="",style="solid", color="black", weight=3]; 124[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];124 -> 164[label="",style="solid", color="black", weight=3]; 125[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];125 -> 165[label="",style="solid", color="black", weight=3]; 1966[label="vuz4100",fontsize=16,color="green",shape="box"];1967 -> 1354[label="",style="dashed", color="red", weight=0]; 1967[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1967 -> 2129[label="",style="dashed", color="magenta", weight=3]; 1967 -> 2130[label="",style="dashed", color="magenta", weight=3]; 1968[label="vuz300",fontsize=16,color="green",shape="box"];1969[label="vuz40",fontsize=16,color="green",shape="box"];1970 -> 1354[label="",style="dashed", color="red", weight=0]; 1970[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1970 -> 2131[label="",style="dashed", color="magenta", weight=3]; 1970 -> 2132[label="",style="dashed", color="magenta", weight=3]; 1971[label="vuz3100",fontsize=16,color="green",shape="box"];1972 -> 1354[label="",style="dashed", color="red", weight=0]; 1972[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1972 -> 2133[label="",style="dashed", color="magenta", weight=3]; 1972 -> 2134[label="",style="dashed", color="magenta", weight=3]; 1965[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos vuz145) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6448[label="vuz145/Succ vuz1450",fontsize=10,color="white",style="solid",shape="box"];1965 -> 6448[label="",style="solid", color="burlywood", weight=9]; 6448 -> 2135[label="",style="solid", color="burlywood", weight=3]; 6449[label="vuz145/Zero",fontsize=10,color="white",style="solid",shape="box"];1965 -> 6449[label="",style="solid", color="burlywood", weight=9]; 6449 -> 2136[label="",style="solid", color="burlywood", weight=3]; 128[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];128 -> 168[label="",style="solid", color="black", weight=3]; 129[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];129 -> 169[label="",style="solid", color="black", weight=3]; 130[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];130 -> 170[label="",style="solid", color="black", weight=3]; 1033[label="vuz4100",fontsize=16,color="green",shape="box"];1034 -> 1016[label="",style="dashed", color="red", weight=0]; 1034[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1034 -> 1070[label="",style="dashed", color="magenta", weight=3]; 1035[label="vuz3100",fontsize=16,color="green",shape="box"];1036[label="vuz300",fontsize=16,color="green",shape="box"];1037[label="vuz40",fontsize=16,color="green",shape="box"];1038 -> 1016[label="",style="dashed", color="red", weight=0]; 1038[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1038 -> 1071[label="",style="dashed", color="magenta", weight=3]; 1039 -> 1016[label="",style="dashed", color="red", weight=0]; 1039[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1039 -> 1072[label="",style="dashed", color="magenta", weight=3]; 1032[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg vuz69) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6450[label="vuz69/Succ vuz690",fontsize=10,color="white",style="solid",shape="box"];1032 -> 6450[label="",style="solid", color="burlywood", weight=9]; 6450 -> 1073[label="",style="solid", color="burlywood", weight=3]; 6451[label="vuz69/Zero",fontsize=10,color="white",style="solid",shape="box"];1032 -> 6451[label="",style="solid", color="burlywood", weight=9]; 6451 -> 1074[label="",style="solid", color="burlywood", weight=3]; 133[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];133 -> 173[label="",style="solid", color="black", weight=3]; 134[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];134 -> 174[label="",style="solid", color="black", weight=3]; 135[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];135 -> 175[label="",style="solid", color="black", weight=3]; 1076[label="vuz4100",fontsize=16,color="green",shape="box"];1077[label="vuz300",fontsize=16,color="green",shape="box"];1078[label="vuz40",fontsize=16,color="green",shape="box"];1079 -> 1016[label="",style="dashed", color="red", weight=0]; 1079[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1079 -> 1113[label="",style="dashed", color="magenta", weight=3]; 1079 -> 1114[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1016[label="",style="dashed", color="red", weight=0]; 1080[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1080 -> 1115[label="",style="dashed", color="magenta", weight=3]; 1080 -> 1116[label="",style="dashed", color="magenta", weight=3]; 1081[label="vuz3100",fontsize=16,color="green",shape="box"];1082 -> 1016[label="",style="dashed", color="red", weight=0]; 1082[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1082 -> 1117[label="",style="dashed", color="magenta", weight=3]; 1082 -> 1118[label="",style="dashed", color="magenta", weight=3]; 1075[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg vuz72) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6452[label="vuz72/Succ vuz720",fontsize=10,color="white",style="solid",shape="box"];1075 -> 6452[label="",style="solid", color="burlywood", weight=9]; 6452 -> 1119[label="",style="solid", color="burlywood", weight=3]; 6453[label="vuz72/Zero",fontsize=10,color="white",style="solid",shape="box"];1075 -> 6453[label="",style="solid", color="burlywood", weight=9]; 6453 -> 1120[label="",style="solid", color="burlywood", weight=3]; 138[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];138 -> 178[label="",style="solid", color="black", weight=3]; 139[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];139 -> 179[label="",style="solid", color="black", weight=3]; 140[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];140 -> 180[label="",style="solid", color="black", weight=3]; 1129[label="vuz300",fontsize=16,color="green",shape="box"];1130[label="vuz40",fontsize=16,color="green",shape="box"];1131 -> 1016[label="",style="dashed", color="red", weight=0]; 1131[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1131 -> 1166[label="",style="dashed", color="magenta", weight=3]; 1132[label="vuz3100",fontsize=16,color="green",shape="box"];1133[label="vuz4100",fontsize=16,color="green",shape="box"];1134 -> 1016[label="",style="dashed", color="red", weight=0]; 1134[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1134 -> 1167[label="",style="dashed", color="magenta", weight=3]; 1135 -> 1016[label="",style="dashed", color="red", weight=0]; 1135[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1135 -> 1168[label="",style="dashed", color="magenta", weight=3]; 1128[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos vuz75) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6454[label="vuz75/Succ vuz750",fontsize=10,color="white",style="solid",shape="box"];1128 -> 6454[label="",style="solid", color="burlywood", weight=9]; 6454 -> 1169[label="",style="solid", color="burlywood", weight=3]; 6455[label="vuz75/Zero",fontsize=10,color="white",style="solid",shape="box"];1128 -> 6455[label="",style="solid", color="burlywood", weight=9]; 6455 -> 1170[label="",style="solid", color="burlywood", weight=3]; 143[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];143 -> 183[label="",style="solid", color="black", weight=3]; 144[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];144 -> 184[label="",style="solid", color="black", weight=3]; 145[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];145 -> 185[label="",style="solid", color="black", weight=3]; 1189 -> 1016[label="",style="dashed", color="red", weight=0]; 1189[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1189 -> 1339[label="",style="dashed", color="magenta", weight=3]; 1189 -> 1340[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1016[label="",style="dashed", color="red", weight=0]; 1190[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1190 -> 1341[label="",style="dashed", color="magenta", weight=3]; 1190 -> 1342[label="",style="dashed", color="magenta", weight=3]; 1191[label="vuz40",fontsize=16,color="green",shape="box"];1192 -> 1016[label="",style="dashed", color="red", weight=0]; 1192[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1192 -> 1343[label="",style="dashed", color="magenta", weight=3]; 1192 -> 1344[label="",style="dashed", color="magenta", weight=3]; 1193[label="vuz3100",fontsize=16,color="green",shape="box"];1194[label="vuz300",fontsize=16,color="green",shape="box"];1195[label="vuz4100",fontsize=16,color="green",shape="box"];1188[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos vuz78) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6456[label="vuz78/Succ vuz780",fontsize=10,color="white",style="solid",shape="box"];1188 -> 6456[label="",style="solid", color="burlywood", weight=9]; 6456 -> 1345[label="",style="solid", color="burlywood", weight=3]; 6457[label="vuz78/Zero",fontsize=10,color="white",style="solid",shape="box"];1188 -> 6457[label="",style="solid", color="burlywood", weight=9]; 6457 -> 1346[label="",style="solid", color="burlywood", weight=3]; 148[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];148 -> 188[label="",style="solid", color="black", weight=3]; 149[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];149 -> 189[label="",style="solid", color="black", weight=3]; 150[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];150 -> 190[label="",style="solid", color="black", weight=3]; 1362[label="vuz3100",fontsize=16,color="green",shape="box"];1363[label="vuz40",fontsize=16,color="green",shape="box"];1364 -> 1016[label="",style="dashed", color="red", weight=0]; 1364[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1364 -> 1519[label="",style="dashed", color="magenta", weight=3]; 1365[label="vuz4100",fontsize=16,color="green",shape="box"];1366 -> 1016[label="",style="dashed", color="red", weight=0]; 1366[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1366 -> 1520[label="",style="dashed", color="magenta", weight=3]; 1367[label="vuz300",fontsize=16,color="green",shape="box"];1368 -> 1016[label="",style="dashed", color="red", weight=0]; 1368[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1368 -> 1521[label="",style="dashed", color="magenta", weight=3]; 1361[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg vuz93) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6458[label="vuz93/Succ vuz930",fontsize=10,color="white",style="solid",shape="box"];1361 -> 6458[label="",style="solid", color="burlywood", weight=9]; 6458 -> 1522[label="",style="solid", color="burlywood", weight=3]; 6459[label="vuz93/Zero",fontsize=10,color="white",style="solid",shape="box"];1361 -> 6459[label="",style="solid", color="burlywood", weight=9]; 6459 -> 1523[label="",style="solid", color="burlywood", weight=3]; 153[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];153 -> 193[label="",style="solid", color="black", weight=3]; 154[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];154 -> 194[label="",style="solid", color="black", weight=3]; 155[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];155 -> 195[label="",style="solid", color="black", weight=3]; 1542 -> 1354[label="",style="dashed", color="red", weight=0]; 1542[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1542 -> 1699[label="",style="dashed", color="magenta", weight=3]; 1542 -> 1700[label="",style="dashed", color="magenta", weight=3]; 1543[label="vuz4100",fontsize=16,color="green",shape="box"];1544[label="vuz40",fontsize=16,color="green",shape="box"];1545[label="vuz300",fontsize=16,color="green",shape="box"];1546 -> 1354[label="",style="dashed", color="red", weight=0]; 1546[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1546 -> 1701[label="",style="dashed", color="magenta", weight=3]; 1546 -> 1702[label="",style="dashed", color="magenta", weight=3]; 1547 -> 1354[label="",style="dashed", color="red", weight=0]; 1547[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1547 -> 1703[label="",style="dashed", color="magenta", weight=3]; 1547 -> 1704[label="",style="dashed", color="magenta", weight=3]; 1548[label="vuz3100",fontsize=16,color="green",shape="box"];1541[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg vuz108) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6460[label="vuz108/Succ vuz1080",fontsize=10,color="white",style="solid",shape="box"];1541 -> 6460[label="",style="solid", color="burlywood", weight=9]; 6460 -> 1705[label="",style="solid", color="burlywood", weight=3]; 6461[label="vuz108/Zero",fontsize=10,color="white",style="solid",shape="box"];1541 -> 6461[label="",style="solid", color="burlywood", weight=9]; 6461 -> 1706[label="",style="solid", color="burlywood", weight=3]; 158[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];158 -> 198[label="",style="solid", color="black", weight=3]; 159[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];159 -> 199[label="",style="solid", color="black", weight=3]; 160[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];160 -> 200[label="",style="solid", color="black", weight=3]; 1725[label="vuz40",fontsize=16,color="green",shape="box"];1726 -> 1354[label="",style="dashed", color="red", weight=0]; 1726[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1726 -> 1875[label="",style="dashed", color="magenta", weight=3]; 1726 -> 1876[label="",style="dashed", color="magenta", weight=3]; 1727[label="vuz3100",fontsize=16,color="green",shape="box"];1728 -> 1354[label="",style="dashed", color="red", weight=0]; 1728[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1728 -> 1877[label="",style="dashed", color="magenta", weight=3]; 1728 -> 1878[label="",style="dashed", color="magenta", weight=3]; 1729[label="vuz4100",fontsize=16,color="green",shape="box"];1730 -> 1354[label="",style="dashed", color="red", weight=0]; 1730[label="primPlusNat (primMulNat vuz4100 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];1730 -> 1879[label="",style="dashed", color="magenta", weight=3]; 1730 -> 1880[label="",style="dashed", color="magenta", weight=3]; 1731[label="vuz300",fontsize=16,color="green",shape="box"];1724[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos vuz123) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];6462[label="vuz123/Succ vuz1230",fontsize=10,color="white",style="solid",shape="box"];1724 -> 6462[label="",style="solid", color="burlywood", weight=9]; 6462 -> 1881[label="",style="solid", color="burlywood", weight=3]; 6463[label="vuz123/Zero",fontsize=10,color="white",style="solid",shape="box"];1724 -> 6463[label="",style="solid", color="burlywood", weight=9]; 6463 -> 1882[label="",style="solid", color="burlywood", weight=3]; 163[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];163 -> 203[label="",style="solid", color="black", weight=3]; 164[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];164 -> 204[label="",style="solid", color="black", weight=3]; 165[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];165 -> 205[label="",style="solid", color="black", weight=3]; 2129[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2130 -> 681[label="",style="dashed", color="red", weight=0]; 2130[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2130 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2130 -> 2150[label="",style="dashed", color="magenta", weight=3]; 1354[label="primPlusNat vuz660 vuz3100",fontsize=16,color="burlywood",shape="triangle"];6464[label="vuz660/Succ vuz6600",fontsize=10,color="white",style="solid",shape="box"];1354 -> 6464[label="",style="solid", color="burlywood", weight=9]; 6464 -> 1536[label="",style="solid", color="burlywood", weight=3]; 6465[label="vuz660/Zero",fontsize=10,color="white",style="solid",shape="box"];1354 -> 6465[label="",style="solid", color="burlywood", weight=9]; 6465 -> 1537[label="",style="solid", color="burlywood", weight=3]; 2131[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2132 -> 681[label="",style="dashed", color="red", weight=0]; 2132[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2132 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2132 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2133[label="Succ vuz3100",fontsize=16,color="green",shape="box"];2134 -> 681[label="",style="dashed", color="red", weight=0]; 2134[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];2134 -> 2153[label="",style="dashed", color="magenta", weight=3]; 2134 -> 2154[label="",style="dashed", color="magenta", weight=3]; 2135[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2135 -> 2155[label="",style="solid", color="black", weight=3]; 2136[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];2136 -> 2156[label="",style="solid", color="black", weight=3]; 168[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];168 -> 209[label="",style="solid", color="black", weight=3]; 169[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];169 -> 210[label="",style="solid", color="black", weight=3]; 170[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Neg vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];170 -> 211[label="",style="solid", color="black", weight=3]; 1070 -> 681[label="",style="dashed", color="red", weight=0]; 1070[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1070 -> 1121[label="",style="dashed", color="magenta", weight=3]; 1016[label="primPlusNat vuz66 (Succ vuz3100)",fontsize=16,color="burlywood",shape="triangle"];6466[label="vuz66/Succ vuz660",fontsize=10,color="white",style="solid",shape="box"];1016 -> 6466[label="",style="solid", color="burlywood", weight=9]; 6466 -> 1122[label="",style="solid", color="burlywood", weight=3]; 6467[label="vuz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1016 -> 6467[label="",style="solid", color="burlywood", weight=9]; 6467 -> 1123[label="",style="solid", color="burlywood", weight=3]; 1071 -> 681[label="",style="dashed", color="red", weight=0]; 1071[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1071 -> 1124[label="",style="dashed", color="magenta", weight=3]; 1072 -> 681[label="",style="dashed", color="red", weight=0]; 1072[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1072 -> 1125[label="",style="dashed", color="magenta", weight=3]; 1073[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1073 -> 1126[label="",style="solid", color="black", weight=3]; 1074[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1074 -> 1127[label="",style="solid", color="black", weight=3]; 173[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];173 -> 215[label="",style="solid", color="black", weight=3]; 174[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];174 -> 216[label="",style="solid", color="black", weight=3]; 175[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Neg vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];175 -> 217[label="",style="solid", color="black", weight=3]; 1113 -> 681[label="",style="dashed", color="red", weight=0]; 1113[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1113 -> 1171[label="",style="dashed", color="magenta", weight=3]; 1113 -> 1172[label="",style="dashed", color="magenta", weight=3]; 1114[label="vuz3100",fontsize=16,color="green",shape="box"];1115 -> 681[label="",style="dashed", color="red", weight=0]; 1115[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1115 -> 1173[label="",style="dashed", color="magenta", weight=3]; 1115 -> 1174[label="",style="dashed", color="magenta", weight=3]; 1116[label="vuz3100",fontsize=16,color="green",shape="box"];1117 -> 681[label="",style="dashed", color="red", weight=0]; 1117[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1117 -> 1175[label="",style="dashed", color="magenta", weight=3]; 1117 -> 1176[label="",style="dashed", color="magenta", weight=3]; 1118[label="vuz3100",fontsize=16,color="green",shape="box"];1119[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1119 -> 1177[label="",style="solid", color="black", weight=3]; 1120[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1120 -> 1178[label="",style="solid", color="black", weight=3]; 178[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];178 -> 221[label="",style="solid", color="black", weight=3]; 179[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Neg vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];179 -> 222[label="",style="solid", color="black", weight=3]; 180[label="reduce2Reduce1 (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Neg vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];180 -> 223[label="",style="solid", color="black", weight=3]; 1166 -> 681[label="",style="dashed", color="red", weight=0]; 1166[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1166 -> 1347[label="",style="dashed", color="magenta", weight=3]; 1167 -> 681[label="",style="dashed", color="red", weight=0]; 1167[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1167 -> 1348[label="",style="dashed", color="magenta", weight=3]; 1168 -> 681[label="",style="dashed", color="red", weight=0]; 1168[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1168 -> 1349[label="",style="dashed", color="magenta", weight=3]; 1169[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1169 -> 1350[label="",style="solid", color="black", weight=3]; 1170[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1170 -> 1351[label="",style="solid", color="black", weight=3]; 183[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];183 -> 227[label="",style="solid", color="black", weight=3]; 184[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Neg vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];184 -> 228[label="",style="solid", color="black", weight=3]; 185[label="reduce2Reduce1 (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Neg vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];185 -> 229[label="",style="solid", color="black", weight=3]; 1339 -> 681[label="",style="dashed", color="red", weight=0]; 1339[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1339 -> 1524[label="",style="dashed", color="magenta", weight=3]; 1339 -> 1525[label="",style="dashed", color="magenta", weight=3]; 1340[label="vuz3100",fontsize=16,color="green",shape="box"];1341 -> 681[label="",style="dashed", color="red", weight=0]; 1341[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1341 -> 1526[label="",style="dashed", color="magenta", weight=3]; 1341 -> 1527[label="",style="dashed", color="magenta", weight=3]; 1342[label="vuz3100",fontsize=16,color="green",shape="box"];1343 -> 681[label="",style="dashed", color="red", weight=0]; 1343[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1343 -> 1528[label="",style="dashed", color="magenta", weight=3]; 1343 -> 1529[label="",style="dashed", color="magenta", weight=3]; 1344[label="vuz3100",fontsize=16,color="green",shape="box"];1345[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1345 -> 1530[label="",style="solid", color="black", weight=3]; 1346[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1346 -> 1531[label="",style="solid", color="black", weight=3]; 188[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];188 -> 233[label="",style="solid", color="black", weight=3]; 189[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];189 -> 234[label="",style="solid", color="black", weight=3]; 190[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) (vuz40 * Pos Zero + Pos vuz300 * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];190 -> 235[label="",style="solid", color="black", weight=3]; 1519 -> 681[label="",style="dashed", color="red", weight=0]; 1519[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1519 -> 1707[label="",style="dashed", color="magenta", weight=3]; 1520 -> 681[label="",style="dashed", color="red", weight=0]; 1520[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1520 -> 1708[label="",style="dashed", color="magenta", weight=3]; 1521 -> 681[label="",style="dashed", color="red", weight=0]; 1521[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1521 -> 1709[label="",style="dashed", color="magenta", weight=3]; 1522[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1522 -> 1710[label="",style="solid", color="black", weight=3]; 1523[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1523 -> 1711[label="",style="solid", color="black", weight=3]; 193[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];193 -> 239[label="",style="solid", color="black", weight=3]; 194[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];194 -> 240[label="",style="solid", color="black", weight=3]; 195[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) (vuz40 * Neg Zero + Pos vuz300 * Pos Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];195 -> 241[label="",style="solid", color="black", weight=3]; 1699[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1700 -> 681[label="",style="dashed", color="red", weight=0]; 1700[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1700 -> 1883[label="",style="dashed", color="magenta", weight=3]; 1700 -> 1884[label="",style="dashed", color="magenta", weight=3]; 1701[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1702 -> 681[label="",style="dashed", color="red", weight=0]; 1702[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1702 -> 1885[label="",style="dashed", color="magenta", weight=3]; 1702 -> 1886[label="",style="dashed", color="magenta", weight=3]; 1703[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1704 -> 681[label="",style="dashed", color="red", weight=0]; 1704[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1704 -> 1887[label="",style="dashed", color="magenta", weight=3]; 1704 -> 1888[label="",style="dashed", color="magenta", weight=3]; 1705[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1705 -> 1889[label="",style="solid", color="black", weight=3]; 1706[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1706 -> 1890[label="",style="solid", color="black", weight=3]; 198[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg (Succ vuz4100)) (Neg Zero) True",fontsize=16,color="black",shape="box"];198 -> 245[label="",style="solid", color="black", weight=3]; 199[label="reduce2Reduce1 (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos (Succ vuz3100) + Pos vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];199 -> 246[label="",style="solid", color="black", weight=3]; 200[label="reduce2Reduce1 (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) (vuz40 * Pos Zero + Pos vuz300 * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];200 -> 247[label="",style="solid", color="black", weight=3]; 1875[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1876 -> 681[label="",style="dashed", color="red", weight=0]; 1876[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1876 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1877[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1878 -> 681[label="",style="dashed", color="red", weight=0]; 1878[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1878 -> 1918[label="",style="dashed", color="magenta", weight=3]; 1879[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1880 -> 681[label="",style="dashed", color="red", weight=0]; 1880[label="primMulNat vuz4100 (Succ vuz3100)",fontsize=16,color="magenta"];1880 -> 1919[label="",style="dashed", color="magenta", weight=3]; 1881[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1881 -> 1920[label="",style="solid", color="black", weight=3]; 1882[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];1882 -> 1921[label="",style="solid", color="black", weight=3]; 203[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg (Succ vuz4100)) (Pos Zero) True",fontsize=16,color="black",shape="box"];203 -> 251[label="",style="solid", color="black", weight=3]; 204[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg (Succ vuz3100) + Pos vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];204 -> 252[label="",style="solid", color="black", weight=3]; 205[label="reduce2Reduce1 (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) (vuz40 * Neg Zero + Pos vuz300 * Neg Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];205 -> 253[label="",style="solid", color="black", weight=3]; 2149[label="vuz3100",fontsize=16,color="green",shape="box"];2150[label="vuz4100",fontsize=16,color="green",shape="box"];681[label="primMulNat vuz41000 (Succ vuz3100)",fontsize=16,color="burlywood",shape="triangle"];6468[label="vuz41000/Succ vuz410000",fontsize=10,color="white",style="solid",shape="box"];681 -> 6468[label="",style="solid", color="burlywood", weight=9]; 6468 -> 781[label="",style="solid", color="burlywood", weight=3]; 6469[label="vuz41000/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 6469[label="",style="solid", color="burlywood", weight=9]; 6469 -> 782[label="",style="solid", color="burlywood", weight=3]; 1536[label="primPlusNat (Succ vuz6600) vuz3100",fontsize=16,color="burlywood",shape="box"];6470[label="vuz3100/Succ vuz31000",fontsize=10,color="white",style="solid",shape="box"];1536 -> 6470[label="",style="solid", color="burlywood", weight=9]; 6470 -> 1717[label="",style="solid", color="burlywood", weight=3]; 6471[label="vuz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];1536 -> 6471[label="",style="solid", color="burlywood", weight=9]; 6471 -> 1718[label="",style="solid", color="burlywood", weight=3]; 1537[label="primPlusNat Zero vuz3100",fontsize=16,color="burlywood",shape="box"];6472[label="vuz3100/Succ vuz31000",fontsize=10,color="white",style="solid",shape="box"];1537 -> 6472[label="",style="solid", color="burlywood", weight=9]; 6472 -> 1719[label="",style="solid", color="burlywood", weight=3]; 6473[label="vuz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];1537 -> 6473[label="",style="solid", color="burlywood", weight=9]; 6473 -> 1720[label="",style="solid", color="burlywood", weight=3]; 2151[label="vuz3100",fontsize=16,color="green",shape="box"];2152[label="vuz4100",fontsize=16,color="green",shape="box"];2153[label="vuz3100",fontsize=16,color="green",shape="box"];2154[label="vuz4100",fontsize=16,color="green",shape="box"];2155[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos (Succ vuz1450)) (Pos Zero))",fontsize=16,color="black",shape="box"];2155 -> 2170[label="",style="solid", color="black", weight=3]; 2156[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];2156 -> 2171[label="",style="solid", color="black", weight=3]; 209[label="error []",fontsize=16,color="black",shape="triangle"];209 -> 257[label="",style="solid", color="black", weight=3]; 210 -> 209[label="",style="dashed", color="red", weight=0]; 210[label="error []",fontsize=16,color="magenta"];211 -> 209[label="",style="dashed", color="red", weight=0]; 211[label="error []",fontsize=16,color="magenta"];1121[label="vuz4100",fontsize=16,color="green",shape="box"];1122[label="primPlusNat (Succ vuz660) (Succ vuz3100)",fontsize=16,color="black",shape="box"];1122 -> 1179[label="",style="solid", color="black", weight=3]; 1123[label="primPlusNat Zero (Succ vuz3100)",fontsize=16,color="black",shape="box"];1123 -> 1180[label="",style="solid", color="black", weight=3]; 1124[label="vuz4100",fontsize=16,color="green",shape="box"];1125[label="vuz4100",fontsize=16,color="green",shape="box"];1126[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg (Succ vuz690)) (Pos Zero))",fontsize=16,color="black",shape="box"];1126 -> 1181[label="",style="solid", color="black", weight=3]; 1127[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1127 -> 1182[label="",style="solid", color="black", weight=3]; 215 -> 209[label="",style="dashed", color="red", weight=0]; 215[label="error []",fontsize=16,color="magenta"];216 -> 209[label="",style="dashed", color="red", weight=0]; 216[label="error []",fontsize=16,color="magenta"];217 -> 209[label="",style="dashed", color="red", weight=0]; 217[label="error []",fontsize=16,color="magenta"];1171[label="vuz3100",fontsize=16,color="green",shape="box"];1172[label="vuz4100",fontsize=16,color="green",shape="box"];1173[label="vuz3100",fontsize=16,color="green",shape="box"];1174[label="vuz4100",fontsize=16,color="green",shape="box"];1175[label="vuz3100",fontsize=16,color="green",shape="box"];1176[label="vuz4100",fontsize=16,color="green",shape="box"];1177[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg (Succ vuz720)) (Pos Zero))",fontsize=16,color="black",shape="box"];1177 -> 1352[label="",style="solid", color="black", weight=3]; 1178[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1178 -> 1353[label="",style="solid", color="black", weight=3]; 221 -> 209[label="",style="dashed", color="red", weight=0]; 221[label="error []",fontsize=16,color="magenta"];222 -> 209[label="",style="dashed", color="red", weight=0]; 222[label="error []",fontsize=16,color="magenta"];223 -> 209[label="",style="dashed", color="red", weight=0]; 223[label="error []",fontsize=16,color="magenta"];1347[label="vuz4100",fontsize=16,color="green",shape="box"];1348[label="vuz4100",fontsize=16,color="green",shape="box"];1349[label="vuz4100",fontsize=16,color="green",shape="box"];1350[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos (Succ vuz750)) (Pos Zero))",fontsize=16,color="black",shape="box"];1350 -> 1532[label="",style="solid", color="black", weight=3]; 1351[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1351 -> 1533[label="",style="solid", color="black", weight=3]; 227 -> 209[label="",style="dashed", color="red", weight=0]; 227[label="error []",fontsize=16,color="magenta"];228 -> 209[label="",style="dashed", color="red", weight=0]; 228[label="error []",fontsize=16,color="magenta"];229 -> 209[label="",style="dashed", color="red", weight=0]; 229[label="error []",fontsize=16,color="magenta"];1524[label="vuz3100",fontsize=16,color="green",shape="box"];1525[label="vuz4100",fontsize=16,color="green",shape="box"];1526[label="vuz3100",fontsize=16,color="green",shape="box"];1527[label="vuz4100",fontsize=16,color="green",shape="box"];1528[label="vuz3100",fontsize=16,color="green",shape="box"];1529[label="vuz4100",fontsize=16,color="green",shape="box"];1530[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos (Succ vuz780)) (Pos Zero))",fontsize=16,color="black",shape="box"];1530 -> 1712[label="",style="solid", color="black", weight=3]; 1531[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1531 -> 1713[label="",style="solid", color="black", weight=3]; 233 -> 209[label="",style="dashed", color="red", weight=0]; 233[label="error []",fontsize=16,color="magenta"];234 -> 209[label="",style="dashed", color="red", weight=0]; 234[label="error []",fontsize=16,color="magenta"];235 -> 209[label="",style="dashed", color="red", weight=0]; 235[label="error []",fontsize=16,color="magenta"];1707[label="vuz4100",fontsize=16,color="green",shape="box"];1708[label="vuz4100",fontsize=16,color="green",shape="box"];1709[label="vuz4100",fontsize=16,color="green",shape="box"];1710[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg (Succ vuz930)) (Pos Zero))",fontsize=16,color="black",shape="box"];1710 -> 1891[label="",style="solid", color="black", weight=3]; 1711[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1711 -> 1892[label="",style="solid", color="black", weight=3]; 239 -> 209[label="",style="dashed", color="red", weight=0]; 239[label="error []",fontsize=16,color="magenta"];240 -> 209[label="",style="dashed", color="red", weight=0]; 240[label="error []",fontsize=16,color="magenta"];241 -> 209[label="",style="dashed", color="red", weight=0]; 241[label="error []",fontsize=16,color="magenta"];1883[label="vuz3100",fontsize=16,color="green",shape="box"];1884[label="vuz4100",fontsize=16,color="green",shape="box"];1885[label="vuz3100",fontsize=16,color="green",shape="box"];1886[label="vuz4100",fontsize=16,color="green",shape="box"];1887[label="vuz3100",fontsize=16,color="green",shape="box"];1888[label="vuz4100",fontsize=16,color="green",shape="box"];1889[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg (Succ vuz1080)) (Pos Zero))",fontsize=16,color="black",shape="box"];1889 -> 1922[label="",style="solid", color="black", weight=3]; 1890[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1890 -> 1923[label="",style="solid", color="black", weight=3]; 245 -> 209[label="",style="dashed", color="red", weight=0]; 245[label="error []",fontsize=16,color="magenta"];246 -> 209[label="",style="dashed", color="red", weight=0]; 246[label="error []",fontsize=16,color="magenta"];247 -> 209[label="",style="dashed", color="red", weight=0]; 247[label="error []",fontsize=16,color="magenta"];1917[label="vuz4100",fontsize=16,color="green",shape="box"];1918[label="vuz4100",fontsize=16,color="green",shape="box"];1919[label="vuz4100",fontsize=16,color="green",shape="box"];1920[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos (Succ vuz1230)) (Pos Zero))",fontsize=16,color="black",shape="box"];1920 -> 1942[label="",style="solid", color="black", weight=3]; 1921[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];1921 -> 1943[label="",style="solid", color="black", weight=3]; 251 -> 209[label="",style="dashed", color="red", weight=0]; 251[label="error []",fontsize=16,color="magenta"];252 -> 209[label="",style="dashed", color="red", weight=0]; 252[label="error []",fontsize=16,color="magenta"];253 -> 209[label="",style="dashed", color="red", weight=0]; 253[label="error []",fontsize=16,color="magenta"];781[label="primMulNat (Succ vuz410000) (Succ vuz3100)",fontsize=16,color="black",shape="box"];781 -> 899[label="",style="solid", color="black", weight=3]; 782[label="primMulNat Zero (Succ vuz3100)",fontsize=16,color="black",shape="box"];782 -> 900[label="",style="solid", color="black", weight=3]; 1717[label="primPlusNat (Succ vuz6600) (Succ vuz31000)",fontsize=16,color="black",shape="box"];1717 -> 1895[label="",style="solid", color="black", weight=3]; 1718[label="primPlusNat (Succ vuz6600) Zero",fontsize=16,color="black",shape="box"];1718 -> 1896[label="",style="solid", color="black", weight=3]; 1719[label="primPlusNat Zero (Succ vuz31000)",fontsize=16,color="black",shape="box"];1719 -> 1897[label="",style="solid", color="black", weight=3]; 1720[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1720 -> 1898[label="",style="solid", color="black", weight=3]; 2170[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) False",fontsize=16,color="black",shape="box"];2170 -> 2187[label="",style="solid", color="black", weight=3]; 2171[label="reduce2Reduce1 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2171 -> 2188[label="",style="solid", color="black", weight=3]; 257[label="error []",fontsize=16,color="red",shape="box"];1179[label="Succ (Succ (primPlusNat vuz660 vuz3100))",fontsize=16,color="green",shape="box"];1179 -> 1354[label="",style="dashed", color="green", weight=3]; 1180[label="Succ vuz3100",fontsize=16,color="green",shape="box"];1181[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) False",fontsize=16,color="black",shape="box"];1181 -> 1355[label="",style="solid", color="black", weight=3]; 1182[label="reduce2Reduce1 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1182 -> 1356[label="",style="solid", color="black", weight=3]; 1352[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) False",fontsize=16,color="black",shape="box"];1352 -> 1534[label="",style="solid", color="black", weight=3]; 1353[label="reduce2Reduce1 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1353 -> 1535[label="",style="solid", color="black", weight=3]; 1532[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) False",fontsize=16,color="black",shape="box"];1532 -> 1714[label="",style="solid", color="black", weight=3]; 1533[label="reduce2Reduce1 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1533 -> 1715[label="",style="solid", color="black", weight=3]; 1712[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) False",fontsize=16,color="black",shape="box"];1712 -> 1893[label="",style="solid", color="black", weight=3]; 1713[label="reduce2Reduce1 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1713 -> 1894[label="",style="solid", color="black", weight=3]; 1891[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) False",fontsize=16,color="black",shape="box"];1891 -> 1924[label="",style="solid", color="black", weight=3]; 1892[label="reduce2Reduce1 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1892 -> 1925[label="",style="solid", color="black", weight=3]; 1922[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) False",fontsize=16,color="black",shape="box"];1922 -> 1944[label="",style="solid", color="black", weight=3]; 1923[label="reduce2Reduce1 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];1923 -> 1945[label="",style="solid", color="black", weight=3]; 1942[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) False",fontsize=16,color="black",shape="box"];1942 -> 2137[label="",style="solid", color="black", weight=3]; 1943[label="reduce2Reduce1 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];1943 -> 2138[label="",style="solid", color="black", weight=3]; 899 -> 1016[label="",style="dashed", color="red", weight=0]; 899[label="primPlusNat (primMulNat vuz410000 (Succ vuz3100)) (Succ vuz3100)",fontsize=16,color="magenta"];899 -> 1017[label="",style="dashed", color="magenta", weight=3]; 900[label="Zero",fontsize=16,color="green",shape="box"];1895[label="Succ (Succ (primPlusNat vuz6600 vuz31000))",fontsize=16,color="green",shape="box"];1895 -> 1927[label="",style="dashed", color="green", weight=3]; 1896[label="Succ vuz6600",fontsize=16,color="green",shape="box"];1897[label="Succ vuz31000",fontsize=16,color="green",shape="box"];1898[label="Zero",fontsize=16,color="green",shape="box"];2187[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) otherwise",fontsize=16,color="black",shape="box"];2187 -> 2206[label="",style="solid", color="black", weight=3]; 2188 -> 209[label="",style="dashed", color="red", weight=0]; 2188[label="error []",fontsize=16,color="magenta"];1355[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) otherwise",fontsize=16,color="black",shape="box"];1355 -> 1538[label="",style="solid", color="black", weight=3]; 1356 -> 209[label="",style="dashed", color="red", weight=0]; 1356[label="error []",fontsize=16,color="magenta"];1534[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) otherwise",fontsize=16,color="black",shape="box"];1534 -> 1716[label="",style="solid", color="black", weight=3]; 1535 -> 209[label="",style="dashed", color="red", weight=0]; 1535[label="error []",fontsize=16,color="magenta"];1714[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) otherwise",fontsize=16,color="black",shape="box"];1714 -> 1899[label="",style="solid", color="black", weight=3]; 1715 -> 209[label="",style="dashed", color="red", weight=0]; 1715[label="error []",fontsize=16,color="magenta"];1893[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) otherwise",fontsize=16,color="black",shape="box"];1893 -> 1926[label="",style="solid", color="black", weight=3]; 1894 -> 209[label="",style="dashed", color="red", weight=0]; 1894[label="error []",fontsize=16,color="magenta"];1924[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) otherwise",fontsize=16,color="black",shape="box"];1924 -> 1946[label="",style="solid", color="black", weight=3]; 1925 -> 209[label="",style="dashed", color="red", weight=0]; 1925[label="error []",fontsize=16,color="magenta"];1944[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) otherwise",fontsize=16,color="black",shape="box"];1944 -> 2139[label="",style="solid", color="black", weight=3]; 1945 -> 209[label="",style="dashed", color="red", weight=0]; 1945[label="error []",fontsize=16,color="magenta"];2137[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) otherwise",fontsize=16,color="black",shape="box"];2137 -> 2157[label="",style="solid", color="black", weight=3]; 2138 -> 209[label="",style="dashed", color="red", weight=0]; 2138[label="error []",fontsize=16,color="magenta"];1017 -> 681[label="",style="dashed", color="red", weight=0]; 1017[label="primMulNat vuz410000 (Succ vuz3100)",fontsize=16,color="magenta"];1017 -> 1183[label="",style="dashed", color="magenta", weight=3]; 1927 -> 1354[label="",style="dashed", color="red", weight=0]; 1927[label="primPlusNat vuz6600 vuz31000",fontsize=16,color="magenta"];1927 -> 1948[label="",style="dashed", color="magenta", weight=3]; 1927 -> 1949[label="",style="dashed", color="magenta", weight=3]; 2206[label="reduce2Reduce0 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz143) True",fontsize=16,color="black",shape="box"];2206 -> 2222[label="",style="solid", color="black", weight=3]; 1538[label="reduce2Reduce0 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz67) True",fontsize=16,color="black",shape="box"];1538 -> 1721[label="",style="solid", color="black", weight=3]; 1716[label="reduce2Reduce0 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz70) True",fontsize=16,color="black",shape="box"];1716 -> 1900[label="",style="solid", color="black", weight=3]; 1899[label="reduce2Reduce0 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz73) True",fontsize=16,color="black",shape="box"];1899 -> 1928[label="",style="solid", color="black", weight=3]; 1926[label="reduce2Reduce0 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz76) True",fontsize=16,color="black",shape="box"];1926 -> 1947[label="",style="solid", color="black", weight=3]; 1946[label="reduce2Reduce0 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz91) True",fontsize=16,color="black",shape="box"];1946 -> 2140[label="",style="solid", color="black", weight=3]; 2139[label="reduce2Reduce0 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz106) True",fontsize=16,color="black",shape="box"];2139 -> 2158[label="",style="solid", color="black", weight=3]; 2157[label="reduce2Reduce0 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz121) True",fontsize=16,color="black",shape="box"];2157 -> 2172[label="",style="solid", color="black", weight=3]; 1183[label="vuz410000",fontsize=16,color="green",shape="box"];1948[label="vuz31000",fontsize=16,color="green",shape="box"];1949[label="vuz6600",fontsize=16,color="green",shape="box"];2222[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144) :% (Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="green",shape="box"];2222 -> 2237[label="",style="dashed", color="green", weight=3]; 2222 -> 2238[label="",style="dashed", color="green", weight=3]; 1721[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68) :% (Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="green",shape="box"];1721 -> 1901[label="",style="dashed", color="green", weight=3]; 1721 -> 1902[label="",style="dashed", color="green", weight=3]; 1900[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71) :% (Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="green",shape="box"];1900 -> 1929[label="",style="dashed", color="green", weight=3]; 1900 -> 1930[label="",style="dashed", color="green", weight=3]; 1928[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74) :% (Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="green",shape="box"];1928 -> 1950[label="",style="dashed", color="green", weight=3]; 1928 -> 1951[label="",style="dashed", color="green", weight=3]; 1947[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77) :% (Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="green",shape="box"];1947 -> 2141[label="",style="dashed", color="green", weight=3]; 1947 -> 2142[label="",style="dashed", color="green", weight=3]; 2140[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92) :% (Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="green",shape="box"];2140 -> 2159[label="",style="dashed", color="green", weight=3]; 2140 -> 2160[label="",style="dashed", color="green", weight=3]; 2158[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107) :% (Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="green",shape="box"];2158 -> 2173[label="",style="dashed", color="green", weight=3]; 2158 -> 2174[label="",style="dashed", color="green", weight=3]; 2172[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122) :% (Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="green",shape="box"];2172 -> 2189[label="",style="dashed", color="green", weight=3]; 2172 -> 2190[label="",style="dashed", color="green", weight=3]; 2237[label="(vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2237 -> 2250[label="",style="solid", color="black", weight=3]; 2238[label="Pos vuz143 `quot` reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];2238 -> 2251[label="",style="solid", color="black", weight=3]; 1901[label="(vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1901 -> 1931[label="",style="solid", color="black", weight=3]; 1902[label="Neg vuz67 `quot` reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];1902 -> 1932[label="",style="solid", color="black", weight=3]; 1929[label="(vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1929 -> 1952[label="",style="solid", color="black", weight=3]; 1930[label="Neg vuz70 `quot` reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];1930 -> 1953[label="",style="solid", color="black", weight=3]; 1950[label="(vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1950 -> 2143[label="",style="solid", color="black", weight=3]; 1951[label="Pos vuz73 `quot` reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];1951 -> 2144[label="",style="solid", color="black", weight=3]; 2141[label="(vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2141 -> 2161[label="",style="solid", color="black", weight=3]; 2142[label="Pos vuz76 `quot` reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];2142 -> 2162[label="",style="solid", color="black", weight=3]; 2159[label="(vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2159 -> 2175[label="",style="solid", color="black", weight=3]; 2160[label="Neg vuz91 `quot` reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];2160 -> 2176[label="",style="solid", color="black", weight=3]; 2173[label="(vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2173 -> 2191[label="",style="solid", color="black", weight=3]; 2174[label="Neg vuz106 `quot` reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];2174 -> 2192[label="",style="solid", color="black", weight=3]; 2189[label="(vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2189 -> 2207[label="",style="solid", color="black", weight=3]; 2190[label="Pos vuz121 `quot` reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];2190 -> 2208[label="",style="solid", color="black", weight=3]; 2250[label="primQuotInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2250 -> 2262[label="",style="solid", color="black", weight=3]; 2251 -> 5046[label="",style="dashed", color="red", weight=0]; 2251[label="primQuotInt (Pos vuz143) (reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144))",fontsize=16,color="magenta"];2251 -> 5047[label="",style="dashed", color="magenta", weight=3]; 2251 -> 5048[label="",style="dashed", color="magenta", weight=3]; 1931[label="primQuotInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="black",shape="box"];1931 -> 1960[label="",style="solid", color="black", weight=3]; 1932 -> 3509[label="",style="dashed", color="red", weight=0]; 1932[label="primQuotInt (Neg vuz67) (reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68))",fontsize=16,color="magenta"];1932 -> 3510[label="",style="dashed", color="magenta", weight=3]; 1932 -> 3511[label="",style="dashed", color="magenta", weight=3]; 1952[label="primQuotInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="black",shape="box"];1952 -> 2145[label="",style="solid", color="black", weight=3]; 1953 -> 3509[label="",style="dashed", color="red", weight=0]; 1953[label="primQuotInt (Neg vuz70) (reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71))",fontsize=16,color="magenta"];1953 -> 3512[label="",style="dashed", color="magenta", weight=3]; 1953 -> 3513[label="",style="dashed", color="magenta", weight=3]; 2143[label="primQuotInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="black",shape="box"];2143 -> 2163[label="",style="solid", color="black", weight=3]; 2144 -> 5046[label="",style="dashed", color="red", weight=0]; 2144[label="primQuotInt (Pos vuz73) (reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74))",fontsize=16,color="magenta"];2144 -> 5049[label="",style="dashed", color="magenta", weight=3]; 2161[label="primQuotInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="black",shape="box"];2161 -> 2177[label="",style="solid", color="black", weight=3]; 2162 -> 5046[label="",style="dashed", color="red", weight=0]; 2162[label="primQuotInt (Pos vuz76) (reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77))",fontsize=16,color="magenta"];2162 -> 5050[label="",style="dashed", color="magenta", weight=3]; 2162 -> 5051[label="",style="dashed", color="magenta", weight=3]; 2175[label="primQuotInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="black",shape="box"];2175 -> 2193[label="",style="solid", color="black", weight=3]; 2176 -> 3509[label="",style="dashed", color="red", weight=0]; 2176[label="primQuotInt (Neg vuz91) (reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92))",fontsize=16,color="magenta"];2176 -> 3514[label="",style="dashed", color="magenta", weight=3]; 2176 -> 3515[label="",style="dashed", color="magenta", weight=3]; 2191[label="primQuotInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="black",shape="box"];2191 -> 2209[label="",style="solid", color="black", weight=3]; 2192 -> 3509[label="",style="dashed", color="red", weight=0]; 2192[label="primQuotInt (Neg vuz106) (reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107))",fontsize=16,color="magenta"];2192 -> 3516[label="",style="dashed", color="magenta", weight=3]; 2192 -> 3517[label="",style="dashed", color="magenta", weight=3]; 2207[label="primQuotInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="black",shape="box"];2207 -> 2223[label="",style="solid", color="black", weight=3]; 2208 -> 5046[label="",style="dashed", color="red", weight=0]; 2208[label="primQuotInt (Pos vuz121) (reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122))",fontsize=16,color="magenta"];2208 -> 5052[label="",style="dashed", color="magenta", weight=3]; 2208 -> 5053[label="",style="dashed", color="magenta", weight=3]; 2262[label="primQuotInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2262 -> 2270[label="",style="solid", color="black", weight=3]; 5047[label="reduce2D (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5047 -> 5683[label="",style="solid", color="black", weight=3]; 5048[label="vuz143",fontsize=16,color="green",shape="box"];5046[label="primQuotInt (Pos vuz73) vuz346",fontsize=16,color="burlywood",shape="triangle"];6474[label="vuz346/Pos vuz3460",fontsize=10,color="white",style="solid",shape="box"];5046 -> 6474[label="",style="solid", color="burlywood", weight=9]; 6474 -> 5684[label="",style="solid", color="burlywood", weight=3]; 6475[label="vuz346/Neg vuz3460",fontsize=10,color="white",style="solid",shape="box"];5046 -> 6475[label="",style="solid", color="burlywood", weight=9]; 6475 -> 5685[label="",style="solid", color="burlywood", weight=3]; 1960[label="primQuotInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];1960 -> 2147[label="",style="solid", color="black", weight=3]; 3510[label="reduce2D (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];3510 -> 4084[label="",style="solid", color="black", weight=3]; 3511[label="vuz67",fontsize=16,color="green",shape="box"];3509[label="primQuotInt (Neg vuz280) vuz281",fontsize=16,color="burlywood",shape="triangle"];6476[label="vuz281/Pos vuz2810",fontsize=10,color="white",style="solid",shape="box"];3509 -> 6476[label="",style="solid", color="burlywood", weight=9]; 6476 -> 4085[label="",style="solid", color="burlywood", weight=3]; 6477[label="vuz281/Neg vuz2810",fontsize=10,color="white",style="solid",shape="box"];3509 -> 6477[label="",style="solid", color="burlywood", weight=9]; 6477 -> 4086[label="",style="solid", color="burlywood", weight=3]; 2145[label="primQuotInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2145 -> 2165[label="",style="solid", color="black", weight=3]; 3512[label="reduce2D (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];3512 -> 4087[label="",style="solid", color="black", weight=3]; 3513[label="vuz70",fontsize=16,color="green",shape="box"];2163[label="primQuotInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2163 -> 2179[label="",style="solid", color="black", weight=3]; 5049[label="reduce2D (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5049 -> 5686[label="",style="solid", color="black", weight=3]; 2177[label="primQuotInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2177 -> 2195[label="",style="solid", color="black", weight=3]; 5050[label="reduce2D (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5050 -> 5687[label="",style="solid", color="black", weight=3]; 5051[label="vuz76",fontsize=16,color="green",shape="box"];2193[label="primQuotInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2193 -> 2211[label="",style="solid", color="black", weight=3]; 3514[label="reduce2D (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];3514 -> 4088[label="",style="solid", color="black", weight=3]; 3515[label="vuz91",fontsize=16,color="green",shape="box"];2209[label="primQuotInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2209 -> 2225[label="",style="solid", color="black", weight=3]; 3516[label="reduce2D (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];3516 -> 4089[label="",style="solid", color="black", weight=3]; 3517[label="vuz106",fontsize=16,color="green",shape="box"];2223[label="primQuotInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2223 -> 2239[label="",style="solid", color="black", weight=3]; 5052[label="reduce2D (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5052 -> 5688[label="",style="solid", color="black", weight=3]; 5053[label="vuz121",fontsize=16,color="green",shape="box"];2270[label="primQuotInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6478[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];2270 -> 6478[label="",style="solid", color="burlywood", weight=9]; 6478 -> 2276[label="",style="solid", color="burlywood", weight=3]; 6479[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];2270 -> 6479[label="",style="solid", color="burlywood", weight=9]; 6479 -> 2277[label="",style="solid", color="burlywood", weight=3]; 5683[label="gcd (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5683 -> 5695[label="",style="solid", color="black", weight=3]; 5684[label="primQuotInt (Pos vuz73) (Pos vuz3460)",fontsize=16,color="burlywood",shape="box"];6480[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5684 -> 6480[label="",style="solid", color="burlywood", weight=9]; 6480 -> 5696[label="",style="solid", color="burlywood", weight=3]; 6481[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5684 -> 6481[label="",style="solid", color="burlywood", weight=9]; 6481 -> 5697[label="",style="solid", color="burlywood", weight=3]; 5685[label="primQuotInt (Pos vuz73) (Neg vuz3460)",fontsize=16,color="burlywood",shape="box"];6482[label="vuz3460/Succ vuz34600",fontsize=10,color="white",style="solid",shape="box"];5685 -> 6482[label="",style="solid", color="burlywood", weight=9]; 6482 -> 5698[label="",style="solid", color="burlywood", weight=3]; 6483[label="vuz3460/Zero",fontsize=10,color="white",style="solid",shape="box"];5685 -> 6483[label="",style="solid", color="burlywood", weight=9]; 6483 -> 5699[label="",style="solid", color="burlywood", weight=3]; 2147[label="primQuotInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6484[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];2147 -> 6484[label="",style="solid", color="burlywood", weight=9]; 6484 -> 2167[label="",style="solid", color="burlywood", weight=3]; 6485[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];2147 -> 6485[label="",style="solid", color="burlywood", weight=9]; 6485 -> 2168[label="",style="solid", color="burlywood", weight=3]; 4084[label="gcd (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4084 -> 4093[label="",style="solid", color="black", weight=3]; 4085[label="primQuotInt (Neg vuz280) (Pos vuz2810)",fontsize=16,color="burlywood",shape="box"];6486[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4085 -> 6486[label="",style="solid", color="burlywood", weight=9]; 6486 -> 4094[label="",style="solid", color="burlywood", weight=3]; 6487[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4085 -> 6487[label="",style="solid", color="burlywood", weight=9]; 6487 -> 4095[label="",style="solid", color="burlywood", weight=3]; 4086[label="primQuotInt (Neg vuz280) (Neg vuz2810)",fontsize=16,color="burlywood",shape="box"];6488[label="vuz2810/Succ vuz28100",fontsize=10,color="white",style="solid",shape="box"];4086 -> 6488[label="",style="solid", color="burlywood", weight=9]; 6488 -> 4096[label="",style="solid", color="burlywood", weight=3]; 6489[label="vuz2810/Zero",fontsize=10,color="white",style="solid",shape="box"];4086 -> 6489[label="",style="solid", color="burlywood", weight=9]; 6489 -> 4097[label="",style="solid", color="burlywood", weight=3]; 2165[label="primQuotInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="burlywood",shape="box"];6490[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];2165 -> 6490[label="",style="solid", color="burlywood", weight=9]; 6490 -> 2181[label="",style="solid", color="burlywood", weight=3]; 6491[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];2165 -> 6491[label="",style="solid", color="burlywood", weight=9]; 6491 -> 2182[label="",style="solid", color="burlywood", weight=3]; 4087[label="gcd (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4087 -> 4098[label="",style="solid", color="black", weight=3]; 2179[label="primQuotInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="burlywood",shape="box"];6492[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];2179 -> 6492[label="",style="solid", color="burlywood", weight=9]; 6492 -> 2197[label="",style="solid", color="burlywood", weight=3]; 6493[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];2179 -> 6493[label="",style="solid", color="burlywood", weight=9]; 6493 -> 2198[label="",style="solid", color="burlywood", weight=3]; 5686[label="gcd (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5686 -> 5700[label="",style="solid", color="black", weight=3]; 2195[label="primQuotInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="burlywood",shape="box"];6494[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];2195 -> 6494[label="",style="solid", color="burlywood", weight=9]; 6494 -> 2213[label="",style="solid", color="burlywood", weight=3]; 6495[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];2195 -> 6495[label="",style="solid", color="burlywood", weight=9]; 6495 -> 2214[label="",style="solid", color="burlywood", weight=3]; 5687[label="gcd (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5687 -> 5701[label="",style="solid", color="black", weight=3]; 2211[label="primQuotInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="burlywood",shape="box"];6496[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2211 -> 6496[label="",style="solid", color="burlywood", weight=9]; 6496 -> 2227[label="",style="solid", color="burlywood", weight=3]; 6497[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2211 -> 6497[label="",style="solid", color="burlywood", weight=9]; 6497 -> 2228[label="",style="solid", color="burlywood", weight=3]; 4088[label="gcd (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4088 -> 4099[label="",style="solid", color="black", weight=3]; 2225[label="primQuotInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="burlywood",shape="box"];6498[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];2225 -> 6498[label="",style="solid", color="burlywood", weight=9]; 6498 -> 2241[label="",style="solid", color="burlywood", weight=3]; 6499[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];2225 -> 6499[label="",style="solid", color="burlywood", weight=9]; 6499 -> 2242[label="",style="solid", color="burlywood", weight=3]; 4089[label="gcd (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4089 -> 4100[label="",style="solid", color="black", weight=3]; 2239[label="primQuotInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="burlywood",shape="box"];6500[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];2239 -> 6500[label="",style="solid", color="burlywood", weight=9]; 6500 -> 2252[label="",style="solid", color="burlywood", weight=3]; 6501[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];2239 -> 6501[label="",style="solid", color="burlywood", weight=9]; 6501 -> 2253[label="",style="solid", color="burlywood", weight=3]; 5688[label="gcd (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5688 -> 5702[label="",style="solid", color="black", weight=3]; 2276[label="primQuotInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2276 -> 2282[label="",style="solid", color="black", weight=3]; 2277[label="primQuotInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2277 -> 2283[label="",style="solid", color="black", weight=3]; 5695[label="gcd3 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5695 -> 5711[label="",style="solid", color="black", weight=3]; 5696[label="primQuotInt (Pos vuz73) (Pos (Succ vuz34600))",fontsize=16,color="black",shape="box"];5696 -> 5712[label="",style="solid", color="black", weight=3]; 5697[label="primQuotInt (Pos vuz73) (Pos Zero)",fontsize=16,color="black",shape="box"];5697 -> 5713[label="",style="solid", color="black", weight=3]; 5698[label="primQuotInt (Pos vuz73) (Neg (Succ vuz34600))",fontsize=16,color="black",shape="box"];5698 -> 5714[label="",style="solid", color="black", weight=3]; 5699[label="primQuotInt (Pos vuz73) (Neg Zero)",fontsize=16,color="black",shape="box"];5699 -> 5715[label="",style="solid", color="black", weight=3]; 2167[label="primQuotInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2167 -> 2184[label="",style="solid", color="black", weight=3]; 2168[label="primQuotInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2168 -> 2185[label="",style="solid", color="black", weight=3]; 4093[label="gcd3 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4093 -> 4106[label="",style="solid", color="black", weight=3]; 4094[label="primQuotInt (Neg vuz280) (Pos (Succ vuz28100))",fontsize=16,color="black",shape="box"];4094 -> 4107[label="",style="solid", color="black", weight=3]; 4095[label="primQuotInt (Neg vuz280) (Pos Zero)",fontsize=16,color="black",shape="box"];4095 -> 4108[label="",style="solid", color="black", weight=3]; 4096[label="primQuotInt (Neg vuz280) (Neg (Succ vuz28100))",fontsize=16,color="black",shape="box"];4096 -> 4109[label="",style="solid", color="black", weight=3]; 4097[label="primQuotInt (Neg vuz280) (Neg Zero)",fontsize=16,color="black",shape="box"];4097 -> 4110[label="",style="solid", color="black", weight=3]; 2181[label="primQuotInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2181 -> 2200[label="",style="solid", color="black", weight=3]; 2182[label="primQuotInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2182 -> 2201[label="",style="solid", color="black", weight=3]; 4098[label="gcd3 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4098 -> 4111[label="",style="solid", color="black", weight=3]; 2197[label="primQuotInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2197 -> 2216[label="",style="solid", color="black", weight=3]; 2198[label="primQuotInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2198 -> 2217[label="",style="solid", color="black", weight=3]; 5700[label="gcd3 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5700 -> 5716[label="",style="solid", color="black", weight=3]; 2213[label="primQuotInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2213 -> 2230[label="",style="solid", color="black", weight=3]; 2214[label="primQuotInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2214 -> 2231[label="",style="solid", color="black", weight=3]; 5701[label="gcd3 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5701 -> 5717[label="",style="solid", color="black", weight=3]; 2227[label="primQuotInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2227 -> 2244[label="",style="solid", color="black", weight=3]; 2228[label="primQuotInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2228 -> 2245[label="",style="solid", color="black", weight=3]; 4099[label="gcd3 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4099 -> 4112[label="",style="solid", color="black", weight=3]; 2241[label="primQuotInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2241 -> 2255[label="",style="solid", color="black", weight=3]; 2242[label="primQuotInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2242 -> 2256[label="",style="solid", color="black", weight=3]; 4100[label="gcd3 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4100 -> 4113[label="",style="solid", color="black", weight=3]; 2252[label="primQuotInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2252 -> 2264[label="",style="solid", color="black", weight=3]; 2253[label="primQuotInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2253 -> 2265[label="",style="solid", color="black", weight=3]; 5702[label="gcd3 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5702 -> 5718[label="",style="solid", color="black", weight=3]; 2282 -> 2289[label="",style="dashed", color="red", weight=0]; 2282[label="primQuotInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2282 -> 2290[label="",style="dashed", color="magenta", weight=3]; 2282 -> 2291[label="",style="dashed", color="magenta", weight=3]; 2283 -> 2292[label="",style="dashed", color="red", weight=0]; 2283[label="primQuotInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="magenta"];2283 -> 2293[label="",style="dashed", color="magenta", weight=3]; 2283 -> 2294[label="",style="dashed", color="magenta", weight=3]; 5711[label="gcd2 (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12) == fromInt (Pos Zero)) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5711 -> 5735[label="",style="solid", color="black", weight=3]; 5712[label="Pos (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5712 -> 5736[label="",style="dashed", color="green", weight=3]; 5713 -> 4108[label="",style="dashed", color="red", weight=0]; 5713[label="error []",fontsize=16,color="magenta"];5714[label="Neg (primDivNatS vuz73 (Succ vuz34600))",fontsize=16,color="green",shape="box"];5714 -> 5737[label="",style="dashed", color="green", weight=3]; 5715 -> 4108[label="",style="dashed", color="red", weight=0]; 5715[label="error []",fontsize=16,color="magenta"];2184 -> 2203[label="",style="dashed", color="red", weight=0]; 2184[label="primQuotInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2184 -> 2204[label="",style="dashed", color="magenta", weight=3]; 2184 -> 2205[label="",style="dashed", color="magenta", weight=3]; 2185 -> 2219[label="",style="dashed", color="red", weight=0]; 2185[label="primQuotInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="magenta"];2185 -> 2220[label="",style="dashed", color="magenta", weight=3]; 2185 -> 2221[label="",style="dashed", color="magenta", weight=3]; 4106[label="gcd2 (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23) == fromInt (Pos Zero)) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4106 -> 4128[label="",style="solid", color="black", weight=3]; 4107[label="Neg (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4107 -> 4129[label="",style="dashed", color="green", weight=3]; 4108[label="error []",fontsize=16,color="black",shape="triangle"];4108 -> 4130[label="",style="solid", color="black", weight=3]; 4109[label="Pos (primDivNatS vuz280 (Succ vuz28100))",fontsize=16,color="green",shape="box"];4109 -> 4131[label="",style="dashed", color="green", weight=3]; 4110 -> 4108[label="",style="dashed", color="red", weight=0]; 4110[label="error []",fontsize=16,color="magenta"];2200 -> 2234[label="",style="dashed", color="red", weight=0]; 2200[label="primQuotInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2200 -> 2235[label="",style="dashed", color="magenta", weight=3]; 2200 -> 2236[label="",style="dashed", color="magenta", weight=3]; 2201 -> 2247[label="",style="dashed", color="red", weight=0]; 2201[label="primQuotInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="magenta"];2201 -> 2248[label="",style="dashed", color="magenta", weight=3]; 2201 -> 2249[label="",style="dashed", color="magenta", weight=3]; 4111[label="gcd2 (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28) == fromInt (Pos Zero)) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4111 -> 4132[label="",style="solid", color="black", weight=3]; 2216 -> 2259[label="",style="dashed", color="red", weight=0]; 2216[label="primQuotInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="magenta"];2216 -> 2260[label="",style="dashed", color="magenta", weight=3]; 2216 -> 2261[label="",style="dashed", color="magenta", weight=3]; 2217 -> 2267[label="",style="dashed", color="red", weight=0]; 2217[label="primQuotInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="magenta"];2217 -> 2268[label="",style="dashed", color="magenta", weight=3]; 2217 -> 2269[label="",style="dashed", color="magenta", weight=3]; 5716[label="gcd2 (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33) == fromInt (Pos Zero)) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5716 -> 5738[label="",style="solid", color="black", weight=3]; 2230 -> 2273[label="",style="dashed", color="red", weight=0]; 2230[label="primQuotInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2230 -> 2274[label="",style="dashed", color="magenta", weight=3]; 2230 -> 2275[label="",style="dashed", color="magenta", weight=3]; 2231 -> 2279[label="",style="dashed", color="red", weight=0]; 2231[label="primQuotInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="magenta"];2231 -> 2280[label="",style="dashed", color="magenta", weight=3]; 2231 -> 2281[label="",style="dashed", color="magenta", weight=3]; 5717[label="gcd2 (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38) == fromInt (Pos Zero)) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5717 -> 5739[label="",style="solid", color="black", weight=3]; 2244 -> 2286[label="",style="dashed", color="red", weight=0]; 2244[label="primQuotInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="magenta"];2244 -> 2287[label="",style="dashed", color="magenta", weight=3]; 2244 -> 2288[label="",style="dashed", color="magenta", weight=3]; 2245 -> 2296[label="",style="dashed", color="red", weight=0]; 2245[label="primQuotInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="magenta"];2245 -> 2297[label="",style="dashed", color="magenta", weight=3]; 2245 -> 2298[label="",style="dashed", color="magenta", weight=3]; 4112[label="gcd2 (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43) == fromInt (Pos Zero)) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4112 -> 4133[label="",style="solid", color="black", weight=3]; 2255 -> 2300[label="",style="dashed", color="red", weight=0]; 2255[label="primQuotInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="magenta"];2255 -> 2301[label="",style="dashed", color="magenta", weight=3]; 2255 -> 2302[label="",style="dashed", color="magenta", weight=3]; 2256 -> 2303[label="",style="dashed", color="red", weight=0]; 2256[label="primQuotInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="magenta"];2256 -> 2304[label="",style="dashed", color="magenta", weight=3]; 2256 -> 2305[label="",style="dashed", color="magenta", weight=3]; 4113[label="gcd2 (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48) == fromInt (Pos Zero)) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4113 -> 4134[label="",style="solid", color="black", weight=3]; 2264 -> 2307[label="",style="dashed", color="red", weight=0]; 2264[label="primQuotInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2264 -> 2308[label="",style="dashed", color="magenta", weight=3]; 2264 -> 2309[label="",style="dashed", color="magenta", weight=3]; 2265 -> 2310[label="",style="dashed", color="red", weight=0]; 2265[label="primQuotInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="magenta"];2265 -> 2311[label="",style="dashed", color="magenta", weight=3]; 2265 -> 2312[label="",style="dashed", color="magenta", weight=3]; 5718[label="gcd2 (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53) == fromInt (Pos Zero)) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5718 -> 5740[label="",style="solid", color="black", weight=3]; 2290 -> 681[label="",style="dashed", color="red", weight=0]; 2290[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2290 -> 2314[label="",style="dashed", color="magenta", weight=3]; 2290 -> 2315[label="",style="dashed", color="magenta", weight=3]; 2291 -> 681[label="",style="dashed", color="red", weight=0]; 2291[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2291 -> 2316[label="",style="dashed", color="magenta", weight=3]; 2291 -> 2317[label="",style="dashed", color="magenta", weight=3]; 2289[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2289 -> 2318[label="",style="solid", color="black", weight=3]; 2293 -> 681[label="",style="dashed", color="red", weight=0]; 2293[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2293 -> 2319[label="",style="dashed", color="magenta", weight=3]; 2293 -> 2320[label="",style="dashed", color="magenta", weight=3]; 2294 -> 681[label="",style="dashed", color="red", weight=0]; 2294[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];2294 -> 2321[label="",style="dashed", color="magenta", weight=3]; 2294 -> 2322[label="",style="dashed", color="magenta", weight=3]; 2292[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz11 * Pos (Succ vuz12))) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2292 -> 2323[label="",style="solid", color="black", weight=3]; 5735[label="gcd2 (primEqInt (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (fromInt (Pos Zero))) (vuz9 * Pos (Succ vuz10) + Neg vuz11 * Pos (Succ vuz12)) (Pos vuz144)",fontsize=16,color="black",shape="box"];5735 -> 5750[label="",style="solid", color="black", weight=3]; 5736 -> 4129[label="",style="dashed", color="red", weight=0]; 5736[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5736 -> 5751[label="",style="dashed", color="magenta", weight=3]; 5736 -> 5752[label="",style="dashed", color="magenta", weight=3]; 5737 -> 4129[label="",style="dashed", color="red", weight=0]; 5737[label="primDivNatS vuz73 (Succ vuz34600)",fontsize=16,color="magenta"];5737 -> 5753[label="",style="dashed", color="magenta", weight=3]; 5737 -> 5754[label="",style="dashed", color="magenta", weight=3]; 2204 -> 681[label="",style="dashed", color="red", weight=0]; 2204[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2204 -> 2325[label="",style="dashed", color="magenta", weight=3]; 2204 -> 2326[label="",style="dashed", color="magenta", weight=3]; 2205 -> 681[label="",style="dashed", color="red", weight=0]; 2205[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2205 -> 2327[label="",style="dashed", color="magenta", weight=3]; 2205 -> 2328[label="",style="dashed", color="magenta", weight=3]; 2203[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2203 -> 2329[label="",style="solid", color="black", weight=3]; 2220 -> 681[label="",style="dashed", color="red", weight=0]; 2220[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2220 -> 2330[label="",style="dashed", color="magenta", weight=3]; 2220 -> 2331[label="",style="dashed", color="magenta", weight=3]; 2221 -> 681[label="",style="dashed", color="red", weight=0]; 2221[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];2221 -> 2332[label="",style="dashed", color="magenta", weight=3]; 2221 -> 2333[label="",style="dashed", color="magenta", weight=3]; 2219[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz22 * Pos (Succ vuz23))) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2219 -> 2334[label="",style="solid", color="black", weight=3]; 4128[label="gcd2 (primEqInt (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (fromInt (Pos Zero))) (vuz20 * Neg (Succ vuz21) + Neg vuz22 * Pos (Succ vuz23)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4128 -> 4144[label="",style="solid", color="black", weight=3]; 4129[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="burlywood",shape="triangle"];6502[label="vuz280/Succ vuz2800",fontsize=10,color="white",style="solid",shape="box"];4129 -> 6502[label="",style="solid", color="burlywood", weight=9]; 6502 -> 4145[label="",style="solid", color="burlywood", weight=3]; 6503[label="vuz280/Zero",fontsize=10,color="white",style="solid",shape="box"];4129 -> 6503[label="",style="solid", color="burlywood", weight=9]; 6503 -> 4146[label="",style="solid", color="burlywood", weight=3]; 4130[label="error []",fontsize=16,color="red",shape="box"];4131 -> 4129[label="",style="dashed", color="red", weight=0]; 4131[label="primDivNatS vuz280 (Succ vuz28100)",fontsize=16,color="magenta"];4131 -> 4147[label="",style="dashed", color="magenta", weight=3]; 2235 -> 681[label="",style="dashed", color="red", weight=0]; 2235[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2235 -> 2336[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2337[label="",style="dashed", color="magenta", weight=3]; 2236 -> 681[label="",style="dashed", color="red", weight=0]; 2236[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2236 -> 2338[label="",style="dashed", color="magenta", weight=3]; 2236 -> 2339[label="",style="dashed", color="magenta", weight=3]; 2234[label="primQuotInt (primPlusInt (Pos vuz171) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Pos vuz172) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2234 -> 2340[label="",style="solid", color="black", weight=3]; 2248 -> 681[label="",style="dashed", color="red", weight=0]; 2248[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2248 -> 2341[label="",style="dashed", color="magenta", weight=3]; 2248 -> 2342[label="",style="dashed", color="magenta", weight=3]; 2249 -> 681[label="",style="dashed", color="red", weight=0]; 2249[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];2249 -> 2343[label="",style="dashed", color="magenta", weight=3]; 2249 -> 2344[label="",style="dashed", color="magenta", weight=3]; 2247[label="primQuotInt (primPlusInt (Neg vuz173) (Neg vuz27 * Neg (Succ vuz28))) (reduce2D (primPlusInt (Neg vuz174) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2247 -> 2345[label="",style="solid", color="black", weight=3]; 4132[label="gcd2 (primEqInt (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (fromInt (Pos Zero))) (vuz25 * Pos (Succ vuz26) + Neg vuz27 * Neg (Succ vuz28)) (Neg vuz71)",fontsize=16,color="black",shape="box"];4132 -> 4148[label="",style="solid", color="black", weight=3]; 2260 -> 681[label="",style="dashed", color="red", weight=0]; 2260[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2260 -> 2347[label="",style="dashed", color="magenta", weight=3]; 2260 -> 2348[label="",style="dashed", color="magenta", weight=3]; 2261 -> 681[label="",style="dashed", color="red", weight=0]; 2261[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2261 -> 2349[label="",style="dashed", color="magenta", weight=3]; 2261 -> 2350[label="",style="dashed", color="magenta", weight=3]; 2259[label="primQuotInt (primPlusInt (Neg vuz175) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Neg vuz176) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2259 -> 2351[label="",style="solid", color="black", weight=3]; 2268 -> 681[label="",style="dashed", color="red", weight=0]; 2268[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2268 -> 2352[label="",style="dashed", color="magenta", weight=3]; 2268 -> 2353[label="",style="dashed", color="magenta", weight=3]; 2269 -> 681[label="",style="dashed", color="red", weight=0]; 2269[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];2269 -> 2354[label="",style="dashed", color="magenta", weight=3]; 2269 -> 2355[label="",style="dashed", color="magenta", weight=3]; 2267[label="primQuotInt (primPlusInt (Pos vuz177) (Neg vuz32 * Neg (Succ vuz33))) (reduce2D (primPlusInt (Pos vuz178) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2267 -> 2356[label="",style="solid", color="black", weight=3]; 5738[label="gcd2 (primEqInt (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (fromInt (Pos Zero))) (vuz30 * Neg (Succ vuz31) + Neg vuz32 * Neg (Succ vuz33)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5738 -> 5755[label="",style="solid", color="black", weight=3]; 2274 -> 681[label="",style="dashed", color="red", weight=0]; 2274[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2274 -> 2358[label="",style="dashed", color="magenta", weight=3]; 2274 -> 2359[label="",style="dashed", color="magenta", weight=3]; 2275 -> 681[label="",style="dashed", color="red", weight=0]; 2275[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2275 -> 2360[label="",style="dashed", color="magenta", weight=3]; 2275 -> 2361[label="",style="dashed", color="magenta", weight=3]; 2273[label="primQuotInt (primPlusInt (Pos vuz179) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Pos vuz180) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2273 -> 2362[label="",style="solid", color="black", weight=3]; 2280 -> 681[label="",style="dashed", color="red", weight=0]; 2280[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2280 -> 2363[label="",style="dashed", color="magenta", weight=3]; 2280 -> 2364[label="",style="dashed", color="magenta", weight=3]; 2281 -> 681[label="",style="dashed", color="red", weight=0]; 2281[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];2281 -> 2365[label="",style="dashed", color="magenta", weight=3]; 2281 -> 2366[label="",style="dashed", color="magenta", weight=3]; 2279[label="primQuotInt (primPlusInt (Neg vuz181) (Pos vuz37 * Pos (Succ vuz38))) (reduce2D (primPlusInt (Neg vuz182) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77))",fontsize=16,color="black",shape="triangle"];2279 -> 2367[label="",style="solid", color="black", weight=3]; 5739[label="gcd2 (primEqInt (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (fromInt (Pos Zero))) (vuz35 * Pos (Succ vuz36) + Pos vuz37 * Pos (Succ vuz38)) (Pos vuz77)",fontsize=16,color="black",shape="box"];5739 -> 5756[label="",style="solid", color="black", weight=3]; 2287 -> 681[label="",style="dashed", color="red", weight=0]; 2287[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2287 -> 2369[label="",style="dashed", color="magenta", weight=3]; 2287 -> 2370[label="",style="dashed", color="magenta", weight=3]; 2288 -> 681[label="",style="dashed", color="red", weight=0]; 2288[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2288 -> 2371[label="",style="dashed", color="magenta", weight=3]; 2288 -> 2372[label="",style="dashed", color="magenta", weight=3]; 2286[label="primQuotInt (primPlusInt (Neg vuz183) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Neg vuz184) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2286 -> 2373[label="",style="solid", color="black", weight=3]; 2297 -> 681[label="",style="dashed", color="red", weight=0]; 2297[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2297 -> 2374[label="",style="dashed", color="magenta", weight=3]; 2297 -> 2375[label="",style="dashed", color="magenta", weight=3]; 2298 -> 681[label="",style="dashed", color="red", weight=0]; 2298[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];2298 -> 2376[label="",style="dashed", color="magenta", weight=3]; 2298 -> 2377[label="",style="dashed", color="magenta", weight=3]; 2296[label="primQuotInt (primPlusInt (Pos vuz189) (Pos vuz42 * Pos (Succ vuz43))) (reduce2D (primPlusInt (Pos vuz190) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92))",fontsize=16,color="black",shape="triangle"];2296 -> 2378[label="",style="solid", color="black", weight=3]; 4133[label="gcd2 (primEqInt (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (fromInt (Pos Zero))) (vuz40 * Neg (Succ vuz41) + Pos vuz42 * Pos (Succ vuz43)) (Neg vuz92)",fontsize=16,color="black",shape="box"];4133 -> 4149[label="",style="solid", color="black", weight=3]; 2301 -> 681[label="",style="dashed", color="red", weight=0]; 2301[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2301 -> 2380[label="",style="dashed", color="magenta", weight=3]; 2301 -> 2381[label="",style="dashed", color="magenta", weight=3]; 2302 -> 681[label="",style="dashed", color="red", weight=0]; 2302[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2302 -> 2382[label="",style="dashed", color="magenta", weight=3]; 2302 -> 2383[label="",style="dashed", color="magenta", weight=3]; 2300[label="primQuotInt (primPlusInt (Pos vuz191) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Pos vuz192) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2300 -> 2384[label="",style="solid", color="black", weight=3]; 2304 -> 681[label="",style="dashed", color="red", weight=0]; 2304[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2304 -> 2385[label="",style="dashed", color="magenta", weight=3]; 2304 -> 2386[label="",style="dashed", color="magenta", weight=3]; 2305 -> 681[label="",style="dashed", color="red", weight=0]; 2305[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];2305 -> 2387[label="",style="dashed", color="magenta", weight=3]; 2305 -> 2388[label="",style="dashed", color="magenta", weight=3]; 2303[label="primQuotInt (primPlusInt (Neg vuz193) (Pos vuz47 * Neg (Succ vuz48))) (reduce2D (primPlusInt (Neg vuz194) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107))",fontsize=16,color="black",shape="triangle"];2303 -> 2389[label="",style="solid", color="black", weight=3]; 4134[label="gcd2 (primEqInt (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (fromInt (Pos Zero))) (vuz45 * Pos (Succ vuz46) + Pos vuz47 * Neg (Succ vuz48)) (Neg vuz107)",fontsize=16,color="black",shape="box"];4134 -> 4150[label="",style="solid", color="black", weight=3]; 2308 -> 681[label="",style="dashed", color="red", weight=0]; 2308[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2308 -> 2391[label="",style="dashed", color="magenta", weight=3]; 2308 -> 2392[label="",style="dashed", color="magenta", weight=3]; 2309 -> 681[label="",style="dashed", color="red", weight=0]; 2309[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2309 -> 2393[label="",style="dashed", color="magenta", weight=3]; 2309 -> 2394[label="",style="dashed", color="magenta", weight=3]; 2307[label="primQuotInt (primPlusInt (Neg vuz195) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Neg vuz196) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2307 -> 2395[label="",style="solid", color="black", weight=3]; 2311 -> 681[label="",style="dashed", color="red", weight=0]; 2311[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2311 -> 2396[label="",style="dashed", color="magenta", weight=3]; 2311 -> 2397[label="",style="dashed", color="magenta", weight=3]; 2312 -> 681[label="",style="dashed", color="red", weight=0]; 2312[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];2312 -> 2398[label="",style="dashed", color="magenta", weight=3]; 2312 -> 2399[label="",style="dashed", color="magenta", weight=3]; 2310[label="primQuotInt (primPlusInt (Pos vuz197) (Pos vuz52 * Neg (Succ vuz53))) (reduce2D (primPlusInt (Pos vuz198) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122))",fontsize=16,color="black",shape="triangle"];2310 -> 2400[label="",style="solid", color="black", weight=3]; 5740[label="gcd2 (primEqInt (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (fromInt (Pos Zero))) (vuz50 * Neg (Succ vuz51) + Pos vuz52 * Neg (Succ vuz53)) (Pos vuz122)",fontsize=16,color="black",shape="box"];5740 -> 5757[label="",style="solid", color="black", weight=3]; 2314[label="vuz10",fontsize=16,color="green",shape="box"];2315[label="vuz90",fontsize=16,color="green",shape="box"];2316[label="vuz10",fontsize=16,color="green",shape="box"];2317[label="vuz90",fontsize=16,color="green",shape="box"];2318[label="primQuotInt (primPlusInt (Pos vuz185) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2318 -> 2402[label="",style="solid", color="black", weight=3]; 2319[label="vuz10",fontsize=16,color="green",shape="box"];2320[label="vuz90",fontsize=16,color="green",shape="box"];2321[label="vuz10",fontsize=16,color="green",shape="box"];2322[label="vuz90",fontsize=16,color="green",shape="box"];2323[label="primQuotInt (primPlusInt (Neg vuz187) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="black",shape="box"];2323 -> 2403[label="",style="solid", color="black", weight=3]; 5750[label="gcd2 (primEqInt (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (vuz9 * Pos (Succ vuz10)) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5750 -> 5769[label="",style="solid", color="black", weight=3]; 5751[label="vuz34600",fontsize=16,color="green",shape="box"];5752[label="vuz73",fontsize=16,color="green",shape="box"];5753[label="vuz34600",fontsize=16,color="green",shape="box"];5754[label="vuz73",fontsize=16,color="green",shape="box"];2325[label="vuz21",fontsize=16,color="green",shape="box"];2326[label="vuz200",fontsize=16,color="green",shape="box"];2327[label="vuz21",fontsize=16,color="green",shape="box"];2328[label="vuz200",fontsize=16,color="green",shape="box"];2329[label="primQuotInt (primPlusInt (Neg vuz167) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2329 -> 2406[label="",style="solid", color="black", weight=3]; 2330[label="vuz21",fontsize=16,color="green",shape="box"];2331[label="vuz200",fontsize=16,color="green",shape="box"];2332[label="vuz21",fontsize=16,color="green",shape="box"];2333[label="vuz200",fontsize=16,color="green",shape="box"];2334[label="primQuotInt (primPlusInt (Pos vuz169) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="black",shape="box"];2334 -> 2407[label="",style="solid", color="black", weight=3]; 4144[label="gcd2 (primEqInt (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (vuz20 * Neg (Succ vuz21)) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4144 -> 4160[label="",style="solid", color="black", weight=3]; 4145[label="primDivNatS (Succ vuz2800) (Succ vuz28100)",fontsize=16,color="black",shape="box"];4145 -> 4161[label="",style="solid", color="black", weight=3]; 4146[label="primDivNatS Zero (Succ vuz28100)",fontsize=16,color="black",shape="box"];4146 -> 4162[label="",style="solid", color="black", weight=3]; 4147[label="vuz28100",fontsize=16,color="green",shape="box"];2336[label="vuz26",fontsize=16,color="green",shape="box"];2337[label="vuz250",fontsize=16,color="green",shape="box"];2338[label="vuz26",fontsize=16,color="green",shape="box"];2339[label="vuz250",fontsize=16,color="green",shape="box"];2340[label="primQuotInt (primPlusInt (Pos vuz171) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2340 -> 2410[label="",style="solid", color="black", weight=3]; 2341[label="vuz26",fontsize=16,color="green",shape="box"];2342[label="vuz250",fontsize=16,color="green",shape="box"];2343[label="vuz26",fontsize=16,color="green",shape="box"];2344[label="vuz250",fontsize=16,color="green",shape="box"];2345[label="primQuotInt (primPlusInt (Neg vuz173) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="black",shape="box"];2345 -> 2411[label="",style="solid", color="black", weight=3]; 4148[label="gcd2 (primEqInt (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (vuz25 * Pos (Succ vuz26)) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4148 -> 4163[label="",style="solid", color="black", weight=3]; 2347[label="vuz31",fontsize=16,color="green",shape="box"];2348[label="vuz300",fontsize=16,color="green",shape="box"];2349[label="vuz31",fontsize=16,color="green",shape="box"];2350[label="vuz300",fontsize=16,color="green",shape="box"];2351[label="primQuotInt (primPlusInt (Neg vuz175) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2351 -> 2414[label="",style="solid", color="black", weight=3]; 2352[label="vuz31",fontsize=16,color="green",shape="box"];2353[label="vuz300",fontsize=16,color="green",shape="box"];2354[label="vuz31",fontsize=16,color="green",shape="box"];2355[label="vuz300",fontsize=16,color="green",shape="box"];2356[label="primQuotInt (primPlusInt (Pos vuz177) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="black",shape="box"];2356 -> 2415[label="",style="solid", color="black", weight=3]; 5755[label="gcd2 (primEqInt (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (vuz30 * Neg (Succ vuz31)) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5755 -> 5770[label="",style="solid", color="black", weight=3]; 2358[label="vuz36",fontsize=16,color="green",shape="box"];2359[label="vuz350",fontsize=16,color="green",shape="box"];2360[label="vuz36",fontsize=16,color="green",shape="box"];2361[label="vuz350",fontsize=16,color="green",shape="box"];2362[label="primQuotInt (primPlusInt (Pos vuz179) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2362 -> 2418[label="",style="solid", color="black", weight=3]; 2363[label="vuz36",fontsize=16,color="green",shape="box"];2364[label="vuz350",fontsize=16,color="green",shape="box"];2365[label="vuz36",fontsize=16,color="green",shape="box"];2366[label="vuz350",fontsize=16,color="green",shape="box"];2367[label="primQuotInt (primPlusInt (Neg vuz181) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="black",shape="box"];2367 -> 2419[label="",style="solid", color="black", weight=3]; 5756[label="gcd2 (primEqInt (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (vuz35 * Pos (Succ vuz36)) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5756 -> 5771[label="",style="solid", color="black", weight=3]; 2369[label="vuz41",fontsize=16,color="green",shape="box"];2370[label="vuz400",fontsize=16,color="green",shape="box"];2371[label="vuz41",fontsize=16,color="green",shape="box"];2372[label="vuz400",fontsize=16,color="green",shape="box"];2373[label="primQuotInt (primPlusInt (Neg vuz183) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2373 -> 2422[label="",style="solid", color="black", weight=3]; 2374[label="vuz41",fontsize=16,color="green",shape="box"];2375[label="vuz400",fontsize=16,color="green",shape="box"];2376[label="vuz41",fontsize=16,color="green",shape="box"];2377[label="vuz400",fontsize=16,color="green",shape="box"];2378[label="primQuotInt (primPlusInt (Pos vuz189) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="black",shape="box"];2378 -> 2423[label="",style="solid", color="black", weight=3]; 4149[label="gcd2 (primEqInt (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (vuz40 * Neg (Succ vuz41)) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4149 -> 4164[label="",style="solid", color="black", weight=3]; 2380[label="vuz46",fontsize=16,color="green",shape="box"];2381[label="vuz450",fontsize=16,color="green",shape="box"];2382[label="vuz46",fontsize=16,color="green",shape="box"];2383[label="vuz450",fontsize=16,color="green",shape="box"];2384[label="primQuotInt (primPlusInt (Pos vuz191) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2384 -> 2426[label="",style="solid", color="black", weight=3]; 2385[label="vuz46",fontsize=16,color="green",shape="box"];2386[label="vuz450",fontsize=16,color="green",shape="box"];2387[label="vuz46",fontsize=16,color="green",shape="box"];2388[label="vuz450",fontsize=16,color="green",shape="box"];2389[label="primQuotInt (primPlusInt (Neg vuz193) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="black",shape="box"];2389 -> 2427[label="",style="solid", color="black", weight=3]; 4150[label="gcd2 (primEqInt (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (vuz45 * Pos (Succ vuz46)) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4150 -> 4165[label="",style="solid", color="black", weight=3]; 2391[label="vuz51",fontsize=16,color="green",shape="box"];2392[label="vuz500",fontsize=16,color="green",shape="box"];2393[label="vuz51",fontsize=16,color="green",shape="box"];2394[label="vuz500",fontsize=16,color="green",shape="box"];2395[label="primQuotInt (primPlusInt (Neg vuz195) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2395 -> 2430[label="",style="solid", color="black", weight=3]; 2396[label="vuz51",fontsize=16,color="green",shape="box"];2397[label="vuz500",fontsize=16,color="green",shape="box"];2398[label="vuz51",fontsize=16,color="green",shape="box"];2399[label="vuz500",fontsize=16,color="green",shape="box"];2400[label="primQuotInt (primPlusInt (Pos vuz197) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="black",shape="box"];2400 -> 2431[label="",style="solid", color="black", weight=3]; 5757[label="gcd2 (primEqInt (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (vuz50 * Neg (Succ vuz51)) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5757 -> 5772[label="",style="solid", color="black", weight=3]; 2402 -> 2434[label="",style="dashed", color="red", weight=0]; 2402[label="primQuotInt (primPlusInt (Pos vuz185) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Pos vuz186) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2402 -> 2435[label="",style="dashed", color="magenta", weight=3]; 2402 -> 2436[label="",style="dashed", color="magenta", weight=3]; 2403 -> 2442[label="",style="dashed", color="red", weight=0]; 2403[label="primQuotInt (primPlusInt (Neg vuz187) (Neg (primMulNat vuz11 (Succ vuz12)))) (reduce2D (primPlusInt (Neg vuz188) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144))",fontsize=16,color="magenta"];2403 -> 2443[label="",style="dashed", color="magenta", weight=3]; 2403 -> 2444[label="",style="dashed", color="magenta", weight=3]; 5769[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz9 (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6504[label="vuz9/Pos vuz90",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6504[label="",style="solid", color="burlywood", weight=9]; 6504 -> 5784[label="",style="solid", color="burlywood", weight=3]; 6505[label="vuz9/Neg vuz90",fontsize=10,color="white",style="solid",shape="box"];5769 -> 6505[label="",style="solid", color="burlywood", weight=9]; 6505 -> 5785[label="",style="solid", color="burlywood", weight=3]; 2406 -> 2452[label="",style="dashed", color="red", weight=0]; 2406[label="primQuotInt (primPlusInt (Neg vuz167) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Neg vuz168) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2406 -> 2453[label="",style="dashed", color="magenta", weight=3]; 2406 -> 2454[label="",style="dashed", color="magenta", weight=3]; 2407 -> 2460[label="",style="dashed", color="red", weight=0]; 2407[label="primQuotInt (primPlusInt (Pos vuz169) (Neg (primMulNat vuz22 (Succ vuz23)))) (reduce2D (primPlusInt (Pos vuz170) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68))",fontsize=16,color="magenta"];2407 -> 2461[label="",style="dashed", color="magenta", weight=3]; 2407 -> 2462[label="",style="dashed", color="magenta", weight=3]; 4160[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz20 (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6506[label="vuz20/Pos vuz200",fontsize=10,color="white",style="solid",shape="box"];4160 -> 6506[label="",style="solid", color="burlywood", weight=9]; 6506 -> 4175[label="",style="solid", color="burlywood", weight=3]; 6507[label="vuz20/Neg vuz200",fontsize=10,color="white",style="solid",shape="box"];4160 -> 6507[label="",style="solid", color="burlywood", weight=9]; 6507 -> 4176[label="",style="solid", color="burlywood", weight=3]; 4161[label="primDivNatS0 vuz2800 vuz28100 (primGEqNatS vuz2800 vuz28100)",fontsize=16,color="burlywood",shape="box"];6508[label="vuz2800/Succ vuz28000",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6508[label="",style="solid", color="burlywood", weight=9]; 6508 -> 4177[label="",style="solid", color="burlywood", weight=3]; 6509[label="vuz2800/Zero",fontsize=10,color="white",style="solid",shape="box"];4161 -> 6509[label="",style="solid", color="burlywood", weight=9]; 6509 -> 4178[label="",style="solid", color="burlywood", weight=3]; 4162[label="Zero",fontsize=16,color="green",shape="box"];2410 -> 2470[label="",style="dashed", color="red", weight=0]; 2410[label="primQuotInt (primPlusInt (Pos vuz171) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Pos vuz172) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2410 -> 2471[label="",style="dashed", color="magenta", weight=3]; 2410 -> 2472[label="",style="dashed", color="magenta", weight=3]; 2411 -> 2478[label="",style="dashed", color="red", weight=0]; 2411[label="primQuotInt (primPlusInt (Neg vuz173) (Pos (primMulNat vuz27 (Succ vuz28)))) (reduce2D (primPlusInt (Neg vuz174) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71))",fontsize=16,color="magenta"];2411 -> 2479[label="",style="dashed", color="magenta", weight=3]; 2411 -> 2480[label="",style="dashed", color="magenta", weight=3]; 4163[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz25 (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6510[label="vuz25/Pos vuz250",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6510[label="",style="solid", color="burlywood", weight=9]; 6510 -> 4179[label="",style="solid", color="burlywood", weight=3]; 6511[label="vuz25/Neg vuz250",fontsize=10,color="white",style="solid",shape="box"];4163 -> 6511[label="",style="solid", color="burlywood", weight=9]; 6511 -> 4180[label="",style="solid", color="burlywood", weight=3]; 2414 -> 2488[label="",style="dashed", color="red", weight=0]; 2414[label="primQuotInt (primPlusInt (Neg vuz175) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Neg vuz176) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2414 -> 2489[label="",style="dashed", color="magenta", weight=3]; 2414 -> 2490[label="",style="dashed", color="magenta", weight=3]; 2415 -> 2496[label="",style="dashed", color="red", weight=0]; 2415[label="primQuotInt (primPlusInt (Pos vuz177) (Pos (primMulNat vuz32 (Succ vuz33)))) (reduce2D (primPlusInt (Pos vuz178) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74))",fontsize=16,color="magenta"];2415 -> 2497[label="",style="dashed", color="magenta", weight=3]; 2415 -> 2498[label="",style="dashed", color="magenta", weight=3]; 5770[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz30 (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6512[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6512[label="",style="solid", color="burlywood", weight=9]; 6512 -> 5786[label="",style="solid", color="burlywood", weight=3]; 6513[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];5770 -> 6513[label="",style="solid", color="burlywood", weight=9]; 6513 -> 5787[label="",style="solid", color="burlywood", weight=3]; 2418 -> 2496[label="",style="dashed", color="red", weight=0]; 2418[label="primQuotInt (primPlusInt (Pos vuz179) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Pos vuz180) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2418 -> 2499[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2500[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2501[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2502[label="",style="dashed", color="magenta", weight=3]; 2418 -> 2503[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2488[label="",style="dashed", color="red", weight=0]; 2419[label="primQuotInt (primPlusInt (Neg vuz181) (Pos (primMulNat vuz37 (Succ vuz38)))) (reduce2D (primPlusInt (Neg vuz182) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77))",fontsize=16,color="magenta"];2419 -> 2491[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2492[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2493[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2494[label="",style="dashed", color="magenta", weight=3]; 2419 -> 2495[label="",style="dashed", color="magenta", weight=3]; 5771[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz35 (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="burlywood",shape="box"];6514[label="vuz35/Pos vuz350",fontsize=10,color="white",style="solid",shape="box"];5771 -> 6514[label="",style="solid", color="burlywood", weight=9]; 6514 -> 5788[label="",style="solid", color="burlywood", weight=3]; 6515[label="vuz35/Neg vuz350",fontsize=10,color="white",style="solid",shape="box"];5771 -> 6515[label="",style="solid", color="burlywood", weight=9]; 6515 -> 5789[label="",style="solid", color="burlywood", weight=3]; 2422 -> 2478[label="",style="dashed", color="red", weight=0]; 2422[label="primQuotInt (primPlusInt (Neg vuz183) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Neg vuz184) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2422 -> 2481[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2482[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2483[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2484[label="",style="dashed", color="magenta", weight=3]; 2422 -> 2485[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2470[label="",style="dashed", color="red", weight=0]; 2423[label="primQuotInt (primPlusInt (Pos vuz189) (Pos (primMulNat vuz42 (Succ vuz43)))) (reduce2D (primPlusInt (Pos vuz190) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92))",fontsize=16,color="magenta"];2423 -> 2473[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2474[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2475[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2476[label="",style="dashed", color="magenta", weight=3]; 2423 -> 2477[label="",style="dashed", color="magenta", weight=3]; 4164[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz40 (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="burlywood",shape="box"];6516[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6516[label="",style="solid", color="burlywood", weight=9]; 6516 -> 4181[label="",style="solid", color="burlywood", weight=3]; 6517[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];4164 -> 6517[label="",style="solid", color="burlywood", weight=9]; 6517 -> 4182[label="",style="solid", color="burlywood", weight=3]; 2426 -> 2460[label="",style="dashed", color="red", weight=0]; 2426[label="primQuotInt (primPlusInt (Pos vuz191) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Pos vuz192) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2426 -> 2463[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2464[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2465[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2466[label="",style="dashed", color="magenta", weight=3]; 2426 -> 2467[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2452[label="",style="dashed", color="red", weight=0]; 2427[label="primQuotInt (primPlusInt (Neg vuz193) (Neg (primMulNat vuz47 (Succ vuz48)))) (reduce2D (primPlusInt (Neg vuz194) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107))",fontsize=16,color="magenta"];2427 -> 2455[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2456[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2457[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2458[label="",style="dashed", color="magenta", weight=3]; 2427 -> 2459[label="",style="dashed", color="magenta", weight=3]; 4165[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz45 (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="burlywood",shape="box"];6518[label="vuz45/Pos vuz450",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6518[label="",style="solid", color="burlywood", weight=9]; 6518 -> 4183[label="",style="solid", color="burlywood", weight=3]; 6519[label="vuz45/Neg vuz450",fontsize=10,color="white",style="solid",shape="box"];4165 -> 6519[label="",style="solid", color="burlywood", weight=9]; 6519 -> 4184[label="",style="solid", color="burlywood", weight=3]; 2430 -> 2442[label="",style="dashed", color="red", weight=0]; 2430[label="primQuotInt (primPlusInt (Neg vuz195) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Neg vuz196) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2430 -> 2445[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2446[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2447[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2448[label="",style="dashed", color="magenta", weight=3]; 2430 -> 2449[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2434[label="",style="dashed", color="red", weight=0]; 2431[label="primQuotInt (primPlusInt (Pos vuz197) (Neg (primMulNat vuz52 (Succ vuz53)))) (reduce2D (primPlusInt (Pos vuz198) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122))",fontsize=16,color="magenta"];2431 -> 2437[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2438[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2439[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2440[label="",style="dashed", color="magenta", weight=3]; 2431 -> 2441[label="",style="dashed", color="magenta", weight=3]; 5772[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz50 (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="burlywood",shape="box"];6520[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6520[label="",style="solid", color="burlywood", weight=9]; 6520 -> 5790[label="",style="solid", color="burlywood", weight=3]; 6521[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];5772 -> 6521[label="",style="solid", color="burlywood", weight=9]; 6521 -> 5791[label="",style="solid", color="burlywood", weight=3]; 2435 -> 681[label="",style="dashed", color="red", weight=0]; 2435[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2435 -> 2514[label="",style="dashed", color="magenta", weight=3]; 2435 -> 2515[label="",style="dashed", color="magenta", weight=3]; 2436 -> 681[label="",style="dashed", color="red", weight=0]; 2436[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2436 -> 2516[label="",style="dashed", color="magenta", weight=3]; 2436 -> 2517[label="",style="dashed", color="magenta", weight=3]; 2434[label="primQuotInt (primPlusInt (Pos vuz185) (Neg vuz199)) (reduce2D (primPlusInt (Pos vuz186) (Neg vuz200)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2434 -> 2518[label="",style="solid", color="black", weight=3]; 2443 -> 681[label="",style="dashed", color="red", weight=0]; 2443[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2443 -> 2519[label="",style="dashed", color="magenta", weight=3]; 2443 -> 2520[label="",style="dashed", color="magenta", weight=3]; 2444 -> 681[label="",style="dashed", color="red", weight=0]; 2444[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];2444 -> 2521[label="",style="dashed", color="magenta", weight=3]; 2444 -> 2522[label="",style="dashed", color="magenta", weight=3]; 2442[label="primQuotInt (primPlusInt (Neg vuz187) (Neg vuz201)) (reduce2D (primPlusInt (Neg vuz188) (Neg vuz202)) (Pos vuz144))",fontsize=16,color="black",shape="triangle"];2442 -> 2523[label="",style="solid", color="black", weight=3]; 5784[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5784 -> 5806[label="",style="solid", color="black", weight=3]; 5785[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz90) (Pos (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5785 -> 5807[label="",style="solid", color="black", weight=3]; 2453 -> 681[label="",style="dashed", color="red", weight=0]; 2453[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2453 -> 2530[label="",style="dashed", color="magenta", weight=3]; 2453 -> 2531[label="",style="dashed", color="magenta", weight=3]; 2454 -> 681[label="",style="dashed", color="red", weight=0]; 2454[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2454 -> 2532[label="",style="dashed", color="magenta", weight=3]; 2454 -> 2533[label="",style="dashed", color="magenta", weight=3]; 2452[label="primQuotInt (primPlusInt (Neg vuz167) (Neg vuz203)) (reduce2D (primPlusInt (Neg vuz168) (Neg vuz204)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2452 -> 2534[label="",style="solid", color="black", weight=3]; 2461 -> 681[label="",style="dashed", color="red", weight=0]; 2461[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2461 -> 2535[label="",style="dashed", color="magenta", weight=3]; 2461 -> 2536[label="",style="dashed", color="magenta", weight=3]; 2462 -> 681[label="",style="dashed", color="red", weight=0]; 2462[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];2462 -> 2537[label="",style="dashed", color="magenta", weight=3]; 2462 -> 2538[label="",style="dashed", color="magenta", weight=3]; 2460[label="primQuotInt (primPlusInt (Pos vuz169) (Neg vuz205)) (reduce2D (primPlusInt (Pos vuz170) (Neg vuz206)) (Neg vuz68))",fontsize=16,color="black",shape="triangle"];2460 -> 2539[label="",style="solid", color="black", weight=3]; 4175[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4175 -> 4194[label="",style="solid", color="black", weight=3]; 4176[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz200) (Neg (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4176 -> 4195[label="",style="solid", color="black", weight=3]; 4177[label="primDivNatS0 (Succ vuz28000) vuz28100 (primGEqNatS (Succ vuz28000) vuz28100)",fontsize=16,color="burlywood",shape="box"];6522[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4177 -> 6522[label="",style="solid", color="burlywood", weight=9]; 6522 -> 4196[label="",style="solid", color="burlywood", weight=3]; 6523[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4177 -> 6523[label="",style="solid", color="burlywood", weight=9]; 6523 -> 4197[label="",style="solid", color="burlywood", weight=3]; 4178[label="primDivNatS0 Zero vuz28100 (primGEqNatS Zero vuz28100)",fontsize=16,color="burlywood",shape="box"];6524[label="vuz28100/Succ vuz281000",fontsize=10,color="white",style="solid",shape="box"];4178 -> 6524[label="",style="solid", color="burlywood", weight=9]; 6524 -> 4198[label="",style="solid", color="burlywood", weight=3]; 6525[label="vuz28100/Zero",fontsize=10,color="white",style="solid",shape="box"];4178 -> 6525[label="",style="solid", color="burlywood", weight=9]; 6525 -> 4199[label="",style="solid", color="burlywood", weight=3]; 2471 -> 681[label="",style="dashed", color="red", weight=0]; 2471[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2471 -> 2546[label="",style="dashed", color="magenta", weight=3]; 2471 -> 2547[label="",style="dashed", color="magenta", weight=3]; 2472 -> 681[label="",style="dashed", color="red", weight=0]; 2472[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2472 -> 2548[label="",style="dashed", color="magenta", weight=3]; 2472 -> 2549[label="",style="dashed", color="magenta", weight=3]; 2470[label="primQuotInt (primPlusInt (Pos vuz171) (Pos vuz207)) (reduce2D (primPlusInt (Pos vuz172) (Pos vuz208)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2470 -> 2550[label="",style="solid", color="black", weight=3]; 2479 -> 681[label="",style="dashed", color="red", weight=0]; 2479[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2479 -> 2551[label="",style="dashed", color="magenta", weight=3]; 2479 -> 2552[label="",style="dashed", color="magenta", weight=3]; 2480 -> 681[label="",style="dashed", color="red", weight=0]; 2480[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];2480 -> 2553[label="",style="dashed", color="magenta", weight=3]; 2480 -> 2554[label="",style="dashed", color="magenta", weight=3]; 2478[label="primQuotInt (primPlusInt (Neg vuz173) (Pos vuz209)) (reduce2D (primPlusInt (Neg vuz174) (Pos vuz210)) (Neg vuz71))",fontsize=16,color="black",shape="triangle"];2478 -> 2555[label="",style="solid", color="black", weight=3]; 4179[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4179 -> 4200[label="",style="solid", color="black", weight=3]; 4180[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz250) (Pos (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4180 -> 4201[label="",style="solid", color="black", weight=3]; 2489 -> 681[label="",style="dashed", color="red", weight=0]; 2489[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2489 -> 2562[label="",style="dashed", color="magenta", weight=3]; 2489 -> 2563[label="",style="dashed", color="magenta", weight=3]; 2490 -> 681[label="",style="dashed", color="red", weight=0]; 2490[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2490 -> 2564[label="",style="dashed", color="magenta", weight=3]; 2490 -> 2565[label="",style="dashed", color="magenta", weight=3]; 2488[label="primQuotInt (primPlusInt (Neg vuz175) (Pos vuz211)) (reduce2D (primPlusInt (Neg vuz176) (Pos vuz212)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2488 -> 2566[label="",style="solid", color="black", weight=3]; 2497 -> 681[label="",style="dashed", color="red", weight=0]; 2497[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2497 -> 2567[label="",style="dashed", color="magenta", weight=3]; 2497 -> 2568[label="",style="dashed", color="magenta", weight=3]; 2498 -> 681[label="",style="dashed", color="red", weight=0]; 2498[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];2498 -> 2569[label="",style="dashed", color="magenta", weight=3]; 2498 -> 2570[label="",style="dashed", color="magenta", weight=3]; 2496[label="primQuotInt (primPlusInt (Pos vuz177) (Pos vuz213)) (reduce2D (primPlusInt (Pos vuz178) (Pos vuz214)) (Pos vuz74))",fontsize=16,color="black",shape="triangle"];2496 -> 2571[label="",style="solid", color="black", weight=3]; 5786[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5786 -> 5808[label="",style="solid", color="black", weight=3]; 5787[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz300) (Neg (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5787 -> 5809[label="",style="solid", color="black", weight=3]; 2499 -> 681[label="",style="dashed", color="red", weight=0]; 2499[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2499 -> 2578[label="",style="dashed", color="magenta", weight=3]; 2499 -> 2579[label="",style="dashed", color="magenta", weight=3]; 2500[label="vuz179",fontsize=16,color="green",shape="box"];2501[label="vuz77",fontsize=16,color="green",shape="box"];2502[label="vuz180",fontsize=16,color="green",shape="box"];2503 -> 681[label="",style="dashed", color="red", weight=0]; 2503[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2503 -> 2580[label="",style="dashed", color="magenta", weight=3]; 2503 -> 2581[label="",style="dashed", color="magenta", weight=3]; 2491 -> 681[label="",style="dashed", color="red", weight=0]; 2491[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2491 -> 2582[label="",style="dashed", color="magenta", weight=3]; 2491 -> 2583[label="",style="dashed", color="magenta", weight=3]; 2492[label="vuz181",fontsize=16,color="green",shape="box"];2493[label="vuz77",fontsize=16,color="green",shape="box"];2494 -> 681[label="",style="dashed", color="red", weight=0]; 2494[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];2494 -> 2584[label="",style="dashed", color="magenta", weight=3]; 2494 -> 2585[label="",style="dashed", color="magenta", weight=3]; 2495[label="vuz182",fontsize=16,color="green",shape="box"];5788[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5788 -> 5810[label="",style="solid", color="black", weight=3]; 5789[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz350) (Pos (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5789 -> 5811[label="",style="solid", color="black", weight=3]; 2481 -> 681[label="",style="dashed", color="red", weight=0]; 2481[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2481 -> 2592[label="",style="dashed", color="magenta", weight=3]; 2481 -> 2593[label="",style="dashed", color="magenta", weight=3]; 2482 -> 681[label="",style="dashed", color="red", weight=0]; 2482[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2482 -> 2594[label="",style="dashed", color="magenta", weight=3]; 2482 -> 2595[label="",style="dashed", color="magenta", weight=3]; 2483[label="vuz92",fontsize=16,color="green",shape="box"];2484[label="vuz184",fontsize=16,color="green",shape="box"];2485[label="vuz183",fontsize=16,color="green",shape="box"];2473 -> 681[label="",style="dashed", color="red", weight=0]; 2473[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2473 -> 2596[label="",style="dashed", color="magenta", weight=3]; 2473 -> 2597[label="",style="dashed", color="magenta", weight=3]; 2474[label="vuz190",fontsize=16,color="green",shape="box"];2475 -> 681[label="",style="dashed", color="red", weight=0]; 2475[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];2475 -> 2598[label="",style="dashed", color="magenta", weight=3]; 2475 -> 2599[label="",style="dashed", color="magenta", weight=3]; 2476[label="vuz189",fontsize=16,color="green",shape="box"];2477[label="vuz92",fontsize=16,color="green",shape="box"];4181[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4181 -> 4202[label="",style="solid", color="black", weight=3]; 4182[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz400) (Neg (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4182 -> 4203[label="",style="solid", color="black", weight=3]; 2463[label="vuz107",fontsize=16,color="green",shape="box"];2464[label="vuz192",fontsize=16,color="green",shape="box"];2465[label="vuz191",fontsize=16,color="green",shape="box"];2466 -> 681[label="",style="dashed", color="red", weight=0]; 2466[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2466 -> 2606[label="",style="dashed", color="magenta", weight=3]; 2466 -> 2607[label="",style="dashed", color="magenta", weight=3]; 2467 -> 681[label="",style="dashed", color="red", weight=0]; 2467[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2467 -> 2608[label="",style="dashed", color="magenta", weight=3]; 2467 -> 2609[label="",style="dashed", color="magenta", weight=3]; 2455[label="vuz107",fontsize=16,color="green",shape="box"];2456[label="vuz194",fontsize=16,color="green",shape="box"];2457 -> 681[label="",style="dashed", color="red", weight=0]; 2457[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2457 -> 2610[label="",style="dashed", color="magenta", weight=3]; 2457 -> 2611[label="",style="dashed", color="magenta", weight=3]; 2458[label="vuz193",fontsize=16,color="green",shape="box"];2459 -> 681[label="",style="dashed", color="red", weight=0]; 2459[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];2459 -> 2612[label="",style="dashed", color="magenta", weight=3]; 2459 -> 2613[label="",style="dashed", color="magenta", weight=3]; 4183[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4183 -> 4204[label="",style="solid", color="black", weight=3]; 4184[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz450) (Pos (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4184 -> 4205[label="",style="solid", color="black", weight=3]; 2445[label="vuz195",fontsize=16,color="green",shape="box"];2446[label="vuz196",fontsize=16,color="green",shape="box"];2447 -> 681[label="",style="dashed", color="red", weight=0]; 2447[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2447 -> 2620[label="",style="dashed", color="magenta", weight=3]; 2447 -> 2621[label="",style="dashed", color="magenta", weight=3]; 2448 -> 681[label="",style="dashed", color="red", weight=0]; 2448[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2448 -> 2622[label="",style="dashed", color="magenta", weight=3]; 2448 -> 2623[label="",style="dashed", color="magenta", weight=3]; 2449[label="vuz122",fontsize=16,color="green",shape="box"];2437 -> 681[label="",style="dashed", color="red", weight=0]; 2437[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2437 -> 2624[label="",style="dashed", color="magenta", weight=3]; 2437 -> 2625[label="",style="dashed", color="magenta", weight=3]; 2438 -> 681[label="",style="dashed", color="red", weight=0]; 2438[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];2438 -> 2626[label="",style="dashed", color="magenta", weight=3]; 2438 -> 2627[label="",style="dashed", color="magenta", weight=3]; 2439[label="vuz197",fontsize=16,color="green",shape="box"];2440[label="vuz198",fontsize=16,color="green",shape="box"];2441[label="vuz122",fontsize=16,color="green",shape="box"];5790[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5790 -> 5812[label="",style="solid", color="black", weight=3]; 5791[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz500) (Neg (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5791 -> 5813[label="",style="solid", color="black", weight=3]; 2514[label="vuz12",fontsize=16,color="green",shape="box"];2515[label="vuz11",fontsize=16,color="green",shape="box"];2516[label="vuz12",fontsize=16,color="green",shape="box"];2517[label="vuz11",fontsize=16,color="green",shape="box"];2518[label="primQuotInt (primMinusNat vuz185 vuz199) (reduce2D (primMinusNat vuz185 vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="triangle"];6526[label="vuz185/Succ vuz1850",fontsize=10,color="white",style="solid",shape="box"];2518 -> 6526[label="",style="solid", color="burlywood", weight=9]; 6526 -> 2634[label="",style="solid", color="burlywood", weight=3]; 6527[label="vuz185/Zero",fontsize=10,color="white",style="solid",shape="box"];2518 -> 6527[label="",style="solid", color="burlywood", weight=9]; 6527 -> 2635[label="",style="solid", color="burlywood", weight=3]; 2519[label="vuz12",fontsize=16,color="green",shape="box"];2520[label="vuz11",fontsize=16,color="green",shape="box"];2521[label="vuz12",fontsize=16,color="green",shape="box"];2522[label="vuz11",fontsize=16,color="green",shape="box"];2523 -> 3509[label="",style="dashed", color="red", weight=0]; 2523[label="primQuotInt (Neg (primPlusNat vuz187 vuz201)) (reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144))",fontsize=16,color="magenta"];2523 -> 3582[label="",style="dashed", color="magenta", weight=3]; 2523 -> 3583[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5826[label="",style="dashed", color="red", weight=0]; 5806[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5806 -> 5827[label="",style="dashed", color="magenta", weight=3]; 5806 -> 5828[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5829[label="",style="dashed", color="red", weight=0]; 5807[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz90 (Succ vuz10))) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="magenta"];5807 -> 5830[label="",style="dashed", color="magenta", weight=3]; 5807 -> 5831[label="",style="dashed", color="magenta", weight=3]; 2530[label="vuz23",fontsize=16,color="green",shape="box"];2531[label="vuz22",fontsize=16,color="green",shape="box"];2532[label="vuz23",fontsize=16,color="green",shape="box"];2533[label="vuz22",fontsize=16,color="green",shape="box"];2534 -> 3509[label="",style="dashed", color="red", weight=0]; 2534[label="primQuotInt (Neg (primPlusNat vuz167 vuz203)) (reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68))",fontsize=16,color="magenta"];2534 -> 3584[label="",style="dashed", color="magenta", weight=3]; 2534 -> 3585[label="",style="dashed", color="magenta", weight=3]; 2535[label="vuz23",fontsize=16,color="green",shape="box"];2536[label="vuz22",fontsize=16,color="green",shape="box"];2537[label="vuz23",fontsize=16,color="green",shape="box"];2538[label="vuz22",fontsize=16,color="green",shape="box"];2539[label="primQuotInt (primMinusNat vuz169 vuz205) (reduce2D (primMinusNat vuz169 vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="triangle"];6528[label="vuz169/Succ vuz1690",fontsize=10,color="white",style="solid",shape="box"];2539 -> 6528[label="",style="solid", color="burlywood", weight=9]; 6528 -> 2652[label="",style="solid", color="burlywood", weight=3]; 6529[label="vuz169/Zero",fontsize=10,color="white",style="solid",shape="box"];2539 -> 6529[label="",style="solid", color="burlywood", weight=9]; 6529 -> 2653[label="",style="solid", color="burlywood", weight=3]; 4194 -> 4216[label="",style="dashed", color="red", weight=0]; 4194[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4194 -> 4217[label="",style="dashed", color="magenta", weight=3]; 4194 -> 4218[label="",style="dashed", color="magenta", weight=3]; 4195 -> 4219[label="",style="dashed", color="red", weight=0]; 4195[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz200 (Succ vuz21))) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="magenta"];4195 -> 4220[label="",style="dashed", color="magenta", weight=3]; 4195 -> 4221[label="",style="dashed", color="magenta", weight=3]; 4196[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS (Succ vuz28000) (Succ vuz281000))",fontsize=16,color="black",shape="box"];4196 -> 4222[label="",style="solid", color="black", weight=3]; 4197[label="primDivNatS0 (Succ vuz28000) Zero (primGEqNatS (Succ vuz28000) Zero)",fontsize=16,color="black",shape="box"];4197 -> 4223[label="",style="solid", color="black", weight=3]; 4198[label="primDivNatS0 Zero (Succ vuz281000) (primGEqNatS Zero (Succ vuz281000))",fontsize=16,color="black",shape="box"];4198 -> 4224[label="",style="solid", color="black", weight=3]; 4199[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4199 -> 4225[label="",style="solid", color="black", weight=3]; 2546[label="vuz28",fontsize=16,color="green",shape="box"];2547[label="vuz27",fontsize=16,color="green",shape="box"];2548[label="vuz28",fontsize=16,color="green",shape="box"];2549[label="vuz27",fontsize=16,color="green",shape="box"];2550 -> 5046[label="",style="dashed", color="red", weight=0]; 2550[label="primQuotInt (Pos (primPlusNat vuz171 vuz207)) (reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71))",fontsize=16,color="magenta"];2550 -> 5114[label="",style="dashed", color="magenta", weight=3]; 2550 -> 5115[label="",style="dashed", color="magenta", weight=3]; 2551[label="vuz28",fontsize=16,color="green",shape="box"];2552[label="vuz27",fontsize=16,color="green",shape="box"];2553[label="vuz28",fontsize=16,color="green",shape="box"];2554[label="vuz27",fontsize=16,color="green",shape="box"];2555 -> 2539[label="",style="dashed", color="red", weight=0]; 2555[label="primQuotInt (primMinusNat vuz209 vuz173) (reduce2D (primMinusNat vuz209 vuz173) (Neg vuz71))",fontsize=16,color="magenta"];2555 -> 2667[label="",style="dashed", color="magenta", weight=3]; 2555 -> 2668[label="",style="dashed", color="magenta", weight=3]; 2555 -> 2669[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4226[label="",style="dashed", color="red", weight=0]; 4200[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4200 -> 4227[label="",style="dashed", color="magenta", weight=3]; 4200 -> 4228[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4229[label="",style="dashed", color="red", weight=0]; 4201[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz250 (Succ vuz26))) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="magenta"];4201 -> 4230[label="",style="dashed", color="magenta", weight=3]; 4201 -> 4231[label="",style="dashed", color="magenta", weight=3]; 2562[label="vuz33",fontsize=16,color="green",shape="box"];2563[label="vuz32",fontsize=16,color="green",shape="box"];2564[label="vuz33",fontsize=16,color="green",shape="box"];2565[label="vuz32",fontsize=16,color="green",shape="box"];2566 -> 2518[label="",style="dashed", color="red", weight=0]; 2566[label="primQuotInt (primMinusNat vuz211 vuz175) (reduce2D (primMinusNat vuz211 vuz175) (Pos vuz74))",fontsize=16,color="magenta"];2566 -> 2680[label="",style="dashed", color="magenta", weight=3]; 2566 -> 2681[label="",style="dashed", color="magenta", weight=3]; 2566 -> 2682[label="",style="dashed", color="magenta", weight=3]; 2567[label="vuz33",fontsize=16,color="green",shape="box"];2568[label="vuz32",fontsize=16,color="green",shape="box"];2569[label="vuz33",fontsize=16,color="green",shape="box"];2570[label="vuz32",fontsize=16,color="green",shape="box"];2571 -> 5046[label="",style="dashed", color="red", weight=0]; 2571[label="primQuotInt (Pos (primPlusNat vuz177 vuz213)) (reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74))",fontsize=16,color="magenta"];2571 -> 5116[label="",style="dashed", color="magenta", weight=3]; 2571 -> 5117[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5832[label="",style="dashed", color="red", weight=0]; 5808[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5808 -> 5833[label="",style="dashed", color="magenta", weight=3]; 5808 -> 5834[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5835[label="",style="dashed", color="red", weight=0]; 5809[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz300 (Succ vuz31))) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="magenta"];5809 -> 5836[label="",style="dashed", color="magenta", weight=3]; 5809 -> 5837[label="",style="dashed", color="magenta", weight=3]; 2578[label="vuz38",fontsize=16,color="green",shape="box"];2579[label="vuz37",fontsize=16,color="green",shape="box"];2580[label="vuz38",fontsize=16,color="green",shape="box"];2581[label="vuz37",fontsize=16,color="green",shape="box"];2582[label="vuz38",fontsize=16,color="green",shape="box"];2583[label="vuz37",fontsize=16,color="green",shape="box"];2584[label="vuz38",fontsize=16,color="green",shape="box"];2585[label="vuz37",fontsize=16,color="green",shape="box"];5810 -> 5838[label="",style="dashed", color="red", weight=0]; 5810[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5810 -> 5839[label="",style="dashed", color="magenta", weight=3]; 5810 -> 5840[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5841[label="",style="dashed", color="red", weight=0]; 5811[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz350 (Succ vuz36))) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="magenta"];5811 -> 5842[label="",style="dashed", color="magenta", weight=3]; 5811 -> 5843[label="",style="dashed", color="magenta", weight=3]; 2592[label="vuz43",fontsize=16,color="green",shape="box"];2593[label="vuz42",fontsize=16,color="green",shape="box"];2594[label="vuz43",fontsize=16,color="green",shape="box"];2595[label="vuz42",fontsize=16,color="green",shape="box"];2596[label="vuz43",fontsize=16,color="green",shape="box"];2597[label="vuz42",fontsize=16,color="green",shape="box"];2598[label="vuz43",fontsize=16,color="green",shape="box"];2599[label="vuz42",fontsize=16,color="green",shape="box"];4202 -> 4232[label="",style="dashed", color="red", weight=0]; 4202[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4202 -> 4233[label="",style="dashed", color="magenta", weight=3]; 4202 -> 4234[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4235[label="",style="dashed", color="red", weight=0]; 4203[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz400 (Succ vuz41))) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="magenta"];4203 -> 4236[label="",style="dashed", color="magenta", weight=3]; 4203 -> 4237[label="",style="dashed", color="magenta", weight=3]; 2606[label="vuz48",fontsize=16,color="green",shape="box"];2607[label="vuz47",fontsize=16,color="green",shape="box"];2608[label="vuz48",fontsize=16,color="green",shape="box"];2609[label="vuz47",fontsize=16,color="green",shape="box"];2610[label="vuz48",fontsize=16,color="green",shape="box"];2611[label="vuz47",fontsize=16,color="green",shape="box"];2612[label="vuz48",fontsize=16,color="green",shape="box"];2613[label="vuz47",fontsize=16,color="green",shape="box"];4204 -> 4238[label="",style="dashed", color="red", weight=0]; 4204[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4204 -> 4239[label="",style="dashed", color="magenta", weight=3]; 4204 -> 4240[label="",style="dashed", color="magenta", weight=3]; 4205 -> 4241[label="",style="dashed", color="red", weight=0]; 4205[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz450 (Succ vuz46))) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="magenta"];4205 -> 4242[label="",style="dashed", color="magenta", weight=3]; 4205 -> 4243[label="",style="dashed", color="magenta", weight=3]; 2620[label="vuz53",fontsize=16,color="green",shape="box"];2621[label="vuz52",fontsize=16,color="green",shape="box"];2622[label="vuz53",fontsize=16,color="green",shape="box"];2623[label="vuz52",fontsize=16,color="green",shape="box"];2624[label="vuz53",fontsize=16,color="green",shape="box"];2625[label="vuz52",fontsize=16,color="green",shape="box"];2626[label="vuz53",fontsize=16,color="green",shape="box"];2627[label="vuz52",fontsize=16,color="green",shape="box"];5812 -> 5844[label="",style="dashed", color="red", weight=0]; 5812[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5812 -> 5845[label="",style="dashed", color="magenta", weight=3]; 5812 -> 5846[label="",style="dashed", color="magenta", weight=3]; 5813 -> 5847[label="",style="dashed", color="red", weight=0]; 5813[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz500 (Succ vuz51))) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="magenta"];5813 -> 5848[label="",style="dashed", color="magenta", weight=3]; 5813 -> 5849[label="",style="dashed", color="magenta", weight=3]; 2634[label="primQuotInt (primMinusNat (Succ vuz1850) vuz199) (reduce2D (primMinusNat (Succ vuz1850) vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6530[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2634 -> 6530[label="",style="solid", color="burlywood", weight=9]; 6530 -> 2736[label="",style="solid", color="burlywood", weight=3]; 6531[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2634 -> 6531[label="",style="solid", color="burlywood", weight=9]; 6531 -> 2737[label="",style="solid", color="burlywood", weight=3]; 2635[label="primQuotInt (primMinusNat Zero vuz199) (reduce2D (primMinusNat Zero vuz199) (Pos vuz144))",fontsize=16,color="burlywood",shape="box"];6532[label="vuz199/Succ vuz1990",fontsize=10,color="white",style="solid",shape="box"];2635 -> 6532[label="",style="solid", color="burlywood", weight=9]; 6532 -> 2738[label="",style="solid", color="burlywood", weight=3]; 6533[label="vuz199/Zero",fontsize=10,color="white",style="solid",shape="box"];2635 -> 6533[label="",style="solid", color="burlywood", weight=9]; 6533 -> 2739[label="",style="solid", color="burlywood", weight=3]; 3582 -> 4090[label="",style="dashed", color="red", weight=0]; 3582[label="reduce2D (Neg (primPlusNat vuz187 vuz201)) (Pos vuz144)",fontsize=16,color="magenta"];3582 -> 4091[label="",style="dashed", color="magenta", weight=3]; 3583 -> 1354[label="",style="dashed", color="red", weight=0]; 3583[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];3583 -> 4101[label="",style="dashed", color="magenta", weight=3]; 3583 -> 4102[label="",style="dashed", color="magenta", weight=3]; 5827 -> 681[label="",style="dashed", color="red", weight=0]; 5827[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5827 -> 5850[label="",style="dashed", color="magenta", weight=3]; 5827 -> 5851[label="",style="dashed", color="magenta", weight=3]; 5828 -> 681[label="",style="dashed", color="red", weight=0]; 5828[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5828 -> 5852[label="",style="dashed", color="magenta", weight=3]; 5828 -> 5853[label="",style="dashed", color="magenta", weight=3]; 5826[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5826 -> 5854[label="",style="solid", color="black", weight=3]; 5830 -> 681[label="",style="dashed", color="red", weight=0]; 5830[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5830 -> 5855[label="",style="dashed", color="magenta", weight=3]; 5830 -> 5856[label="",style="dashed", color="magenta", weight=3]; 5831 -> 681[label="",style="dashed", color="red", weight=0]; 5831[label="primMulNat vuz90 (Succ vuz10)",fontsize=16,color="magenta"];5831 -> 5857[label="",style="dashed", color="magenta", weight=3]; 5831 -> 5858[label="",style="dashed", color="magenta", weight=3]; 5829[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz11 * Pos (Succ vuz12))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz11 * Pos (Succ vuz12))) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5829 -> 5859[label="",style="solid", color="black", weight=3]; 3584 -> 4103[label="",style="dashed", color="red", weight=0]; 3584[label="reduce2D (Neg (primPlusNat vuz167 vuz203)) (Neg vuz68)",fontsize=16,color="magenta"];3584 -> 4104[label="",style="dashed", color="magenta", weight=3]; 3585 -> 1354[label="",style="dashed", color="red", weight=0]; 3585[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];3585 -> 4114[label="",style="dashed", color="magenta", weight=3]; 3585 -> 4115[label="",style="dashed", color="magenta", weight=3]; 2652[label="primQuotInt (primMinusNat (Succ vuz1690) vuz205) (reduce2D (primMinusNat (Succ vuz1690) vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6534[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2652 -> 6534[label="",style="solid", color="burlywood", weight=9]; 6534 -> 2752[label="",style="solid", color="burlywood", weight=3]; 6535[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2652 -> 6535[label="",style="solid", color="burlywood", weight=9]; 6535 -> 2753[label="",style="solid", color="burlywood", weight=3]; 2653[label="primQuotInt (primMinusNat Zero vuz205) (reduce2D (primMinusNat Zero vuz205) (Neg vuz68))",fontsize=16,color="burlywood",shape="box"];6536[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];2653 -> 6536[label="",style="solid", color="burlywood", weight=9]; 6536 -> 2754[label="",style="solid", color="burlywood", weight=3]; 6537[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];2653 -> 6537[label="",style="solid", color="burlywood", weight=9]; 6537 -> 2755[label="",style="solid", color="burlywood", weight=3]; 4217 -> 681[label="",style="dashed", color="red", weight=0]; 4217[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4217 -> 4244[label="",style="dashed", color="magenta", weight=3]; 4217 -> 4245[label="",style="dashed", color="magenta", weight=3]; 4218 -> 681[label="",style="dashed", color="red", weight=0]; 4218[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4218 -> 4246[label="",style="dashed", color="magenta", weight=3]; 4218 -> 4247[label="",style="dashed", color="magenta", weight=3]; 4216[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4216 -> 4248[label="",style="solid", color="black", weight=3]; 4220 -> 681[label="",style="dashed", color="red", weight=0]; 4220[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4220 -> 4249[label="",style="dashed", color="magenta", weight=3]; 4220 -> 4250[label="",style="dashed", color="magenta", weight=3]; 4221 -> 681[label="",style="dashed", color="red", weight=0]; 4221[label="primMulNat vuz200 (Succ vuz21)",fontsize=16,color="magenta"];4221 -> 4251[label="",style="dashed", color="magenta", weight=3]; 4221 -> 4252[label="",style="dashed", color="magenta", weight=3]; 4219[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz22 * Pos (Succ vuz23))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz22 * Pos (Succ vuz23))) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4219 -> 4253[label="",style="solid", color="black", weight=3]; 4222 -> 4927[label="",style="dashed", color="red", weight=0]; 4222[label="primDivNatS0 (Succ vuz28000) (Succ vuz281000) (primGEqNatS vuz28000 vuz281000)",fontsize=16,color="magenta"];4222 -> 4928[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4929[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4930[label="",style="dashed", color="magenta", weight=3]; 4222 -> 4931[label="",style="dashed", color="magenta", weight=3]; 4223[label="primDivNatS0 (Succ vuz28000) Zero True",fontsize=16,color="black",shape="box"];4223 -> 4256[label="",style="solid", color="black", weight=3]; 4224[label="primDivNatS0 Zero (Succ vuz281000) False",fontsize=16,color="black",shape="box"];4224 -> 4257[label="",style="solid", color="black", weight=3]; 4225[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];4225 -> 4258[label="",style="solid", color="black", weight=3]; 5114 -> 5689[label="",style="dashed", color="red", weight=0]; 5114[label="reduce2D (Pos (primPlusNat vuz171 vuz207)) (Neg vuz71)",fontsize=16,color="magenta"];5114 -> 5690[label="",style="dashed", color="magenta", weight=3]; 5115 -> 1354[label="",style="dashed", color="red", weight=0]; 5115[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5115 -> 5703[label="",style="dashed", color="magenta", weight=3]; 5115 -> 5704[label="",style="dashed", color="magenta", weight=3]; 2667[label="vuz71",fontsize=16,color="green",shape="box"];2668[label="vuz209",fontsize=16,color="green",shape="box"];2669[label="vuz173",fontsize=16,color="green",shape="box"];4227 -> 681[label="",style="dashed", color="red", weight=0]; 4227[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4227 -> 4259[label="",style="dashed", color="magenta", weight=3]; 4227 -> 4260[label="",style="dashed", color="magenta", weight=3]; 4228 -> 681[label="",style="dashed", color="red", weight=0]; 4228[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4228 -> 4261[label="",style="dashed", color="magenta", weight=3]; 4228 -> 4262[label="",style="dashed", color="magenta", weight=3]; 4226[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4226 -> 4263[label="",style="solid", color="black", weight=3]; 4230 -> 681[label="",style="dashed", color="red", weight=0]; 4230[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4230 -> 4264[label="",style="dashed", color="magenta", weight=3]; 4230 -> 4265[label="",style="dashed", color="magenta", weight=3]; 4231 -> 681[label="",style="dashed", color="red", weight=0]; 4231[label="primMulNat vuz250 (Succ vuz26)",fontsize=16,color="magenta"];4231 -> 4266[label="",style="dashed", color="magenta", weight=3]; 4231 -> 4267[label="",style="dashed", color="magenta", weight=3]; 4229[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Neg vuz27 * Neg (Succ vuz28))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Neg vuz27 * Neg (Succ vuz28))) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4229 -> 4268[label="",style="solid", color="black", weight=3]; 2680[label="vuz175",fontsize=16,color="green",shape="box"];2681[label="vuz211",fontsize=16,color="green",shape="box"];2682[label="vuz74",fontsize=16,color="green",shape="box"];5116 -> 5705[label="",style="dashed", color="red", weight=0]; 5116[label="reduce2D (Pos (primPlusNat vuz177 vuz213)) (Pos vuz74)",fontsize=16,color="magenta"];5116 -> 5706[label="",style="dashed", color="magenta", weight=3]; 5117 -> 1354[label="",style="dashed", color="red", weight=0]; 5117[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5117 -> 5719[label="",style="dashed", color="magenta", weight=3]; 5117 -> 5720[label="",style="dashed", color="magenta", weight=3]; 5833 -> 681[label="",style="dashed", color="red", weight=0]; 5833[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5833 -> 5860[label="",style="dashed", color="magenta", weight=3]; 5833 -> 5861[label="",style="dashed", color="magenta", weight=3]; 5834 -> 681[label="",style="dashed", color="red", weight=0]; 5834[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5834 -> 5862[label="",style="dashed", color="magenta", weight=3]; 5834 -> 5863[label="",style="dashed", color="magenta", weight=3]; 5832[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5832 -> 5864[label="",style="solid", color="black", weight=3]; 5836 -> 681[label="",style="dashed", color="red", weight=0]; 5836[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5836 -> 5865[label="",style="dashed", color="magenta", weight=3]; 5836 -> 5866[label="",style="dashed", color="magenta", weight=3]; 5837 -> 681[label="",style="dashed", color="red", weight=0]; 5837[label="primMulNat vuz300 (Succ vuz31)",fontsize=16,color="magenta"];5837 -> 5867[label="",style="dashed", color="magenta", weight=3]; 5837 -> 5868[label="",style="dashed", color="magenta", weight=3]; 5835[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Neg vuz32 * Neg (Succ vuz33))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Neg vuz32 * Neg (Succ vuz33))) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5835 -> 5869[label="",style="solid", color="black", weight=3]; 5839 -> 681[label="",style="dashed", color="red", weight=0]; 5839[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5839 -> 5870[label="",style="dashed", color="magenta", weight=3]; 5839 -> 5871[label="",style="dashed", color="magenta", weight=3]; 5840 -> 681[label="",style="dashed", color="red", weight=0]; 5840[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5840 -> 5872[label="",style="dashed", color="magenta", weight=3]; 5840 -> 5873[label="",style="dashed", color="magenta", weight=3]; 5838[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5838 -> 5874[label="",style="solid", color="black", weight=3]; 5842 -> 681[label="",style="dashed", color="red", weight=0]; 5842[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5842 -> 5875[label="",style="dashed", color="magenta", weight=3]; 5842 -> 5876[label="",style="dashed", color="magenta", weight=3]; 5843 -> 681[label="",style="dashed", color="red", weight=0]; 5843[label="primMulNat vuz350 (Succ vuz36)",fontsize=16,color="magenta"];5843 -> 5877[label="",style="dashed", color="magenta", weight=3]; 5843 -> 5878[label="",style="dashed", color="magenta", weight=3]; 5841[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos vuz37 * Pos (Succ vuz38))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos vuz37 * Pos (Succ vuz38))) (Pos vuz77)",fontsize=16,color="black",shape="triangle"];5841 -> 5879[label="",style="solid", color="black", weight=3]; 4233 -> 681[label="",style="dashed", color="red", weight=0]; 4233[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4233 -> 4269[label="",style="dashed", color="magenta", weight=3]; 4233 -> 4270[label="",style="dashed", color="magenta", weight=3]; 4234 -> 681[label="",style="dashed", color="red", weight=0]; 4234[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4234 -> 4271[label="",style="dashed", color="magenta", weight=3]; 4234 -> 4272[label="",style="dashed", color="magenta", weight=3]; 4232[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4232 -> 4273[label="",style="solid", color="black", weight=3]; 4236 -> 681[label="",style="dashed", color="red", weight=0]; 4236[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4236 -> 4274[label="",style="dashed", color="magenta", weight=3]; 4236 -> 4275[label="",style="dashed", color="magenta", weight=3]; 4237 -> 681[label="",style="dashed", color="red", weight=0]; 4237[label="primMulNat vuz400 (Succ vuz41)",fontsize=16,color="magenta"];4237 -> 4276[label="",style="dashed", color="magenta", weight=3]; 4237 -> 4277[label="",style="dashed", color="magenta", weight=3]; 4235[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos vuz42 * Pos (Succ vuz43))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos vuz42 * Pos (Succ vuz43))) (Neg vuz92)",fontsize=16,color="black",shape="triangle"];4235 -> 4278[label="",style="solid", color="black", weight=3]; 4239 -> 681[label="",style="dashed", color="red", weight=0]; 4239[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4239 -> 4279[label="",style="dashed", color="magenta", weight=3]; 4239 -> 4280[label="",style="dashed", color="magenta", weight=3]; 4240 -> 681[label="",style="dashed", color="red", weight=0]; 4240[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4240 -> 4281[label="",style="dashed", color="magenta", weight=3]; 4240 -> 4282[label="",style="dashed", color="magenta", weight=3]; 4238[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4238 -> 4283[label="",style="solid", color="black", weight=3]; 4242 -> 681[label="",style="dashed", color="red", weight=0]; 4242[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4242 -> 4284[label="",style="dashed", color="magenta", weight=3]; 4242 -> 4285[label="",style="dashed", color="magenta", weight=3]; 4243 -> 681[label="",style="dashed", color="red", weight=0]; 4243[label="primMulNat vuz450 (Succ vuz46)",fontsize=16,color="magenta"];4243 -> 4286[label="",style="dashed", color="magenta", weight=3]; 4243 -> 4287[label="",style="dashed", color="magenta", weight=3]; 4241[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Pos vuz47 * Neg (Succ vuz48))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Pos vuz47 * Neg (Succ vuz48))) (Neg vuz107)",fontsize=16,color="black",shape="triangle"];4241 -> 4288[label="",style="solid", color="black", weight=3]; 5845 -> 681[label="",style="dashed", color="red", weight=0]; 5845[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5845 -> 5880[label="",style="dashed", color="magenta", weight=3]; 5845 -> 5881[label="",style="dashed", color="magenta", weight=3]; 5846 -> 681[label="",style="dashed", color="red", weight=0]; 5846[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5846 -> 5882[label="",style="dashed", color="magenta", weight=3]; 5846 -> 5883[label="",style="dashed", color="magenta", weight=3]; 5844[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5844 -> 5884[label="",style="solid", color="black", weight=3]; 5848 -> 681[label="",style="dashed", color="red", weight=0]; 5848[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5848 -> 5885[label="",style="dashed", color="magenta", weight=3]; 5848 -> 5886[label="",style="dashed", color="magenta", weight=3]; 5849 -> 681[label="",style="dashed", color="red", weight=0]; 5849[label="primMulNat vuz500 (Succ vuz51)",fontsize=16,color="magenta"];5849 -> 5887[label="",style="dashed", color="magenta", weight=3]; 5849 -> 5888[label="",style="dashed", color="magenta", weight=3]; 5847[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Pos vuz52 * Neg (Succ vuz53))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Pos vuz52 * Neg (Succ vuz53))) (Pos vuz122)",fontsize=16,color="black",shape="triangle"];5847 -> 5889[label="",style="solid", color="black", weight=3]; 2736[label="primQuotInt (primMinusNat (Succ vuz1850) (Succ vuz1990)) (reduce2D (primMinusNat (Succ vuz1850) (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2736 -> 2780[label="",style="solid", color="black", weight=3]; 2737[label="primQuotInt (primMinusNat (Succ vuz1850) Zero) (reduce2D (primMinusNat (Succ vuz1850) Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2737 -> 2781[label="",style="solid", color="black", weight=3]; 2738[label="primQuotInt (primMinusNat Zero (Succ vuz1990)) (reduce2D (primMinusNat Zero (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="black",shape="box"];2738 -> 2782[label="",style="solid", color="black", weight=3]; 2739[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Pos vuz144))",fontsize=16,color="black",shape="box"];2739 -> 2783[label="",style="solid", color="black", weight=3]; 4091 -> 1354[label="",style="dashed", color="red", weight=0]; 4091[label="primPlusNat vuz187 vuz201",fontsize=16,color="magenta"];4091 -> 4116[label="",style="dashed", color="magenta", weight=3]; 4091 -> 4117[label="",style="dashed", color="magenta", weight=3]; 4090[label="reduce2D (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];4090 -> 4118[label="",style="solid", color="black", weight=3]; 4101[label="vuz201",fontsize=16,color="green",shape="box"];4102[label="vuz187",fontsize=16,color="green",shape="box"];5850[label="vuz10",fontsize=16,color="green",shape="box"];5851[label="vuz90",fontsize=16,color="green",shape="box"];5852[label="vuz10",fontsize=16,color="green",shape="box"];5853[label="vuz90",fontsize=16,color="green",shape="box"];5854[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5854 -> 5900[label="",style="solid", color="black", weight=3]; 5855[label="vuz10",fontsize=16,color="green",shape="box"];5856[label="vuz90",fontsize=16,color="green",shape="box"];5857[label="vuz10",fontsize=16,color="green",shape="box"];5858[label="vuz90",fontsize=16,color="green",shape="box"];5859[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (primMulInt (Neg vuz11) (Pos (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="black",shape="box"];5859 -> 5901[label="",style="solid", color="black", weight=3]; 4104 -> 1354[label="",style="dashed", color="red", weight=0]; 4104[label="primPlusNat vuz167 vuz203",fontsize=16,color="magenta"];4104 -> 4119[label="",style="dashed", color="magenta", weight=3]; 4104 -> 4120[label="",style="dashed", color="magenta", weight=3]; 4103[label="reduce2D (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4103 -> 4121[label="",style="solid", color="black", weight=3]; 4114[label="vuz203",fontsize=16,color="green",shape="box"];4115[label="vuz167",fontsize=16,color="green",shape="box"];2752[label="primQuotInt (primMinusNat (Succ vuz1690) (Succ vuz2050)) (reduce2D (primMinusNat (Succ vuz1690) (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2752 -> 2804[label="",style="solid", color="black", weight=3]; 2753[label="primQuotInt (primMinusNat (Succ vuz1690) Zero) (reduce2D (primMinusNat (Succ vuz1690) Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2753 -> 2805[label="",style="solid", color="black", weight=3]; 2754[label="primQuotInt (primMinusNat Zero (Succ vuz2050)) (reduce2D (primMinusNat Zero (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="black",shape="box"];2754 -> 2806[label="",style="solid", color="black", weight=3]; 2755[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Neg vuz68))",fontsize=16,color="black",shape="box"];2755 -> 2807[label="",style="solid", color="black", weight=3]; 4244[label="vuz21",fontsize=16,color="green",shape="box"];4245[label="vuz200",fontsize=16,color="green",shape="box"];4246[label="vuz21",fontsize=16,color="green",shape="box"];4247[label="vuz200",fontsize=16,color="green",shape="box"];4248[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4248 -> 4297[label="",style="solid", color="black", weight=3]; 4249[label="vuz21",fontsize=16,color="green",shape="box"];4250[label="vuz200",fontsize=16,color="green",shape="box"];4251[label="vuz21",fontsize=16,color="green",shape="box"];4252[label="vuz200",fontsize=16,color="green",shape="box"];4253[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (primMulInt (Neg vuz22) (Pos (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="black",shape="box"];4253 -> 4298[label="",style="solid", color="black", weight=3]; 4928[label="vuz28000",fontsize=16,color="green",shape="box"];4929[label="vuz281000",fontsize=16,color="green",shape="box"];4930[label="vuz281000",fontsize=16,color="green",shape="box"];4931[label="vuz28000",fontsize=16,color="green",shape="box"];4927[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz340 vuz341)",fontsize=16,color="burlywood",shape="triangle"];6538[label="vuz340/Succ vuz3400",fontsize=10,color="white",style="solid",shape="box"];4927 -> 6538[label="",style="solid", color="burlywood", weight=9]; 6538 -> 4968[label="",style="solid", color="burlywood", weight=3]; 6539[label="vuz340/Zero",fontsize=10,color="white",style="solid",shape="box"];4927 -> 6539[label="",style="solid", color="burlywood", weight=9]; 6539 -> 4969[label="",style="solid", color="burlywood", weight=3]; 4256[label="Succ (primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4256 -> 4303[label="",style="dashed", color="green", weight=3]; 4257[label="Zero",fontsize=16,color="green",shape="box"];4258[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];4258 -> 4304[label="",style="dashed", color="green", weight=3]; 5690 -> 1354[label="",style="dashed", color="red", weight=0]; 5690[label="primPlusNat vuz171 vuz207",fontsize=16,color="magenta"];5690 -> 5721[label="",style="dashed", color="magenta", weight=3]; 5690 -> 5722[label="",style="dashed", color="magenta", weight=3]; 5689[label="reduce2D (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];5689 -> 5723[label="",style="solid", color="black", weight=3]; 5703[label="vuz207",fontsize=16,color="green",shape="box"];5704[label="vuz171",fontsize=16,color="green",shape="box"];4259[label="vuz26",fontsize=16,color="green",shape="box"];4260[label="vuz250",fontsize=16,color="green",shape="box"];4261[label="vuz26",fontsize=16,color="green",shape="box"];4262[label="vuz250",fontsize=16,color="green",shape="box"];4263[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4263 -> 4305[label="",style="solid", color="black", weight=3]; 4264[label="vuz26",fontsize=16,color="green",shape="box"];4265[label="vuz250",fontsize=16,color="green",shape="box"];4266[label="vuz26",fontsize=16,color="green",shape="box"];4267[label="vuz250",fontsize=16,color="green",shape="box"];4268[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (primMulInt (Neg vuz27) (Neg (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="black",shape="box"];4268 -> 4306[label="",style="solid", color="black", weight=3]; 5706 -> 1354[label="",style="dashed", color="red", weight=0]; 5706[label="primPlusNat vuz177 vuz213",fontsize=16,color="magenta"];5706 -> 5724[label="",style="dashed", color="magenta", weight=3]; 5706 -> 5725[label="",style="dashed", color="magenta", weight=3]; 5705[label="reduce2D (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5705 -> 5726[label="",style="solid", color="black", weight=3]; 5719[label="vuz213",fontsize=16,color="green",shape="box"];5720[label="vuz177",fontsize=16,color="green",shape="box"];5860[label="vuz31",fontsize=16,color="green",shape="box"];5861[label="vuz300",fontsize=16,color="green",shape="box"];5862[label="vuz31",fontsize=16,color="green",shape="box"];5863[label="vuz300",fontsize=16,color="green",shape="box"];5864[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5864 -> 5902[label="",style="solid", color="black", weight=3]; 5865[label="vuz31",fontsize=16,color="green",shape="box"];5866[label="vuz300",fontsize=16,color="green",shape="box"];5867[label="vuz31",fontsize=16,color="green",shape="box"];5868[label="vuz300",fontsize=16,color="green",shape="box"];5869[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (primMulInt (Neg vuz32) (Neg (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="black",shape="box"];5869 -> 5903[label="",style="solid", color="black", weight=3]; 5870[label="vuz36",fontsize=16,color="green",shape="box"];5871[label="vuz350",fontsize=16,color="green",shape="box"];5872[label="vuz36",fontsize=16,color="green",shape="box"];5873[label="vuz350",fontsize=16,color="green",shape="box"];5874[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5874 -> 5904[label="",style="solid", color="black", weight=3]; 5875[label="vuz36",fontsize=16,color="green",shape="box"];5876[label="vuz350",fontsize=16,color="green",shape="box"];5877[label="vuz36",fontsize=16,color="green",shape="box"];5878[label="vuz350",fontsize=16,color="green",shape="box"];5879[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (primMulInt (Pos vuz37) (Pos (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="black",shape="box"];5879 -> 5905[label="",style="solid", color="black", weight=3]; 4269[label="vuz41",fontsize=16,color="green",shape="box"];4270[label="vuz400",fontsize=16,color="green",shape="box"];4271[label="vuz41",fontsize=16,color="green",shape="box"];4272[label="vuz400",fontsize=16,color="green",shape="box"];4273[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4273 -> 4307[label="",style="solid", color="black", weight=3]; 4274[label="vuz41",fontsize=16,color="green",shape="box"];4275[label="vuz400",fontsize=16,color="green",shape="box"];4276[label="vuz41",fontsize=16,color="green",shape="box"];4277[label="vuz400",fontsize=16,color="green",shape="box"];4278[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (primMulInt (Pos vuz42) (Pos (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="black",shape="box"];4278 -> 4308[label="",style="solid", color="black", weight=3]; 4279[label="vuz46",fontsize=16,color="green",shape="box"];4280[label="vuz450",fontsize=16,color="green",shape="box"];4281[label="vuz46",fontsize=16,color="green",shape="box"];4282[label="vuz450",fontsize=16,color="green",shape="box"];4283[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4283 -> 4309[label="",style="solid", color="black", weight=3]; 4284[label="vuz46",fontsize=16,color="green",shape="box"];4285[label="vuz450",fontsize=16,color="green",shape="box"];4286[label="vuz46",fontsize=16,color="green",shape="box"];4287[label="vuz450",fontsize=16,color="green",shape="box"];4288[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (primMulInt (Pos vuz47) (Neg (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="black",shape="box"];4288 -> 4310[label="",style="solid", color="black", weight=3]; 5880[label="vuz51",fontsize=16,color="green",shape="box"];5881[label="vuz500",fontsize=16,color="green",shape="box"];5882[label="vuz51",fontsize=16,color="green",shape="box"];5883[label="vuz500",fontsize=16,color="green",shape="box"];5884[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5884 -> 5906[label="",style="solid", color="black", weight=3]; 5885[label="vuz51",fontsize=16,color="green",shape="box"];5886[label="vuz500",fontsize=16,color="green",shape="box"];5887[label="vuz51",fontsize=16,color="green",shape="box"];5888[label="vuz500",fontsize=16,color="green",shape="box"];5889[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (primMulInt (Pos vuz52) (Neg (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="black",shape="box"];5889 -> 5907[label="",style="solid", color="black", weight=3]; 2780 -> 2518[label="",style="dashed", color="red", weight=0]; 2780[label="primQuotInt (primMinusNat vuz1850 vuz1990) (reduce2D (primMinusNat vuz1850 vuz1990) (Pos vuz144))",fontsize=16,color="magenta"];2780 -> 2864[label="",style="dashed", color="magenta", weight=3]; 2780 -> 2865[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5046[label="",style="dashed", color="red", weight=0]; 2781[label="primQuotInt (Pos (Succ vuz1850)) (reduce2D (Pos (Succ vuz1850)) (Pos vuz144))",fontsize=16,color="magenta"];2781 -> 5164[label="",style="dashed", color="magenta", weight=3]; 2781 -> 5165[label="",style="dashed", color="magenta", weight=3]; 2782 -> 3509[label="",style="dashed", color="red", weight=0]; 2782[label="primQuotInt (Neg (Succ vuz1990)) (reduce2D (Neg (Succ vuz1990)) (Pos vuz144))",fontsize=16,color="magenta"];2782 -> 3642[label="",style="dashed", color="magenta", weight=3]; 2782 -> 3643[label="",style="dashed", color="magenta", weight=3]; 2783 -> 5046[label="",style="dashed", color="red", weight=0]; 2783[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz144))",fontsize=16,color="magenta"];2783 -> 5166[label="",style="dashed", color="magenta", weight=3]; 2783 -> 5167[label="",style="dashed", color="magenta", weight=3]; 4116[label="vuz201",fontsize=16,color="green",shape="box"];4117[label="vuz187",fontsize=16,color="green",shape="box"];4118[label="gcd (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4118 -> 4135[label="",style="solid", color="black", weight=3]; 5900 -> 5920[label="",style="dashed", color="red", weight=0]; 5900[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5900 -> 5921[label="",style="dashed", color="magenta", weight=3]; 5900 -> 5922[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5928[label="",style="dashed", color="red", weight=0]; 5901[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg (primMulNat vuz11 (Succ vuz12)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg (primMulNat vuz11 (Succ vuz12)))) (Pos vuz144)",fontsize=16,color="magenta"];5901 -> 5929[label="",style="dashed", color="magenta", weight=3]; 5901 -> 5930[label="",style="dashed", color="magenta", weight=3]; 4119[label="vuz203",fontsize=16,color="green",shape="box"];4120[label="vuz167",fontsize=16,color="green",shape="box"];4121[label="gcd (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4121 -> 4136[label="",style="solid", color="black", weight=3]; 2804 -> 2539[label="",style="dashed", color="red", weight=0]; 2804[label="primQuotInt (primMinusNat vuz1690 vuz2050) (reduce2D (primMinusNat vuz1690 vuz2050) (Neg vuz68))",fontsize=16,color="magenta"];2804 -> 2886[label="",style="dashed", color="magenta", weight=3]; 2804 -> 2887[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5046[label="",style="dashed", color="red", weight=0]; 2805[label="primQuotInt (Pos (Succ vuz1690)) (reduce2D (Pos (Succ vuz1690)) (Neg vuz68))",fontsize=16,color="magenta"];2805 -> 5172[label="",style="dashed", color="magenta", weight=3]; 2805 -> 5173[label="",style="dashed", color="magenta", weight=3]; 2806 -> 3509[label="",style="dashed", color="red", weight=0]; 2806[label="primQuotInt (Neg (Succ vuz2050)) (reduce2D (Neg (Succ vuz2050)) (Neg vuz68))",fontsize=16,color="magenta"];2806 -> 3648[label="",style="dashed", color="magenta", weight=3]; 2806 -> 3649[label="",style="dashed", color="magenta", weight=3]; 2807 -> 5046[label="",style="dashed", color="red", weight=0]; 2807[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz68))",fontsize=16,color="magenta"];2807 -> 5174[label="",style="dashed", color="magenta", weight=3]; 2807 -> 5175[label="",style="dashed", color="magenta", weight=3]; 4297 -> 4319[label="",style="dashed", color="red", weight=0]; 4297[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4297 -> 4320[label="",style="dashed", color="magenta", weight=3]; 4297 -> 4321[label="",style="dashed", color="magenta", weight=3]; 4298 -> 4327[label="",style="dashed", color="red", weight=0]; 4298[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg (primMulNat vuz22 (Succ vuz23)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg (primMulNat vuz22 (Succ vuz23)))) (Neg vuz68)",fontsize=16,color="magenta"];4298 -> 4328[label="",style="dashed", color="magenta", weight=3]; 4298 -> 4329[label="",style="dashed", color="magenta", weight=3]; 4968[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) vuz341)",fontsize=16,color="burlywood",shape="box"];6540[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4968 -> 6540[label="",style="solid", color="burlywood", weight=9]; 6540 -> 4992[label="",style="solid", color="burlywood", weight=3]; 6541[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4968 -> 6541[label="",style="solid", color="burlywood", weight=9]; 6541 -> 4993[label="",style="solid", color="burlywood", weight=3]; 4969[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero vuz341)",fontsize=16,color="burlywood",shape="box"];6542[label="vuz341/Succ vuz3410",fontsize=10,color="white",style="solid",shape="box"];4969 -> 6542[label="",style="solid", color="burlywood", weight=9]; 6542 -> 4994[label="",style="solid", color="burlywood", weight=3]; 6543[label="vuz341/Zero",fontsize=10,color="white",style="solid",shape="box"];4969 -> 6543[label="",style="solid", color="burlywood", weight=9]; 6543 -> 4995[label="",style="solid", color="burlywood", weight=3]; 4303 -> 4129[label="",style="dashed", color="red", weight=0]; 4303[label="primDivNatS (primMinusNatS (Succ vuz28000) Zero) (Succ Zero)",fontsize=16,color="magenta"];4303 -> 4339[label="",style="dashed", color="magenta", weight=3]; 4303 -> 4340[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4129[label="",style="dashed", color="red", weight=0]; 4304[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];4304 -> 4341[label="",style="dashed", color="magenta", weight=3]; 4304 -> 4342[label="",style="dashed", color="magenta", weight=3]; 5721[label="vuz207",fontsize=16,color="green",shape="box"];5722[label="vuz171",fontsize=16,color="green",shape="box"];5723[label="gcd (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5723 -> 5741[label="",style="solid", color="black", weight=3]; 4305 -> 4343[label="",style="dashed", color="red", weight=0]; 4305[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4305 -> 4344[label="",style="dashed", color="magenta", weight=3]; 4305 -> 4345[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4351[label="",style="dashed", color="red", weight=0]; 4306[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos (primMulNat vuz27 (Succ vuz28)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos (primMulNat vuz27 (Succ vuz28)))) (Neg vuz71)",fontsize=16,color="magenta"];4306 -> 4352[label="",style="dashed", color="magenta", weight=3]; 4306 -> 4353[label="",style="dashed", color="magenta", weight=3]; 5724[label="vuz213",fontsize=16,color="green",shape="box"];5725[label="vuz177",fontsize=16,color="green",shape="box"];5726[label="gcd (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5726 -> 5742[label="",style="solid", color="black", weight=3]; 5902 -> 5936[label="",style="dashed", color="red", weight=0]; 5902[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5902 -> 5937[label="",style="dashed", color="magenta", weight=3]; 5902 -> 5938[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5944[label="",style="dashed", color="red", weight=0]; 5903[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos (primMulNat vuz32 (Succ vuz33)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos (primMulNat vuz32 (Succ vuz33)))) (Pos vuz74)",fontsize=16,color="magenta"];5903 -> 5945[label="",style="dashed", color="magenta", weight=3]; 5903 -> 5946[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5944[label="",style="dashed", color="red", weight=0]; 5904[label="gcd2 (primEqInt (primPlusInt (Pos vuz358) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz357) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5904 -> 5947[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5948[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5949[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5950[label="",style="dashed", color="magenta", weight=3]; 5904 -> 5951[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5936[label="",style="dashed", color="red", weight=0]; 5905[label="gcd2 (primEqInt (primPlusInt (Neg vuz360) (Pos (primMulNat vuz37 (Succ vuz38)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz359) (Pos (primMulNat vuz37 (Succ vuz38)))) (Pos vuz77)",fontsize=16,color="magenta"];5905 -> 5939[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5940[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5941[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5942[label="",style="dashed", color="magenta", weight=3]; 5905 -> 5943[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4351[label="",style="dashed", color="red", weight=0]; 4307[label="gcd2 (primEqInt (primPlusInt (Neg vuz293) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz292) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4307 -> 4354[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4355[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4356[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4357[label="",style="dashed", color="magenta", weight=3]; 4307 -> 4358[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4343[label="",style="dashed", color="red", weight=0]; 4308[label="gcd2 (primEqInt (primPlusInt (Pos vuz295) (Pos (primMulNat vuz42 (Succ vuz43)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz294) (Pos (primMulNat vuz42 (Succ vuz43)))) (Neg vuz92)",fontsize=16,color="magenta"];4308 -> 4346[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4347[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4348[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4349[label="",style="dashed", color="magenta", weight=3]; 4308 -> 4350[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4327[label="",style="dashed", color="red", weight=0]; 4309[label="gcd2 (primEqInt (primPlusInt (Pos vuz297) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz296) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4309 -> 4330[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4331[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4332[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4333[label="",style="dashed", color="magenta", weight=3]; 4309 -> 4334[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4319[label="",style="dashed", color="red", weight=0]; 4310[label="gcd2 (primEqInt (primPlusInt (Neg vuz299) (Neg (primMulNat vuz47 (Succ vuz48)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz298) (Neg (primMulNat vuz47 (Succ vuz48)))) (Neg vuz107)",fontsize=16,color="magenta"];4310 -> 4322[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4323[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4324[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4325[label="",style="dashed", color="magenta", weight=3]; 4310 -> 4326[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5928[label="",style="dashed", color="red", weight=0]; 5906[label="gcd2 (primEqInt (primPlusInt (Neg vuz362) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz361) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5906 -> 5931[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5932[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5933[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5934[label="",style="dashed", color="magenta", weight=3]; 5906 -> 5935[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5920[label="",style="dashed", color="red", weight=0]; 5907[label="gcd2 (primEqInt (primPlusInt (Pos vuz364) (Neg (primMulNat vuz52 (Succ vuz53)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz363) (Neg (primMulNat vuz52 (Succ vuz53)))) (Pos vuz122)",fontsize=16,color="magenta"];5907 -> 5923[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5924[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5925[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5926[label="",style="dashed", color="magenta", weight=3]; 5907 -> 5927[label="",style="dashed", color="magenta", weight=3]; 2864[label="vuz1990",fontsize=16,color="green",shape="box"];2865[label="vuz1850",fontsize=16,color="green",shape="box"];5164 -> 5705[label="",style="dashed", color="red", weight=0]; 5164[label="reduce2D (Pos (Succ vuz1850)) (Pos vuz144)",fontsize=16,color="magenta"];5164 -> 5707[label="",style="dashed", color="magenta", weight=3]; 5164 -> 5708[label="",style="dashed", color="magenta", weight=3]; 5165[label="Succ vuz1850",fontsize=16,color="green",shape="box"];3642 -> 4090[label="",style="dashed", color="red", weight=0]; 3642[label="reduce2D (Neg (Succ vuz1990)) (Pos vuz144)",fontsize=16,color="magenta"];3642 -> 4092[label="",style="dashed", color="magenta", weight=3]; 3643[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5166 -> 5705[label="",style="dashed", color="red", weight=0]; 5166[label="reduce2D (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];5166 -> 5709[label="",style="dashed", color="magenta", weight=3]; 5166 -> 5710[label="",style="dashed", color="magenta", weight=3]; 5167[label="Zero",fontsize=16,color="green",shape="box"];4135[label="gcd3 (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4135 -> 4151[label="",style="solid", color="black", weight=3]; 5921 -> 681[label="",style="dashed", color="red", weight=0]; 5921[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5921 -> 5952[label="",style="dashed", color="magenta", weight=3]; 5921 -> 5953[label="",style="dashed", color="magenta", weight=3]; 5922 -> 681[label="",style="dashed", color="red", weight=0]; 5922[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5922 -> 5954[label="",style="dashed", color="magenta", weight=3]; 5922 -> 5955[label="",style="dashed", color="magenta", weight=3]; 5920[label="gcd2 (primEqInt (primPlusInt (Pos vuz350) (Neg vuz366)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz349) (Neg vuz365)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5920 -> 5956[label="",style="solid", color="black", weight=3]; 5929 -> 681[label="",style="dashed", color="red", weight=0]; 5929[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5929 -> 5957[label="",style="dashed", color="magenta", weight=3]; 5929 -> 5958[label="",style="dashed", color="magenta", weight=3]; 5930 -> 681[label="",style="dashed", color="red", weight=0]; 5930[label="primMulNat vuz11 (Succ vuz12)",fontsize=16,color="magenta"];5930 -> 5959[label="",style="dashed", color="magenta", weight=3]; 5930 -> 5960[label="",style="dashed", color="magenta", weight=3]; 5928[label="gcd2 (primEqInt (primPlusInt (Neg vuz352) (Neg vuz368)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz351) (Neg vuz367)) (Pos vuz144)",fontsize=16,color="black",shape="triangle"];5928 -> 5961[label="",style="solid", color="black", weight=3]; 4136[label="gcd3 (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4136 -> 4152[label="",style="solid", color="black", weight=3]; 2886[label="vuz1690",fontsize=16,color="green",shape="box"];2887[label="vuz2050",fontsize=16,color="green",shape="box"];5172 -> 5689[label="",style="dashed", color="red", weight=0]; 5172[label="reduce2D (Pos (Succ vuz1690)) (Neg vuz68)",fontsize=16,color="magenta"];5172 -> 5691[label="",style="dashed", color="magenta", weight=3]; 5172 -> 5692[label="",style="dashed", color="magenta", weight=3]; 5173[label="Succ vuz1690",fontsize=16,color="green",shape="box"];3648 -> 4103[label="",style="dashed", color="red", weight=0]; 3648[label="reduce2D (Neg (Succ vuz2050)) (Neg vuz68)",fontsize=16,color="magenta"];3648 -> 4105[label="",style="dashed", color="magenta", weight=3]; 3649[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5174 -> 5689[label="",style="dashed", color="red", weight=0]; 5174[label="reduce2D (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];5174 -> 5693[label="",style="dashed", color="magenta", weight=3]; 5174 -> 5694[label="",style="dashed", color="magenta", weight=3]; 5175[label="Zero",fontsize=16,color="green",shape="box"];4320 -> 681[label="",style="dashed", color="red", weight=0]; 4320[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4320 -> 4359[label="",style="dashed", color="magenta", weight=3]; 4320 -> 4360[label="",style="dashed", color="magenta", weight=3]; 4321 -> 681[label="",style="dashed", color="red", weight=0]; 4321[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4321 -> 4361[label="",style="dashed", color="magenta", weight=3]; 4321 -> 4362[label="",style="dashed", color="magenta", weight=3]; 4319[label="gcd2 (primEqInt (primPlusInt (Neg vuz285) (Neg vuz301)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz284) (Neg vuz300)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4319 -> 4363[label="",style="solid", color="black", weight=3]; 4328 -> 681[label="",style="dashed", color="red", weight=0]; 4328[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4328 -> 4364[label="",style="dashed", color="magenta", weight=3]; 4328 -> 4365[label="",style="dashed", color="magenta", weight=3]; 4329 -> 681[label="",style="dashed", color="red", weight=0]; 4329[label="primMulNat vuz22 (Succ vuz23)",fontsize=16,color="magenta"];4329 -> 4366[label="",style="dashed", color="magenta", weight=3]; 4329 -> 4367[label="",style="dashed", color="magenta", weight=3]; 4327[label="gcd2 (primEqInt (primPlusInt (Pos vuz287) (Neg vuz303)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz286) (Neg vuz302)) (Neg vuz68)",fontsize=16,color="black",shape="triangle"];4327 -> 4368[label="",style="solid", color="black", weight=3]; 4992[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) (Succ vuz3410))",fontsize=16,color="black",shape="box"];4992 -> 5003[label="",style="solid", color="black", weight=3]; 4993[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS (Succ vuz3400) Zero)",fontsize=16,color="black",shape="box"];4993 -> 5004[label="",style="solid", color="black", weight=3]; 4994[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero (Succ vuz3410))",fontsize=16,color="black",shape="box"];4994 -> 5005[label="",style="solid", color="black", weight=3]; 4995[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];4995 -> 5006[label="",style="solid", color="black", weight=3]; 4339[label="Zero",fontsize=16,color="green",shape="box"];4340[label="primMinusNatS (Succ vuz28000) Zero",fontsize=16,color="black",shape="triangle"];4340 -> 4374[label="",style="solid", color="black", weight=3]; 4341[label="Zero",fontsize=16,color="green",shape="box"];4342[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];4342 -> 4375[label="",style="solid", color="black", weight=3]; 5741[label="gcd3 (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5741 -> 5758[label="",style="solid", color="black", weight=3]; 4344 -> 681[label="",style="dashed", color="red", weight=0]; 4344[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4344 -> 4376[label="",style="dashed", color="magenta", weight=3]; 4344 -> 4377[label="",style="dashed", color="magenta", weight=3]; 4345 -> 681[label="",style="dashed", color="red", weight=0]; 4345[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4345 -> 4378[label="",style="dashed", color="magenta", weight=3]; 4345 -> 4379[label="",style="dashed", color="magenta", weight=3]; 4343[label="gcd2 (primEqInt (primPlusInt (Pos vuz289) (Pos vuz305)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz288) (Pos vuz304)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4343 -> 4380[label="",style="solid", color="black", weight=3]; 4352 -> 681[label="",style="dashed", color="red", weight=0]; 4352[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4352 -> 4381[label="",style="dashed", color="magenta", weight=3]; 4352 -> 4382[label="",style="dashed", color="magenta", weight=3]; 4353 -> 681[label="",style="dashed", color="red", weight=0]; 4353[label="primMulNat vuz27 (Succ vuz28)",fontsize=16,color="magenta"];4353 -> 4383[label="",style="dashed", color="magenta", weight=3]; 4353 -> 4384[label="",style="dashed", color="magenta", weight=3]; 4351[label="gcd2 (primEqInt (primPlusInt (Neg vuz291) (Pos vuz307)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz290) (Pos vuz306)) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4351 -> 4385[label="",style="solid", color="black", weight=3]; 5742[label="gcd3 (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5742 -> 5759[label="",style="solid", color="black", weight=3]; 5937 -> 681[label="",style="dashed", color="red", weight=0]; 5937[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5937 -> 5962[label="",style="dashed", color="magenta", weight=3]; 5937 -> 5963[label="",style="dashed", color="magenta", weight=3]; 5938 -> 681[label="",style="dashed", color="red", weight=0]; 5938[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5938 -> 5964[label="",style="dashed", color="magenta", weight=3]; 5938 -> 5965[label="",style="dashed", color="magenta", weight=3]; 5936[label="gcd2 (primEqInt (primPlusInt (Neg vuz354) (Pos vuz370)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz353) (Pos vuz369)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5936 -> 5966[label="",style="solid", color="black", weight=3]; 5945 -> 681[label="",style="dashed", color="red", weight=0]; 5945[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5945 -> 5967[label="",style="dashed", color="magenta", weight=3]; 5945 -> 5968[label="",style="dashed", color="magenta", weight=3]; 5946 -> 681[label="",style="dashed", color="red", weight=0]; 5946[label="primMulNat vuz32 (Succ vuz33)",fontsize=16,color="magenta"];5946 -> 5969[label="",style="dashed", color="magenta", weight=3]; 5946 -> 5970[label="",style="dashed", color="magenta", weight=3]; 5944[label="gcd2 (primEqInt (primPlusInt (Pos vuz356) (Pos vuz372)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz355) (Pos vuz371)) (Pos vuz74)",fontsize=16,color="black",shape="triangle"];5944 -> 5971[label="",style="solid", color="black", weight=3]; 5947 -> 681[label="",style="dashed", color="red", weight=0]; 5947[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5947 -> 5972[label="",style="dashed", color="magenta", weight=3]; 5947 -> 5973[label="",style="dashed", color="magenta", weight=3]; 5948[label="vuz77",fontsize=16,color="green",shape="box"];5949 -> 681[label="",style="dashed", color="red", weight=0]; 5949[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5949 -> 5974[label="",style="dashed", color="magenta", weight=3]; 5949 -> 5975[label="",style="dashed", color="magenta", weight=3]; 5950[label="vuz358",fontsize=16,color="green",shape="box"];5951[label="vuz357",fontsize=16,color="green",shape="box"];5939 -> 681[label="",style="dashed", color="red", weight=0]; 5939[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5939 -> 5976[label="",style="dashed", color="magenta", weight=3]; 5939 -> 5977[label="",style="dashed", color="magenta", weight=3]; 5940[label="vuz77",fontsize=16,color="green",shape="box"];5941[label="vuz360",fontsize=16,color="green",shape="box"];5942[label="vuz359",fontsize=16,color="green",shape="box"];5943 -> 681[label="",style="dashed", color="red", weight=0]; 5943[label="primMulNat vuz37 (Succ vuz38)",fontsize=16,color="magenta"];5943 -> 5978[label="",style="dashed", color="magenta", weight=3]; 5943 -> 5979[label="",style="dashed", color="magenta", weight=3]; 4354 -> 681[label="",style="dashed", color="red", weight=0]; 4354[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4354 -> 4386[label="",style="dashed", color="magenta", weight=3]; 4354 -> 4387[label="",style="dashed", color="magenta", weight=3]; 4355[label="vuz293",fontsize=16,color="green",shape="box"];4356 -> 681[label="",style="dashed", color="red", weight=0]; 4356[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4356 -> 4388[label="",style="dashed", color="magenta", weight=3]; 4356 -> 4389[label="",style="dashed", color="magenta", weight=3]; 4357[label="vuz292",fontsize=16,color="green",shape="box"];4358[label="vuz92",fontsize=16,color="green",shape="box"];4346[label="vuz294",fontsize=16,color="green",shape="box"];4347[label="vuz92",fontsize=16,color="green",shape="box"];4348 -> 681[label="",style="dashed", color="red", weight=0]; 4348[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4348 -> 4390[label="",style="dashed", color="magenta", weight=3]; 4348 -> 4391[label="",style="dashed", color="magenta", weight=3]; 4349 -> 681[label="",style="dashed", color="red", weight=0]; 4349[label="primMulNat vuz42 (Succ vuz43)",fontsize=16,color="magenta"];4349 -> 4392[label="",style="dashed", color="magenta", weight=3]; 4349 -> 4393[label="",style="dashed", color="magenta", weight=3]; 4350[label="vuz295",fontsize=16,color="green",shape="box"];4330[label="vuz107",fontsize=16,color="green",shape="box"];4331[label="vuz297",fontsize=16,color="green",shape="box"];4332[label="vuz296",fontsize=16,color="green",shape="box"];4333 -> 681[label="",style="dashed", color="red", weight=0]; 4333[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4333 -> 4394[label="",style="dashed", color="magenta", weight=3]; 4333 -> 4395[label="",style="dashed", color="magenta", weight=3]; 4334 -> 681[label="",style="dashed", color="red", weight=0]; 4334[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4334 -> 4396[label="",style="dashed", color="magenta", weight=3]; 4334 -> 4397[label="",style="dashed", color="magenta", weight=3]; 4322 -> 681[label="",style="dashed", color="red", weight=0]; 4322[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4322 -> 4398[label="",style="dashed", color="magenta", weight=3]; 4322 -> 4399[label="",style="dashed", color="magenta", weight=3]; 4323[label="vuz107",fontsize=16,color="green",shape="box"];4324[label="vuz299",fontsize=16,color="green",shape="box"];4325[label="vuz298",fontsize=16,color="green",shape="box"];4326 -> 681[label="",style="dashed", color="red", weight=0]; 4326[label="primMulNat vuz47 (Succ vuz48)",fontsize=16,color="magenta"];4326 -> 4400[label="",style="dashed", color="magenta", weight=3]; 4326 -> 4401[label="",style="dashed", color="magenta", weight=3]; 5931[label="vuz361",fontsize=16,color="green",shape="box"];5932 -> 681[label="",style="dashed", color="red", weight=0]; 5932[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5932 -> 5980[label="",style="dashed", color="magenta", weight=3]; 5932 -> 5981[label="",style="dashed", color="magenta", weight=3]; 5933[label="vuz362",fontsize=16,color="green",shape="box"];5934 -> 681[label="",style="dashed", color="red", weight=0]; 5934[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5934 -> 5982[label="",style="dashed", color="magenta", weight=3]; 5934 -> 5983[label="",style="dashed", color="magenta", weight=3]; 5935[label="vuz122",fontsize=16,color="green",shape="box"];5923 -> 681[label="",style="dashed", color="red", weight=0]; 5923[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5923 -> 5984[label="",style="dashed", color="magenta", weight=3]; 5923 -> 5985[label="",style="dashed", color="magenta", weight=3]; 5924[label="vuz364",fontsize=16,color="green",shape="box"];5925 -> 681[label="",style="dashed", color="red", weight=0]; 5925[label="primMulNat vuz52 (Succ vuz53)",fontsize=16,color="magenta"];5925 -> 5986[label="",style="dashed", color="magenta", weight=3]; 5925 -> 5987[label="",style="dashed", color="magenta", weight=3]; 5926[label="vuz363",fontsize=16,color="green",shape="box"];5927[label="vuz122",fontsize=16,color="green",shape="box"];5707[label="Succ vuz1850",fontsize=16,color="green",shape="box"];5708[label="vuz144",fontsize=16,color="green",shape="box"];4092[label="Succ vuz1990",fontsize=16,color="green",shape="box"];5709[label="Zero",fontsize=16,color="green",shape="box"];5710[label="vuz144",fontsize=16,color="green",shape="box"];4151[label="gcd2 (Neg vuz282 == fromInt (Pos Zero)) (Neg vuz282) (Pos vuz144)",fontsize=16,color="black",shape="box"];4151 -> 4166[label="",style="solid", color="black", weight=3]; 5952[label="vuz12",fontsize=16,color="green",shape="box"];5953[label="vuz11",fontsize=16,color="green",shape="box"];5954[label="vuz12",fontsize=16,color="green",shape="box"];5955[label="vuz11",fontsize=16,color="green",shape="box"];5956[label="gcd2 (primEqInt (primMinusNat vuz350 vuz366) (fromInt (Pos Zero))) (primMinusNat vuz350 vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6544[label="vuz350/Succ vuz3500",fontsize=10,color="white",style="solid",shape="box"];5956 -> 6544[label="",style="solid", color="burlywood", weight=9]; 6544 -> 6004[label="",style="solid", color="burlywood", weight=3]; 6545[label="vuz350/Zero",fontsize=10,color="white",style="solid",shape="box"];5956 -> 6545[label="",style="solid", color="burlywood", weight=9]; 6545 -> 6005[label="",style="solid", color="burlywood", weight=3]; 5957[label="vuz12",fontsize=16,color="green",shape="box"];5958[label="vuz11",fontsize=16,color="green",shape="box"];5959[label="vuz12",fontsize=16,color="green",shape="box"];5960[label="vuz11",fontsize=16,color="green",shape="box"];5961 -> 4166[label="",style="dashed", color="red", weight=0]; 5961[label="gcd2 (primEqInt (Neg (primPlusNat vuz352 vuz368)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz352 vuz368)) (Pos vuz144)",fontsize=16,color="magenta"];5961 -> 6006[label="",style="dashed", color="magenta", weight=3]; 4152[label="gcd2 (Neg vuz283 == fromInt (Pos Zero)) (Neg vuz283) (Neg vuz68)",fontsize=16,color="black",shape="box"];4152 -> 4167[label="",style="solid", color="black", weight=3]; 5691[label="Succ vuz1690",fontsize=16,color="green",shape="box"];5692[label="vuz68",fontsize=16,color="green",shape="box"];4105[label="Succ vuz2050",fontsize=16,color="green",shape="box"];5693[label="Zero",fontsize=16,color="green",shape="box"];5694[label="vuz68",fontsize=16,color="green",shape="box"];4359[label="vuz23",fontsize=16,color="green",shape="box"];4360[label="vuz22",fontsize=16,color="green",shape="box"];4361[label="vuz23",fontsize=16,color="green",shape="box"];4362[label="vuz22",fontsize=16,color="green",shape="box"];4363 -> 4167[label="",style="dashed", color="red", weight=0]; 4363[label="gcd2 (primEqInt (Neg (primPlusNat vuz285 vuz301)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz285 vuz301)) (Neg vuz68)",fontsize=16,color="magenta"];4363 -> 4410[label="",style="dashed", color="magenta", weight=3]; 4364[label="vuz23",fontsize=16,color="green",shape="box"];4365[label="vuz22",fontsize=16,color="green",shape="box"];4366[label="vuz23",fontsize=16,color="green",shape="box"];4367[label="vuz22",fontsize=16,color="green",shape="box"];4368[label="gcd2 (primEqInt (primMinusNat vuz287 vuz303) (fromInt (Pos Zero))) (primMinusNat vuz287 vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6546[label="vuz287/Succ vuz2870",fontsize=10,color="white",style="solid",shape="box"];4368 -> 6546[label="",style="solid", color="burlywood", weight=9]; 6546 -> 4411[label="",style="solid", color="burlywood", weight=3]; 6547[label="vuz287/Zero",fontsize=10,color="white",style="solid",shape="box"];4368 -> 6547[label="",style="solid", color="burlywood", weight=9]; 6547 -> 4412[label="",style="solid", color="burlywood", weight=3]; 5003 -> 4927[label="",style="dashed", color="red", weight=0]; 5003[label="primDivNatS0 (Succ vuz338) (Succ vuz339) (primGEqNatS vuz3400 vuz3410)",fontsize=16,color="magenta"];5003 -> 5013[label="",style="dashed", color="magenta", weight=3]; 5003 -> 5014[label="",style="dashed", color="magenta", weight=3]; 5004[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="black",shape="triangle"];5004 -> 5015[label="",style="solid", color="black", weight=3]; 5005[label="primDivNatS0 (Succ vuz338) (Succ vuz339) False",fontsize=16,color="black",shape="box"];5005 -> 5016[label="",style="solid", color="black", weight=3]; 5006 -> 5004[label="",style="dashed", color="red", weight=0]; 5006[label="primDivNatS0 (Succ vuz338) (Succ vuz339) True",fontsize=16,color="magenta"];4374[label="Succ vuz28000",fontsize=16,color="green",shape="box"];4375[label="Zero",fontsize=16,color="green",shape="box"];5758[label="gcd2 (Pos vuz347 == fromInt (Pos Zero)) (Pos vuz347) (Neg vuz71)",fontsize=16,color="black",shape="box"];5758 -> 5773[label="",style="solid", color="black", weight=3]; 4376[label="vuz28",fontsize=16,color="green",shape="box"];4377[label="vuz27",fontsize=16,color="green",shape="box"];4378[label="vuz28",fontsize=16,color="green",shape="box"];4379[label="vuz27",fontsize=16,color="green",shape="box"];4380 -> 4419[label="",style="dashed", color="red", weight=0]; 4380[label="gcd2 (primEqInt (Pos (primPlusNat vuz289 vuz305)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz289 vuz305)) (Neg vuz71)",fontsize=16,color="magenta"];4380 -> 4420[label="",style="dashed", color="magenta", weight=3]; 4380 -> 4421[label="",style="dashed", color="magenta", weight=3]; 4381[label="vuz28",fontsize=16,color="green",shape="box"];4382[label="vuz27",fontsize=16,color="green",shape="box"];4383[label="vuz28",fontsize=16,color="green",shape="box"];4384[label="vuz27",fontsize=16,color="green",shape="box"];4385 -> 4368[label="",style="dashed", color="red", weight=0]; 4385[label="gcd2 (primEqInt (primMinusNat vuz307 vuz291) (fromInt (Pos Zero))) (primMinusNat vuz307 vuz291) (Neg vuz71)",fontsize=16,color="magenta"];4385 -> 4422[label="",style="dashed", color="magenta", weight=3]; 4385 -> 4423[label="",style="dashed", color="magenta", weight=3]; 4385 -> 4424[label="",style="dashed", color="magenta", weight=3]; 5759[label="gcd2 (Pos vuz348 == fromInt (Pos Zero)) (Pos vuz348) (Pos vuz74)",fontsize=16,color="black",shape="box"];5759 -> 5774[label="",style="solid", color="black", weight=3]; 5962[label="vuz33",fontsize=16,color="green",shape="box"];5963[label="vuz32",fontsize=16,color="green",shape="box"];5964[label="vuz33",fontsize=16,color="green",shape="box"];5965[label="vuz32",fontsize=16,color="green",shape="box"];5966 -> 5956[label="",style="dashed", color="red", weight=0]; 5966[label="gcd2 (primEqInt (primMinusNat vuz370 vuz354) (fromInt (Pos Zero))) (primMinusNat vuz370 vuz354) (Pos vuz74)",fontsize=16,color="magenta"];5966 -> 6007[label="",style="dashed", color="magenta", weight=3]; 5966 -> 6008[label="",style="dashed", color="magenta", weight=3]; 5966 -> 6009[label="",style="dashed", color="magenta", weight=3]; 5967[label="vuz33",fontsize=16,color="green",shape="box"];5968[label="vuz32",fontsize=16,color="green",shape="box"];5969[label="vuz33",fontsize=16,color="green",shape="box"];5970[label="vuz32",fontsize=16,color="green",shape="box"];5971 -> 5774[label="",style="dashed", color="red", weight=0]; 5971[label="gcd2 (primEqInt (Pos (primPlusNat vuz356 vuz372)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz356 vuz372)) (Pos vuz74)",fontsize=16,color="magenta"];5971 -> 6010[label="",style="dashed", color="magenta", weight=3]; 5972[label="vuz38",fontsize=16,color="green",shape="box"];5973[label="vuz37",fontsize=16,color="green",shape="box"];5974[label="vuz38",fontsize=16,color="green",shape="box"];5975[label="vuz37",fontsize=16,color="green",shape="box"];5976[label="vuz38",fontsize=16,color="green",shape="box"];5977[label="vuz37",fontsize=16,color="green",shape="box"];5978[label="vuz38",fontsize=16,color="green",shape="box"];5979[label="vuz37",fontsize=16,color="green",shape="box"];4386[label="vuz43",fontsize=16,color="green",shape="box"];4387[label="vuz42",fontsize=16,color="green",shape="box"];4388[label="vuz43",fontsize=16,color="green",shape="box"];4389[label="vuz42",fontsize=16,color="green",shape="box"];4390[label="vuz43",fontsize=16,color="green",shape="box"];4391[label="vuz42",fontsize=16,color="green",shape="box"];4392[label="vuz43",fontsize=16,color="green",shape="box"];4393[label="vuz42",fontsize=16,color="green",shape="box"];4394[label="vuz48",fontsize=16,color="green",shape="box"];4395[label="vuz47",fontsize=16,color="green",shape="box"];4396[label="vuz48",fontsize=16,color="green",shape="box"];4397[label="vuz47",fontsize=16,color="green",shape="box"];4398[label="vuz48",fontsize=16,color="green",shape="box"];4399[label="vuz47",fontsize=16,color="green",shape="box"];4400[label="vuz48",fontsize=16,color="green",shape="box"];4401[label="vuz47",fontsize=16,color="green",shape="box"];5980[label="vuz53",fontsize=16,color="green",shape="box"];5981[label="vuz52",fontsize=16,color="green",shape="box"];5982[label="vuz53",fontsize=16,color="green",shape="box"];5983[label="vuz52",fontsize=16,color="green",shape="box"];5984[label="vuz53",fontsize=16,color="green",shape="box"];5985[label="vuz52",fontsize=16,color="green",shape="box"];5986[label="vuz53",fontsize=16,color="green",shape="box"];5987[label="vuz52",fontsize=16,color="green",shape="box"];4166[label="gcd2 (primEqInt (Neg vuz282) (fromInt (Pos Zero))) (Neg vuz282) (Pos vuz144)",fontsize=16,color="burlywood",shape="triangle"];6548[label="vuz282/Succ vuz2820",fontsize=10,color="white",style="solid",shape="box"];4166 -> 6548[label="",style="solid", color="burlywood", weight=9]; 6548 -> 4185[label="",style="solid", color="burlywood", weight=3]; 6549[label="vuz282/Zero",fontsize=10,color="white",style="solid",shape="box"];4166 -> 6549[label="",style="solid", color="burlywood", weight=9]; 6549 -> 4186[label="",style="solid", color="burlywood", weight=3]; 6004[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) vuz366) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6550[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6004 -> 6550[label="",style="solid", color="burlywood", weight=9]; 6550 -> 6026[label="",style="solid", color="burlywood", weight=3]; 6551[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6004 -> 6551[label="",style="solid", color="burlywood", weight=9]; 6551 -> 6027[label="",style="solid", color="burlywood", weight=3]; 6005[label="gcd2 (primEqInt (primMinusNat Zero vuz366) (fromInt (Pos Zero))) (primMinusNat Zero vuz366) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6552[label="vuz366/Succ vuz3660",fontsize=10,color="white",style="solid",shape="box"];6005 -> 6552[label="",style="solid", color="burlywood", weight=9]; 6552 -> 6028[label="",style="solid", color="burlywood", weight=3]; 6553[label="vuz366/Zero",fontsize=10,color="white",style="solid",shape="box"];6005 -> 6553[label="",style="solid", color="burlywood", weight=9]; 6553 -> 6029[label="",style="solid", color="burlywood", weight=3]; 6006 -> 1354[label="",style="dashed", color="red", weight=0]; 6006[label="primPlusNat vuz352 vuz368",fontsize=16,color="magenta"];6006 -> 6030[label="",style="dashed", color="magenta", weight=3]; 6006 -> 6031[label="",style="dashed", color="magenta", weight=3]; 4167[label="gcd2 (primEqInt (Neg vuz283) (fromInt (Pos Zero))) (Neg vuz283) (Neg vuz68)",fontsize=16,color="burlywood",shape="triangle"];6554[label="vuz283/Succ vuz2830",fontsize=10,color="white",style="solid",shape="box"];4167 -> 6554[label="",style="solid", color="burlywood", weight=9]; 6554 -> 4187[label="",style="solid", color="burlywood", weight=3]; 6555[label="vuz283/Zero",fontsize=10,color="white",style="solid",shape="box"];4167 -> 6555[label="",style="solid", color="burlywood", weight=9]; 6555 -> 4188[label="",style="solid", color="burlywood", weight=3]; 4410 -> 1354[label="",style="dashed", color="red", weight=0]; 4410[label="primPlusNat vuz285 vuz301",fontsize=16,color="magenta"];4410 -> 4425[label="",style="dashed", color="magenta", weight=3]; 4410 -> 4426[label="",style="dashed", color="magenta", weight=3]; 4411[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) vuz303) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6556[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4411 -> 6556[label="",style="solid", color="burlywood", weight=9]; 6556 -> 4427[label="",style="solid", color="burlywood", weight=3]; 6557[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4411 -> 6557[label="",style="solid", color="burlywood", weight=9]; 6557 -> 4428[label="",style="solid", color="burlywood", weight=3]; 4412[label="gcd2 (primEqInt (primMinusNat Zero vuz303) (fromInt (Pos Zero))) (primMinusNat Zero vuz303) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6558[label="vuz303/Succ vuz3030",fontsize=10,color="white",style="solid",shape="box"];4412 -> 6558[label="",style="solid", color="burlywood", weight=9]; 6558 -> 4429[label="",style="solid", color="burlywood", weight=3]; 6559[label="vuz303/Zero",fontsize=10,color="white",style="solid",shape="box"];4412 -> 6559[label="",style="solid", color="burlywood", weight=9]; 6559 -> 4430[label="",style="solid", color="burlywood", weight=3]; 5013[label="vuz3400",fontsize=16,color="green",shape="box"];5014[label="vuz3410",fontsize=16,color="green",shape="box"];5015[label="Succ (primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339)))",fontsize=16,color="green",shape="box"];5015 -> 5039[label="",style="dashed", color="green", weight=3]; 5016[label="Zero",fontsize=16,color="green",shape="box"];5773 -> 4419[label="",style="dashed", color="red", weight=0]; 5773[label="gcd2 (primEqInt (Pos vuz347) (fromInt (Pos Zero))) (Pos vuz347) (Neg vuz71)",fontsize=16,color="magenta"];5773 -> 5792[label="",style="dashed", color="magenta", weight=3]; 5773 -> 5793[label="",style="dashed", color="magenta", weight=3]; 4420 -> 1354[label="",style="dashed", color="red", weight=0]; 4420[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4420 -> 4439[label="",style="dashed", color="magenta", weight=3]; 4420 -> 4440[label="",style="dashed", color="magenta", weight=3]; 4421 -> 1354[label="",style="dashed", color="red", weight=0]; 4421[label="primPlusNat vuz289 vuz305",fontsize=16,color="magenta"];4421 -> 4441[label="",style="dashed", color="magenta", weight=3]; 4421 -> 4442[label="",style="dashed", color="magenta", weight=3]; 4419[label="gcd2 (primEqInt (Pos vuz309) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="triangle"];6560[label="vuz309/Succ vuz3090",fontsize=10,color="white",style="solid",shape="box"];4419 -> 6560[label="",style="solid", color="burlywood", weight=9]; 6560 -> 4443[label="",style="solid", color="burlywood", weight=3]; 6561[label="vuz309/Zero",fontsize=10,color="white",style="solid",shape="box"];4419 -> 6561[label="",style="solid", color="burlywood", weight=9]; 6561 -> 4444[label="",style="solid", color="burlywood", weight=3]; 4422[label="vuz71",fontsize=16,color="green",shape="box"];4423[label="vuz307",fontsize=16,color="green",shape="box"];4424[label="vuz291",fontsize=16,color="green",shape="box"];5774[label="gcd2 (primEqInt (Pos vuz348) (fromInt (Pos Zero))) (Pos vuz348) (Pos vuz74)",fontsize=16,color="burlywood",shape="triangle"];6562[label="vuz348/Succ vuz3480",fontsize=10,color="white",style="solid",shape="box"];5774 -> 6562[label="",style="solid", color="burlywood", weight=9]; 6562 -> 5794[label="",style="solid", color="burlywood", weight=3]; 6563[label="vuz348/Zero",fontsize=10,color="white",style="solid",shape="box"];5774 -> 6563[label="",style="solid", color="burlywood", weight=9]; 6563 -> 5795[label="",style="solid", color="burlywood", weight=3]; 6007[label="vuz370",fontsize=16,color="green",shape="box"];6008[label="vuz354",fontsize=16,color="green",shape="box"];6009[label="vuz74",fontsize=16,color="green",shape="box"];6010 -> 1354[label="",style="dashed", color="red", weight=0]; 6010[label="primPlusNat vuz356 vuz372",fontsize=16,color="magenta"];6010 -> 6032[label="",style="dashed", color="magenta", weight=3]; 6010 -> 6033[label="",style="dashed", color="magenta", weight=3]; 4185[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (fromInt (Pos Zero))) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4185 -> 4206[label="",style="solid", color="black", weight=3]; 4186[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4186 -> 4207[label="",style="solid", color="black", weight=3]; 6026[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6026 -> 6049[label="",style="solid", color="black", weight=3]; 6027[label="gcd2 (primEqInt (primMinusNat (Succ vuz3500) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3500) Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6027 -> 6050[label="",style="solid", color="black", weight=3]; 6028[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3660)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="black",shape="box"];6028 -> 6051[label="",style="solid", color="black", weight=3]; 6029[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];6029 -> 6052[label="",style="solid", color="black", weight=3]; 6030[label="vuz368",fontsize=16,color="green",shape="box"];6031[label="vuz352",fontsize=16,color="green",shape="box"];4187[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (fromInt (Pos Zero))) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4187 -> 4208[label="",style="solid", color="black", weight=3]; 4188[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4188 -> 4209[label="",style="solid", color="black", weight=3]; 4425[label="vuz301",fontsize=16,color="green",shape="box"];4426[label="vuz285",fontsize=16,color="green",shape="box"];4427[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4427 -> 4455[label="",style="solid", color="black", weight=3]; 4428[label="gcd2 (primEqInt (primMinusNat (Succ vuz2870) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz2870) Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4428 -> 4456[label="",style="solid", color="black", weight=3]; 4429[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz3030)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4429 -> 4457[label="",style="solid", color="black", weight=3]; 4430[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4430 -> 4458[label="",style="solid", color="black", weight=3]; 5039 -> 4129[label="",style="dashed", color="red", weight=0]; 5039[label="primDivNatS (primMinusNatS (Succ vuz338) (Succ vuz339)) (Succ (Succ vuz339))",fontsize=16,color="magenta"];5039 -> 5727[label="",style="dashed", color="magenta", weight=3]; 5039 -> 5728[label="",style="dashed", color="magenta", weight=3]; 5792[label="vuz347",fontsize=16,color="green",shape="box"];5793[label="vuz347",fontsize=16,color="green",shape="box"];4439[label="vuz305",fontsize=16,color="green",shape="box"];4440[label="vuz289",fontsize=16,color="green",shape="box"];4441[label="vuz305",fontsize=16,color="green",shape="box"];4442[label="vuz289",fontsize=16,color="green",shape="box"];4443[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4443 -> 4466[label="",style="solid", color="black", weight=3]; 4444[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4444 -> 4467[label="",style="solid", color="black", weight=3]; 5794[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (fromInt (Pos Zero))) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5794 -> 5814[label="",style="solid", color="black", weight=3]; 5795[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5795 -> 5815[label="",style="solid", color="black", weight=3]; 6032[label="vuz372",fontsize=16,color="green",shape="box"];6033[label="vuz356",fontsize=16,color="green",shape="box"];4206[label="gcd2 (primEqInt (Neg (Succ vuz2820)) (Pos Zero)) (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4206 -> 4289[label="",style="solid", color="black", weight=3]; 4207[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4207 -> 4290[label="",style="solid", color="black", weight=3]; 6049 -> 5956[label="",style="dashed", color="red", weight=0]; 6049[label="gcd2 (primEqInt (primMinusNat vuz3500 vuz3660) (fromInt (Pos Zero))) (primMinusNat vuz3500 vuz3660) (Pos vuz144)",fontsize=16,color="magenta"];6049 -> 6059[label="",style="dashed", color="magenta", weight=3]; 6049 -> 6060[label="",style="dashed", color="magenta", weight=3]; 6050 -> 5774[label="",style="dashed", color="red", weight=0]; 6050[label="gcd2 (primEqInt (Pos (Succ vuz3500)) (fromInt (Pos Zero))) (Pos (Succ vuz3500)) (Pos vuz144)",fontsize=16,color="magenta"];6050 -> 6061[label="",style="dashed", color="magenta", weight=3]; 6050 -> 6062[label="",style="dashed", color="magenta", weight=3]; 6051 -> 4166[label="",style="dashed", color="red", weight=0]; 6051[label="gcd2 (primEqInt (Neg (Succ vuz3660)) (fromInt (Pos Zero))) (Neg (Succ vuz3660)) (Pos vuz144)",fontsize=16,color="magenta"];6051 -> 6063[label="",style="dashed", color="magenta", weight=3]; 6052 -> 5774[label="",style="dashed", color="red", weight=0]; 6052[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz144)",fontsize=16,color="magenta"];6052 -> 6064[label="",style="dashed", color="magenta", weight=3]; 6052 -> 6065[label="",style="dashed", color="magenta", weight=3]; 4208[label="gcd2 (primEqInt (Neg (Succ vuz2830)) (Pos Zero)) (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4208 -> 4291[label="",style="solid", color="black", weight=3]; 4209[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4209 -> 4292[label="",style="solid", color="black", weight=3]; 4455 -> 4368[label="",style="dashed", color="red", weight=0]; 4455[label="gcd2 (primEqInt (primMinusNat vuz2870 vuz3030) (fromInt (Pos Zero))) (primMinusNat vuz2870 vuz3030) (Neg vuz68)",fontsize=16,color="magenta"];4455 -> 4478[label="",style="dashed", color="magenta", weight=3]; 4455 -> 4479[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4419[label="",style="dashed", color="red", weight=0]; 4456[label="gcd2 (primEqInt (Pos (Succ vuz2870)) (fromInt (Pos Zero))) (Pos (Succ vuz2870)) (Neg vuz68)",fontsize=16,color="magenta"];4456 -> 4480[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4481[label="",style="dashed", color="magenta", weight=3]; 4456 -> 4482[label="",style="dashed", color="magenta", weight=3]; 4457 -> 4167[label="",style="dashed", color="red", weight=0]; 4457[label="gcd2 (primEqInt (Neg (Succ vuz3030)) (fromInt (Pos Zero))) (Neg (Succ vuz3030)) (Neg vuz68)",fontsize=16,color="magenta"];4457 -> 4483[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4419[label="",style="dashed", color="red", weight=0]; 4458[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz68)",fontsize=16,color="magenta"];4458 -> 4484[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4485[label="",style="dashed", color="magenta", weight=3]; 4458 -> 4486[label="",style="dashed", color="magenta", weight=3]; 5727[label="Succ vuz339",fontsize=16,color="green",shape="box"];5728[label="primMinusNatS (Succ vuz338) (Succ vuz339)",fontsize=16,color="black",shape="box"];5728 -> 5743[label="",style="solid", color="black", weight=3]; 4466[label="gcd2 (primEqInt (Pos (Succ vuz3090)) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4466 -> 4494[label="",style="solid", color="black", weight=3]; 4467[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4467 -> 4495[label="",style="solid", color="black", weight=3]; 5814[label="gcd2 (primEqInt (Pos (Succ vuz3480)) (Pos Zero)) (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5814 -> 5890[label="",style="solid", color="black", weight=3]; 5815[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5815 -> 5891[label="",style="solid", color="black", weight=3]; 4289[label="gcd2 False (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4289 -> 4311[label="",style="solid", color="black", weight=3]; 4290[label="gcd2 True (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4290 -> 4312[label="",style="solid", color="black", weight=3]; 6059[label="vuz3500",fontsize=16,color="green",shape="box"];6060[label="vuz3660",fontsize=16,color="green",shape="box"];6061[label="Succ vuz3500",fontsize=16,color="green",shape="box"];6062[label="vuz144",fontsize=16,color="green",shape="box"];6063[label="Succ vuz3660",fontsize=16,color="green",shape="box"];6064[label="Zero",fontsize=16,color="green",shape="box"];6065[label="vuz144",fontsize=16,color="green",shape="box"];4291[label="gcd2 False (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4291 -> 4313[label="",style="solid", color="black", weight=3]; 4292[label="gcd2 True (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4292 -> 4314[label="",style="solid", color="black", weight=3]; 4478[label="vuz2870",fontsize=16,color="green",shape="box"];4479[label="vuz3030",fontsize=16,color="green",shape="box"];4480[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4481[label="vuz68",fontsize=16,color="green",shape="box"];4482[label="Succ vuz2870",fontsize=16,color="green",shape="box"];4483[label="Succ vuz3030",fontsize=16,color="green",shape="box"];4484[label="Zero",fontsize=16,color="green",shape="box"];4485[label="vuz68",fontsize=16,color="green",shape="box"];4486[label="Zero",fontsize=16,color="green",shape="box"];5743[label="primMinusNatS vuz338 vuz339",fontsize=16,color="burlywood",shape="triangle"];6564[label="vuz338/Succ vuz3380",fontsize=10,color="white",style="solid",shape="box"];5743 -> 6564[label="",style="solid", color="burlywood", weight=9]; 6564 -> 5760[label="",style="solid", color="burlywood", weight=3]; 6565[label="vuz338/Zero",fontsize=10,color="white",style="solid",shape="box"];5743 -> 6565[label="",style="solid", color="burlywood", weight=9]; 6565 -> 5761[label="",style="solid", color="burlywood", weight=3]; 4494[label="gcd2 False (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4494 -> 4517[label="",style="solid", color="black", weight=3]; 4495[label="gcd2 True (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4495 -> 4518[label="",style="solid", color="black", weight=3]; 5890[label="gcd2 False (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5890 -> 5908[label="",style="solid", color="black", weight=3]; 5891[label="gcd2 True (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5891 -> 5909[label="",style="solid", color="black", weight=3]; 4311[label="gcd0 (Neg (Succ vuz2820)) (Pos vuz144)",fontsize=16,color="black",shape="box"];4311 -> 4402[label="",style="solid", color="black", weight=3]; 4312[label="gcd1 (Pos vuz144 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz144)",fontsize=16,color="black",shape="box"];4312 -> 4403[label="",style="solid", color="black", weight=3]; 4313[label="gcd0 (Neg (Succ vuz2830)) (Neg vuz68)",fontsize=16,color="black",shape="box"];4313 -> 4404[label="",style="solid", color="black", weight=3]; 4314[label="gcd1 (Neg vuz68 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz68)",fontsize=16,color="black",shape="box"];4314 -> 4405[label="",style="solid", color="black", weight=3]; 5760[label="primMinusNatS (Succ vuz3380) vuz339",fontsize=16,color="burlywood",shape="box"];6566[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5760 -> 6566[label="",style="solid", color="burlywood", weight=9]; 6566 -> 5775[label="",style="solid", color="burlywood", weight=3]; 6567[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5760 -> 6567[label="",style="solid", color="burlywood", weight=9]; 6567 -> 5776[label="",style="solid", color="burlywood", weight=3]; 5761[label="primMinusNatS Zero vuz339",fontsize=16,color="burlywood",shape="box"];6568[label="vuz339/Succ vuz3390",fontsize=10,color="white",style="solid",shape="box"];5761 -> 6568[label="",style="solid", color="burlywood", weight=9]; 6568 -> 5777[label="",style="solid", color="burlywood", weight=3]; 6569[label="vuz339/Zero",fontsize=10,color="white",style="solid",shape="box"];5761 -> 6569[label="",style="solid", color="burlywood", weight=9]; 6569 -> 5778[label="",style="solid", color="burlywood", weight=3]; 4517[label="gcd0 (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="triangle"];4517 -> 4539[label="",style="solid", color="black", weight=3]; 4518[label="gcd1 (Neg vuz71 == fromInt (Pos Zero)) (Pos vuz308) (Neg vuz71)",fontsize=16,color="black",shape="box"];4518 -> 4540[label="",style="solid", color="black", weight=3]; 5908[label="gcd0 (Pos (Succ vuz3480)) (Pos vuz74)",fontsize=16,color="black",shape="box"];5908 -> 5988[label="",style="solid", color="black", weight=3]; 5909[label="gcd1 (Pos vuz74 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz74)",fontsize=16,color="black",shape="box"];5909 -> 5989[label="",style="solid", color="black", weight=3]; 4402 -> 6011[label="",style="dashed", color="red", weight=0]; 4402[label="gcd0Gcd' (abs (Neg (Succ vuz2820))) (abs (Pos vuz144))",fontsize=16,color="magenta"];4402 -> 6012[label="",style="dashed", color="magenta", weight=3]; 4402 -> 6013[label="",style="dashed", color="magenta", weight=3]; 4403[label="gcd1 (primEqInt (Pos vuz144) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz144)",fontsize=16,color="burlywood",shape="box"];6570[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6570[label="",style="solid", color="burlywood", weight=9]; 6570 -> 4446[label="",style="solid", color="burlywood", weight=3]; 6571[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];4403 -> 6571[label="",style="solid", color="burlywood", weight=9]; 6571 -> 4447[label="",style="solid", color="burlywood", weight=3]; 4404 -> 6011[label="",style="dashed", color="red", weight=0]; 4404[label="gcd0Gcd' (abs (Neg (Succ vuz2830))) (abs (Neg vuz68))",fontsize=16,color="magenta"];4404 -> 6014[label="",style="dashed", color="magenta", weight=3]; 4404 -> 6015[label="",style="dashed", color="magenta", weight=3]; 4405[label="gcd1 (primEqInt (Neg vuz68) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz68)",fontsize=16,color="burlywood",shape="box"];6572[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];4405 -> 6572[label="",style="solid", color="burlywood", weight=9]; 6572 -> 4449[label="",style="solid", color="burlywood", weight=3]; 6573[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];4405 -> 6573[label="",style="solid", color="burlywood", weight=9]; 6573 -> 4450[label="",style="solid", color="burlywood", weight=3]; 5775[label="primMinusNatS (Succ vuz3380) (Succ vuz3390)",fontsize=16,color="black",shape="box"];5775 -> 5796[label="",style="solid", color="black", weight=3]; 5776[label="primMinusNatS (Succ vuz3380) Zero",fontsize=16,color="black",shape="box"];5776 -> 5797[label="",style="solid", color="black", weight=3]; 5777[label="primMinusNatS Zero (Succ vuz3390)",fontsize=16,color="black",shape="box"];5777 -> 5798[label="",style="solid", color="black", weight=3]; 5778[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];5778 -> 5799[label="",style="solid", color="black", weight=3]; 4539 -> 6011[label="",style="dashed", color="red", weight=0]; 4539[label="gcd0Gcd' (abs (Pos vuz308)) (abs (Neg vuz71))",fontsize=16,color="magenta"];4539 -> 6016[label="",style="dashed", color="magenta", weight=3]; 4539 -> 6017[label="",style="dashed", color="magenta", weight=3]; 4540[label="gcd1 (primEqInt (Neg vuz71) (fromInt (Pos Zero))) (Pos vuz308) (Neg vuz71)",fontsize=16,color="burlywood",shape="box"];6574[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];4540 -> 6574[label="",style="solid", color="burlywood", weight=9]; 6574 -> 4559[label="",style="solid", color="burlywood", weight=3]; 6575[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];4540 -> 6575[label="",style="solid", color="burlywood", weight=9]; 6575 -> 4560[label="",style="solid", color="burlywood", weight=3]; 5988 -> 6011[label="",style="dashed", color="red", weight=0]; 5988[label="gcd0Gcd' (abs (Pos (Succ vuz3480))) (abs (Pos vuz74))",fontsize=16,color="magenta"];5988 -> 6018[label="",style="dashed", color="magenta", weight=3]; 5988 -> 6019[label="",style="dashed", color="magenta", weight=3]; 5989[label="gcd1 (primEqInt (Pos vuz74) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz74)",fontsize=16,color="burlywood",shape="box"];6576[label="vuz74/Succ vuz740",fontsize=10,color="white",style="solid",shape="box"];5989 -> 6576[label="",style="solid", color="burlywood", weight=9]; 6576 -> 6034[label="",style="solid", color="burlywood", weight=3]; 6577[label="vuz74/Zero",fontsize=10,color="white",style="solid",shape="box"];5989 -> 6577[label="",style="solid", color="burlywood", weight=9]; 6577 -> 6035[label="",style="solid", color="burlywood", weight=3]; 6012[label="abs (Pos vuz144)",fontsize=16,color="black",shape="triangle"];6012 -> 6036[label="",style="solid", color="black", weight=3]; 6013[label="abs (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6013 -> 6037[label="",style="solid", color="black", weight=3]; 6011[label="gcd0Gcd' vuz374 vuz373",fontsize=16,color="black",shape="triangle"];6011 -> 6038[label="",style="solid", color="black", weight=3]; 4446[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4446 -> 4469[label="",style="solid", color="black", weight=3]; 4447[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4447 -> 4470[label="",style="solid", color="black", weight=3]; 6014[label="abs (Neg vuz68)",fontsize=16,color="black",shape="triangle"];6014 -> 6039[label="",style="solid", color="black", weight=3]; 6015 -> 6014[label="",style="dashed", color="red", weight=0]; 6015[label="abs (Neg (Succ vuz2830))",fontsize=16,color="magenta"];6015 -> 6040[label="",style="dashed", color="magenta", weight=3]; 4449[label="gcd1 (primEqInt (Neg (Succ vuz680)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4449 -> 4472[label="",style="solid", color="black", weight=3]; 4450[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4450 -> 4473[label="",style="solid", color="black", weight=3]; 5796 -> 5743[label="",style="dashed", color="red", weight=0]; 5796[label="primMinusNatS vuz3380 vuz3390",fontsize=16,color="magenta"];5796 -> 5816[label="",style="dashed", color="magenta", weight=3]; 5796 -> 5817[label="",style="dashed", color="magenta", weight=3]; 5797[label="Succ vuz3380",fontsize=16,color="green",shape="box"];5798[label="Zero",fontsize=16,color="green",shape="box"];5799[label="Zero",fontsize=16,color="green",shape="box"];6016 -> 6014[label="",style="dashed", color="red", weight=0]; 6016[label="abs (Neg vuz71)",fontsize=16,color="magenta"];6016 -> 6041[label="",style="dashed", color="magenta", weight=3]; 6017 -> 6012[label="",style="dashed", color="red", weight=0]; 6017[label="abs (Pos vuz308)",fontsize=16,color="magenta"];6017 -> 6042[label="",style="dashed", color="magenta", weight=3]; 4559[label="gcd1 (primEqInt (Neg (Succ vuz710)) (fromInt (Pos Zero))) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4559 -> 4579[label="",style="solid", color="black", weight=3]; 4560[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4560 -> 4580[label="",style="solid", color="black", weight=3]; 6018 -> 6012[label="",style="dashed", color="red", weight=0]; 6018[label="abs (Pos vuz74)",fontsize=16,color="magenta"];6018 -> 6043[label="",style="dashed", color="magenta", weight=3]; 6019 -> 6012[label="",style="dashed", color="red", weight=0]; 6019[label="abs (Pos (Succ vuz3480))",fontsize=16,color="magenta"];6019 -> 6044[label="",style="dashed", color="magenta", weight=3]; 6034[label="gcd1 (primEqInt (Pos (Succ vuz740)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6034 -> 6053[label="",style="solid", color="black", weight=3]; 6035[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6035 -> 6054[label="",style="solid", color="black", weight=3]; 6036[label="absReal (Pos vuz144)",fontsize=16,color="black",shape="box"];6036 -> 6055[label="",style="solid", color="black", weight=3]; 6037[label="absReal (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6037 -> 6056[label="",style="solid", color="black", weight=3]; 6038[label="gcd0Gcd'2 vuz374 vuz373",fontsize=16,color="black",shape="box"];6038 -> 6057[label="",style="solid", color="black", weight=3]; 4469[label="gcd1 (primEqInt (Pos (Succ vuz1440)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4469 -> 4497[label="",style="solid", color="black", weight=3]; 4470[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4470 -> 4498[label="",style="solid", color="black", weight=3]; 6039[label="absReal (Neg vuz68)",fontsize=16,color="black",shape="box"];6039 -> 6058[label="",style="solid", color="black", weight=3]; 6040[label="Succ vuz2830",fontsize=16,color="green",shape="box"];4472[label="gcd1 (primEqInt (Neg (Succ vuz680)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4472 -> 4500[label="",style="solid", color="black", weight=3]; 4473[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4473 -> 4501[label="",style="solid", color="black", weight=3]; 5816[label="vuz3390",fontsize=16,color="green",shape="box"];5817[label="vuz3380",fontsize=16,color="green",shape="box"];6041[label="vuz71",fontsize=16,color="green",shape="box"];6042[label="vuz308",fontsize=16,color="green",shape="box"];4579[label="gcd1 (primEqInt (Neg (Succ vuz710)) (Pos Zero)) (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4579 -> 4602[label="",style="solid", color="black", weight=3]; 4580[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4580 -> 4603[label="",style="solid", color="black", weight=3]; 6043[label="vuz74",fontsize=16,color="green",shape="box"];6044[label="Succ vuz3480",fontsize=16,color="green",shape="box"];6053[label="gcd1 (primEqInt (Pos (Succ vuz740)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6053 -> 6066[label="",style="solid", color="black", weight=3]; 6054[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6054 -> 6067[label="",style="solid", color="black", weight=3]; 6055[label="absReal2 (Pos vuz144)",fontsize=16,color="black",shape="box"];6055 -> 6068[label="",style="solid", color="black", weight=3]; 6056[label="absReal2 (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6056 -> 6069[label="",style="solid", color="black", weight=3]; 6057[label="gcd0Gcd'1 (vuz373 == fromInt (Pos Zero)) vuz374 vuz373",fontsize=16,color="black",shape="box"];6057 -> 6070[label="",style="solid", color="black", weight=3]; 4497[label="gcd1 False (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4497 -> 4520[label="",style="solid", color="black", weight=3]; 4498[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];4498 -> 4521[label="",style="solid", color="black", weight=3]; 6058[label="absReal2 (Neg vuz68)",fontsize=16,color="black",shape="box"];6058 -> 6071[label="",style="solid", color="black", weight=3]; 4500[label="gcd1 False (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4500 -> 4523[label="",style="solid", color="black", weight=3]; 4501[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];4501 -> 4524[label="",style="solid", color="black", weight=3]; 4602[label="gcd1 False (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="black",shape="box"];4602 -> 4625[label="",style="solid", color="black", weight=3]; 4603[label="gcd1 True (Pos vuz308) (Neg Zero)",fontsize=16,color="black",shape="box"];4603 -> 4626[label="",style="solid", color="black", weight=3]; 6066[label="gcd1 False (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6066 -> 6072[label="",style="solid", color="black", weight=3]; 6067[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6067 -> 6073[label="",style="solid", color="black", weight=3]; 6068[label="absReal1 (Pos vuz144) (Pos vuz144 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6068 -> 6074[label="",style="solid", color="black", weight=3]; 6069[label="absReal1 (Neg (Succ vuz2820)) (Neg (Succ vuz2820) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6069 -> 6075[label="",style="solid", color="black", weight=3]; 6070[label="gcd0Gcd'1 (primEqInt vuz373 (fromInt (Pos Zero))) vuz374 vuz373",fontsize=16,color="burlywood",shape="box"];6578[label="vuz373/Pos vuz3730",fontsize=10,color="white",style="solid",shape="box"];6070 -> 6578[label="",style="solid", color="burlywood", weight=9]; 6578 -> 6076[label="",style="solid", color="burlywood", weight=3]; 6579[label="vuz373/Neg vuz3730",fontsize=10,color="white",style="solid",shape="box"];6070 -> 6579[label="",style="solid", color="burlywood", weight=9]; 6579 -> 6077[label="",style="solid", color="burlywood", weight=3]; 4520[label="gcd0 (Neg Zero) (Pos (Succ vuz1440))",fontsize=16,color="black",shape="box"];4520 -> 4542[label="",style="solid", color="black", weight=3]; 4521 -> 4108[label="",style="dashed", color="red", weight=0]; 4521[label="error []",fontsize=16,color="magenta"];6071[label="absReal1 (Neg vuz68) (Neg vuz68 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6071 -> 6078[label="",style="solid", color="black", weight=3]; 4523[label="gcd0 (Neg Zero) (Neg (Succ vuz680))",fontsize=16,color="black",shape="box"];4523 -> 4544[label="",style="solid", color="black", weight=3]; 4524 -> 4108[label="",style="dashed", color="red", weight=0]; 4524[label="error []",fontsize=16,color="magenta"];4625 -> 4517[label="",style="dashed", color="red", weight=0]; 4625[label="gcd0 (Pos vuz308) (Neg (Succ vuz710))",fontsize=16,color="magenta"];4625 -> 4648[label="",style="dashed", color="magenta", weight=3]; 4626 -> 4108[label="",style="dashed", color="red", weight=0]; 4626[label="error []",fontsize=16,color="magenta"];6072[label="gcd0 (Pos Zero) (Pos (Succ vuz740))",fontsize=16,color="black",shape="box"];6072 -> 6079[label="",style="solid", color="black", weight=3]; 6073 -> 4108[label="",style="dashed", color="red", weight=0]; 6073[label="error []",fontsize=16,color="magenta"];6074[label="absReal1 (Pos vuz144) (compare (Pos vuz144) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6074 -> 6080[label="",style="solid", color="black", weight=3]; 6075[label="absReal1 (Neg (Succ vuz2820)) (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6075 -> 6081[label="",style="solid", color="black", weight=3]; 6076[label="gcd0Gcd'1 (primEqInt (Pos vuz3730) (fromInt (Pos Zero))) vuz374 (Pos vuz3730)",fontsize=16,color="burlywood",shape="box"];6580[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6076 -> 6580[label="",style="solid", color="burlywood", weight=9]; 6580 -> 6082[label="",style="solid", color="burlywood", weight=3]; 6581[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6076 -> 6581[label="",style="solid", color="burlywood", weight=9]; 6581 -> 6083[label="",style="solid", color="burlywood", weight=3]; 6077[label="gcd0Gcd'1 (primEqInt (Neg vuz3730) (fromInt (Pos Zero))) vuz374 (Neg vuz3730)",fontsize=16,color="burlywood",shape="box"];6582[label="vuz3730/Succ vuz37300",fontsize=10,color="white",style="solid",shape="box"];6077 -> 6582[label="",style="solid", color="burlywood", weight=9]; 6582 -> 6084[label="",style="solid", color="burlywood", weight=3]; 6583[label="vuz3730/Zero",fontsize=10,color="white",style="solid",shape="box"];6077 -> 6583[label="",style="solid", color="burlywood", weight=9]; 6583 -> 6085[label="",style="solid", color="burlywood", weight=3]; 4542 -> 6011[label="",style="dashed", color="red", weight=0]; 4542[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz1440)))",fontsize=16,color="magenta"];4542 -> 6020[label="",style="dashed", color="magenta", weight=3]; 4542 -> 6021[label="",style="dashed", color="magenta", weight=3]; 6078[label="absReal1 (Neg vuz68) (compare (Neg vuz68) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6078 -> 6086[label="",style="solid", color="black", weight=3]; 4544 -> 6011[label="",style="dashed", color="red", weight=0]; 4544[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz680)))",fontsize=16,color="magenta"];4544 -> 6022[label="",style="dashed", color="magenta", weight=3]; 4544 -> 6023[label="",style="dashed", color="magenta", weight=3]; 4648[label="Succ vuz710",fontsize=16,color="green",shape="box"];6079 -> 6011[label="",style="dashed", color="red", weight=0]; 6079[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz740)))",fontsize=16,color="magenta"];6079 -> 6087[label="",style="dashed", color="magenta", weight=3]; 6079 -> 6088[label="",style="dashed", color="magenta", weight=3]; 6080[label="absReal1 (Pos vuz144) (not (compare (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6080 -> 6089[label="",style="solid", color="black", weight=3]; 6081[label="absReal1 (Neg (Succ vuz2820)) (not (compare (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6081 -> 6090[label="",style="solid", color="black", weight=3]; 6082[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6082 -> 6091[label="",style="solid", color="black", weight=3]; 6083[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6083 -> 6092[label="",style="solid", color="black", weight=3]; 6084[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (fromInt (Pos Zero))) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6084 -> 6093[label="",style="solid", color="black", weight=3]; 6085[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6085 -> 6094[label="",style="solid", color="black", weight=3]; 6020 -> 6012[label="",style="dashed", color="red", weight=0]; 6020[label="abs (Pos (Succ vuz1440))",fontsize=16,color="magenta"];6020 -> 6045[label="",style="dashed", color="magenta", weight=3]; 6021 -> 6014[label="",style="dashed", color="red", weight=0]; 6021[label="abs (Neg Zero)",fontsize=16,color="magenta"];6021 -> 6046[label="",style="dashed", color="magenta", weight=3]; 6086[label="absReal1 (Neg vuz68) (not (compare (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6086 -> 6095[label="",style="solid", color="black", weight=3]; 6022 -> 6014[label="",style="dashed", color="red", weight=0]; 6022[label="abs (Neg (Succ vuz680))",fontsize=16,color="magenta"];6022 -> 6047[label="",style="dashed", color="magenta", weight=3]; 6023 -> 6014[label="",style="dashed", color="red", weight=0]; 6023[label="abs (Neg Zero)",fontsize=16,color="magenta"];6023 -> 6048[label="",style="dashed", color="magenta", weight=3]; 6087 -> 6012[label="",style="dashed", color="red", weight=0]; 6087[label="abs (Pos (Succ vuz740))",fontsize=16,color="magenta"];6087 -> 6096[label="",style="dashed", color="magenta", weight=3]; 6088 -> 6012[label="",style="dashed", color="red", weight=0]; 6088[label="abs (Pos Zero)",fontsize=16,color="magenta"];6088 -> 6097[label="",style="dashed", color="magenta", weight=3]; 6089[label="absReal1 (Pos vuz144) (not (primCmpInt (Pos vuz144) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6584[label="vuz144/Succ vuz1440",fontsize=10,color="white",style="solid",shape="box"];6089 -> 6584[label="",style="solid", color="burlywood", weight=9]; 6584 -> 6098[label="",style="solid", color="burlywood", weight=3]; 6585[label="vuz144/Zero",fontsize=10,color="white",style="solid",shape="box"];6089 -> 6585[label="",style="solid", color="burlywood", weight=9]; 6585 -> 6099[label="",style="solid", color="burlywood", weight=3]; 6090[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6090 -> 6100[label="",style="solid", color="black", weight=3]; 6091[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz37300)) (Pos Zero)) vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6091 -> 6101[label="",style="solid", color="black", weight=3]; 6092[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6092 -> 6102[label="",style="solid", color="black", weight=3]; 6093[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz37300)) (Pos Zero)) vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6093 -> 6103[label="",style="solid", color="black", weight=3]; 6094[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6094 -> 6104[label="",style="solid", color="black", weight=3]; 6045[label="Succ vuz1440",fontsize=16,color="green",shape="box"];6046[label="Zero",fontsize=16,color="green",shape="box"];6095[label="absReal1 (Neg vuz68) (not (primCmpInt (Neg vuz68) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6586[label="vuz68/Succ vuz680",fontsize=10,color="white",style="solid",shape="box"];6095 -> 6586[label="",style="solid", color="burlywood", weight=9]; 6586 -> 6105[label="",style="solid", color="burlywood", weight=3]; 6587[label="vuz68/Zero",fontsize=10,color="white",style="solid",shape="box"];6095 -> 6587[label="",style="solid", color="burlywood", weight=9]; 6587 -> 6106[label="",style="solid", color="burlywood", weight=3]; 6047[label="Succ vuz680",fontsize=16,color="green",shape="box"];6048[label="Zero",fontsize=16,color="green",shape="box"];6096[label="Succ vuz740",fontsize=16,color="green",shape="box"];6097[label="Zero",fontsize=16,color="green",shape="box"];6098[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6098 -> 6107[label="",style="solid", color="black", weight=3]; 6099[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6099 -> 6108[label="",style="solid", color="black", weight=3]; 6100[label="absReal1 (Neg (Succ vuz2820)) (not (primCmpInt (Neg (Succ vuz2820)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];6100 -> 6109[label="",style="solid", color="black", weight=3]; 6101[label="gcd0Gcd'1 False vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6101 -> 6110[label="",style="solid", color="black", weight=3]; 6102[label="gcd0Gcd'1 True vuz374 (Pos Zero)",fontsize=16,color="black",shape="box"];6102 -> 6111[label="",style="solid", color="black", weight=3]; 6103[label="gcd0Gcd'1 False vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6103 -> 6112[label="",style="solid", color="black", weight=3]; 6104[label="gcd0Gcd'1 True vuz374 (Neg Zero)",fontsize=16,color="black",shape="box"];6104 -> 6113[label="",style="solid", color="black", weight=3]; 6105[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6105 -> 6114[label="",style="solid", color="black", weight=3]; 6106[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6106 -> 6115[label="",style="solid", color="black", weight=3]; 6107[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpInt (Pos (Succ vuz1440)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6107 -> 6116[label="",style="solid", color="black", weight=3]; 6108[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6108 -> 6117[label="",style="solid", color="black", weight=3]; 6109[label="absReal1 (Neg (Succ vuz2820)) (not (LT == LT))",fontsize=16,color="black",shape="box"];6109 -> 6118[label="",style="solid", color="black", weight=3]; 6110[label="gcd0Gcd'0 vuz374 (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6110 -> 6119[label="",style="solid", color="black", weight=3]; 6111[label="vuz374",fontsize=16,color="green",shape="box"];6112[label="gcd0Gcd'0 vuz374 (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6112 -> 6120[label="",style="solid", color="black", weight=3]; 6113[label="vuz374",fontsize=16,color="green",shape="box"];6114 -> 6100[label="",style="dashed", color="red", weight=0]; 6114[label="absReal1 (Neg (Succ vuz680)) (not (primCmpInt (Neg (Succ vuz680)) (Pos Zero) == LT))",fontsize=16,color="magenta"];6114 -> 6121[label="",style="dashed", color="magenta", weight=3]; 6115[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6115 -> 6122[label="",style="solid", color="black", weight=3]; 6116[label="absReal1 (Pos (Succ vuz1440)) (not (primCmpNat (Succ vuz1440) Zero == LT))",fontsize=16,color="black",shape="box"];6116 -> 6123[label="",style="solid", color="black", weight=3]; 6117[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6117 -> 6124[label="",style="solid", color="black", weight=3]; 6118[label="absReal1 (Neg (Succ vuz2820)) (not True)",fontsize=16,color="black",shape="box"];6118 -> 6125[label="",style="solid", color="black", weight=3]; 6119 -> 6011[label="",style="dashed", color="red", weight=0]; 6119[label="gcd0Gcd' (Pos (Succ vuz37300)) (vuz374 `rem` Pos (Succ vuz37300))",fontsize=16,color="magenta"];6119 -> 6126[label="",style="dashed", color="magenta", weight=3]; 6119 -> 6127[label="",style="dashed", color="magenta", weight=3]; 6120 -> 6011[label="",style="dashed", color="red", weight=0]; 6120[label="gcd0Gcd' (Neg (Succ vuz37300)) (vuz374 `rem` Neg (Succ vuz37300))",fontsize=16,color="magenta"];6120 -> 6128[label="",style="dashed", color="magenta", weight=3]; 6120 -> 6129[label="",style="dashed", color="magenta", weight=3]; 6121[label="vuz680",fontsize=16,color="green",shape="box"];6122[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6122 -> 6130[label="",style="solid", color="black", weight=3]; 6123[label="absReal1 (Pos (Succ vuz1440)) (not (GT == LT))",fontsize=16,color="black",shape="box"];6123 -> 6131[label="",style="solid", color="black", weight=3]; 6124[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];6124 -> 6132[label="",style="solid", color="black", weight=3]; 6125[label="absReal1 (Neg (Succ vuz2820)) False",fontsize=16,color="black",shape="box"];6125 -> 6133[label="",style="solid", color="black", weight=3]; 6126[label="vuz374 `rem` Pos (Succ vuz37300)",fontsize=16,color="black",shape="box"];6126 -> 6134[label="",style="solid", color="black", weight=3]; 6127[label="Pos (Succ vuz37300)",fontsize=16,color="green",shape="box"];6128[label="vuz374 `rem` Neg (Succ vuz37300)",fontsize=16,color="black",shape="box"];6128 -> 6135[label="",style="solid", color="black", weight=3]; 6129[label="Neg (Succ vuz37300)",fontsize=16,color="green",shape="box"];6130[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];6130 -> 6136[label="",style="solid", color="black", weight=3]; 6131[label="absReal1 (Pos (Succ vuz1440)) (not False)",fontsize=16,color="black",shape="box"];6131 -> 6137[label="",style="solid", color="black", weight=3]; 6132[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];6132 -> 6138[label="",style="solid", color="black", weight=3]; 6133[label="absReal0 (Neg (Succ vuz2820)) otherwise",fontsize=16,color="black",shape="box"];6133 -> 6139[label="",style="solid", color="black", weight=3]; 6134[label="primRemInt vuz374 (Pos (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6588[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6134 -> 6588[label="",style="solid", color="burlywood", weight=9]; 6588 -> 6140[label="",style="solid", color="burlywood", weight=3]; 6589[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6134 -> 6589[label="",style="solid", color="burlywood", weight=9]; 6589 -> 6141[label="",style="solid", color="burlywood", weight=3]; 6135[label="primRemInt vuz374 (Neg (Succ vuz37300))",fontsize=16,color="burlywood",shape="box"];6590[label="vuz374/Pos vuz3740",fontsize=10,color="white",style="solid",shape="box"];6135 -> 6590[label="",style="solid", color="burlywood", weight=9]; 6590 -> 6142[label="",style="solid", color="burlywood", weight=3]; 6591[label="vuz374/Neg vuz3740",fontsize=10,color="white",style="solid",shape="box"];6135 -> 6591[label="",style="solid", color="burlywood", weight=9]; 6591 -> 6143[label="",style="solid", color="burlywood", weight=3]; 6136[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];6136 -> 6144[label="",style="solid", color="black", weight=3]; 6137[label="absReal1 (Pos (Succ vuz1440)) True",fontsize=16,color="black",shape="box"];6137 -> 6145[label="",style="solid", color="black", weight=3]; 6138[label="Pos Zero",fontsize=16,color="green",shape="box"];6139[label="absReal0 (Neg (Succ vuz2820)) True",fontsize=16,color="black",shape="box"];6139 -> 6146[label="",style="solid", color="black", weight=3]; 6140[label="primRemInt (Pos vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6140 -> 6147[label="",style="solid", color="black", weight=3]; 6141[label="primRemInt (Neg vuz3740) (Pos (Succ vuz37300))",fontsize=16,color="black",shape="box"];6141 -> 6148[label="",style="solid", color="black", weight=3]; 6142[label="primRemInt (Pos vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6142 -> 6149[label="",style="solid", color="black", weight=3]; 6143[label="primRemInt (Neg vuz3740) (Neg (Succ vuz37300))",fontsize=16,color="black",shape="box"];6143 -> 6150[label="",style="solid", color="black", weight=3]; 6144[label="Neg Zero",fontsize=16,color="green",shape="box"];6145[label="Pos (Succ vuz1440)",fontsize=16,color="green",shape="box"];6146[label="`negate` Neg (Succ vuz2820)",fontsize=16,color="black",shape="box"];6146 -> 6151[label="",style="solid", color="black", weight=3]; 6147[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6147 -> 6152[label="",style="dashed", color="green", weight=3]; 6148[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6148 -> 6153[label="",style="dashed", color="green", weight=3]; 6149[label="Pos (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6149 -> 6154[label="",style="dashed", color="green", weight=3]; 6150[label="Neg (primModNatS vuz3740 (Succ vuz37300))",fontsize=16,color="green",shape="box"];6150 -> 6155[label="",style="dashed", color="green", weight=3]; 6151[label="primNegInt (Neg (Succ vuz2820))",fontsize=16,color="black",shape="box"];6151 -> 6156[label="",style="solid", color="black", weight=3]; 6152[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="burlywood",shape="triangle"];6592[label="vuz3740/Succ vuz37400",fontsize=10,color="white",style="solid",shape="box"];6152 -> 6592[label="",style="solid", color="burlywood", weight=9]; 6592 -> 6157[label="",style="solid", color="burlywood", weight=3]; 6593[label="vuz3740/Zero",fontsize=10,color="white",style="solid",shape="box"];6152 -> 6593[label="",style="solid", color="burlywood", weight=9]; 6593 -> 6158[label="",style="solid", color="burlywood", weight=3]; 6153 -> 6152[label="",style="dashed", color="red", weight=0]; 6153[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6153 -> 6159[label="",style="dashed", color="magenta", weight=3]; 6154 -> 6152[label="",style="dashed", color="red", weight=0]; 6154[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6154 -> 6160[label="",style="dashed", color="magenta", weight=3]; 6155 -> 6152[label="",style="dashed", color="red", weight=0]; 6155[label="primModNatS vuz3740 (Succ vuz37300)",fontsize=16,color="magenta"];6155 -> 6161[label="",style="dashed", color="magenta", weight=3]; 6155 -> 6162[label="",style="dashed", color="magenta", weight=3]; 6156[label="Pos (Succ vuz2820)",fontsize=16,color="green",shape="box"];6157[label="primModNatS (Succ vuz37400) (Succ vuz37300)",fontsize=16,color="black",shape="box"];6157 -> 6163[label="",style="solid", color="black", weight=3]; 6158[label="primModNatS Zero (Succ vuz37300)",fontsize=16,color="black",shape="box"];6158 -> 6164[label="",style="solid", color="black", weight=3]; 6159[label="vuz3740",fontsize=16,color="green",shape="box"];6160[label="vuz37300",fontsize=16,color="green",shape="box"];6161[label="vuz37300",fontsize=16,color="green",shape="box"];6162[label="vuz3740",fontsize=16,color="green",shape="box"];6163[label="primModNatS0 vuz37400 vuz37300 (primGEqNatS vuz37400 vuz37300)",fontsize=16,color="burlywood",shape="box"];6594[label="vuz37400/Succ vuz374000",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6594[label="",style="solid", color="burlywood", weight=9]; 6594 -> 6165[label="",style="solid", color="burlywood", weight=3]; 6595[label="vuz37400/Zero",fontsize=10,color="white",style="solid",shape="box"];6163 -> 6595[label="",style="solid", color="burlywood", weight=9]; 6595 -> 6166[label="",style="solid", color="burlywood", weight=3]; 6164[label="Zero",fontsize=16,color="green",shape="box"];6165[label="primModNatS0 (Succ vuz374000) vuz37300 (primGEqNatS (Succ vuz374000) vuz37300)",fontsize=16,color="burlywood",shape="box"];6596[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6165 -> 6596[label="",style="solid", color="burlywood", weight=9]; 6596 -> 6167[label="",style="solid", color="burlywood", weight=3]; 6597[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6165 -> 6597[label="",style="solid", color="burlywood", weight=9]; 6597 -> 6168[label="",style="solid", color="burlywood", weight=3]; 6166[label="primModNatS0 Zero vuz37300 (primGEqNatS Zero vuz37300)",fontsize=16,color="burlywood",shape="box"];6598[label="vuz37300/Succ vuz373000",fontsize=10,color="white",style="solid",shape="box"];6166 -> 6598[label="",style="solid", color="burlywood", weight=9]; 6598 -> 6169[label="",style="solid", color="burlywood", weight=3]; 6599[label="vuz37300/Zero",fontsize=10,color="white",style="solid",shape="box"];6166 -> 6599[label="",style="solid", color="burlywood", weight=9]; 6599 -> 6170[label="",style="solid", color="burlywood", weight=3]; 6167[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS (Succ vuz374000) (Succ vuz373000))",fontsize=16,color="black",shape="box"];6167 -> 6171[label="",style="solid", color="black", weight=3]; 6168[label="primModNatS0 (Succ vuz374000) Zero (primGEqNatS (Succ vuz374000) Zero)",fontsize=16,color="black",shape="box"];6168 -> 6172[label="",style="solid", color="black", weight=3]; 6169[label="primModNatS0 Zero (Succ vuz373000) (primGEqNatS Zero (Succ vuz373000))",fontsize=16,color="black",shape="box"];6169 -> 6173[label="",style="solid", color="black", weight=3]; 6170[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6170 -> 6174[label="",style="solid", color="black", weight=3]; 6171 -> 6333[label="",style="dashed", color="red", weight=0]; 6171[label="primModNatS0 (Succ vuz374000) (Succ vuz373000) (primGEqNatS vuz374000 vuz373000)",fontsize=16,color="magenta"];6171 -> 6334[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6335[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6336[label="",style="dashed", color="magenta", weight=3]; 6171 -> 6337[label="",style="dashed", color="magenta", weight=3]; 6172[label="primModNatS0 (Succ vuz374000) Zero True",fontsize=16,color="black",shape="box"];6172 -> 6177[label="",style="solid", color="black", weight=3]; 6173[label="primModNatS0 Zero (Succ vuz373000) False",fontsize=16,color="black",shape="box"];6173 -> 6178[label="",style="solid", color="black", weight=3]; 6174[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];6174 -> 6179[label="",style="solid", color="black", weight=3]; 6334[label="vuz373000",fontsize=16,color="green",shape="box"];6335[label="vuz373000",fontsize=16,color="green",shape="box"];6336[label="vuz374000",fontsize=16,color="green",shape="box"];6337[label="vuz374000",fontsize=16,color="green",shape="box"];6333[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz393 vuz394)",fontsize=16,color="burlywood",shape="triangle"];6600[label="vuz393/Succ vuz3930",fontsize=10,color="white",style="solid",shape="box"];6333 -> 6600[label="",style="solid", color="burlywood", weight=9]; 6600 -> 6366[label="",style="solid", color="burlywood", weight=3]; 6601[label="vuz393/Zero",fontsize=10,color="white",style="solid",shape="box"];6333 -> 6601[label="",style="solid", color="burlywood", weight=9]; 6601 -> 6367[label="",style="solid", color="burlywood", weight=3]; 6177 -> 6152[label="",style="dashed", color="red", weight=0]; 6177[label="primModNatS (primMinusNatS (Succ vuz374000) Zero) (Succ Zero)",fontsize=16,color="magenta"];6177 -> 6184[label="",style="dashed", color="magenta", weight=3]; 6177 -> 6185[label="",style="dashed", color="magenta", weight=3]; 6178[label="Succ Zero",fontsize=16,color="green",shape="box"];6179 -> 6152[label="",style="dashed", color="red", weight=0]; 6179[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];6179 -> 6186[label="",style="dashed", color="magenta", weight=3]; 6179 -> 6187[label="",style="dashed", color="magenta", weight=3]; 6366[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) vuz394)",fontsize=16,color="burlywood",shape="box"];6602[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6366 -> 6602[label="",style="solid", color="burlywood", weight=9]; 6602 -> 6368[label="",style="solid", color="burlywood", weight=3]; 6603[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6366 -> 6603[label="",style="solid", color="burlywood", weight=9]; 6603 -> 6369[label="",style="solid", color="burlywood", weight=3]; 6367[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero vuz394)",fontsize=16,color="burlywood",shape="box"];6604[label="vuz394/Succ vuz3940",fontsize=10,color="white",style="solid",shape="box"];6367 -> 6604[label="",style="solid", color="burlywood", weight=9]; 6604 -> 6370[label="",style="solid", color="burlywood", weight=3]; 6605[label="vuz394/Zero",fontsize=10,color="white",style="solid",shape="box"];6367 -> 6605[label="",style="solid", color="burlywood", weight=9]; 6605 -> 6371[label="",style="solid", color="burlywood", weight=3]; 6184[label="Zero",fontsize=16,color="green",shape="box"];6185 -> 5743[label="",style="dashed", color="red", weight=0]; 6185[label="primMinusNatS (Succ vuz374000) Zero",fontsize=16,color="magenta"];6185 -> 6192[label="",style="dashed", color="magenta", weight=3]; 6185 -> 6193[label="",style="dashed", color="magenta", weight=3]; 6186[label="Zero",fontsize=16,color="green",shape="box"];6187 -> 5743[label="",style="dashed", color="red", weight=0]; 6187[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];6187 -> 6194[label="",style="dashed", color="magenta", weight=3]; 6187 -> 6195[label="",style="dashed", color="magenta", weight=3]; 6368[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) (Succ vuz3940))",fontsize=16,color="black",shape="box"];6368 -> 6372[label="",style="solid", color="black", weight=3]; 6369[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS (Succ vuz3930) Zero)",fontsize=16,color="black",shape="box"];6369 -> 6373[label="",style="solid", color="black", weight=3]; 6370[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero (Succ vuz3940))",fontsize=16,color="black",shape="box"];6370 -> 6374[label="",style="solid", color="black", weight=3]; 6371[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6371 -> 6375[label="",style="solid", color="black", weight=3]; 6192[label="Zero",fontsize=16,color="green",shape="box"];6193[label="Succ vuz374000",fontsize=16,color="green",shape="box"];6194[label="Zero",fontsize=16,color="green",shape="box"];6195[label="Zero",fontsize=16,color="green",shape="box"];6372 -> 6333[label="",style="dashed", color="red", weight=0]; 6372[label="primModNatS0 (Succ vuz391) (Succ vuz392) (primGEqNatS vuz3930 vuz3940)",fontsize=16,color="magenta"];6372 -> 6376[label="",style="dashed", color="magenta", weight=3]; 6372 -> 6377[label="",style="dashed", color="magenta", weight=3]; 6373[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="black",shape="triangle"];6373 -> 6378[label="",style="solid", color="black", weight=3]; 6374[label="primModNatS0 (Succ vuz391) (Succ vuz392) False",fontsize=16,color="black",shape="box"];6374 -> 6379[label="",style="solid", color="black", weight=3]; 6375 -> 6373[label="",style="dashed", color="red", weight=0]; 6375[label="primModNatS0 (Succ vuz391) (Succ vuz392) True",fontsize=16,color="magenta"];6376[label="vuz3940",fontsize=16,color="green",shape="box"];6377[label="vuz3930",fontsize=16,color="green",shape="box"];6378 -> 6152[label="",style="dashed", color="red", weight=0]; 6378[label="primModNatS (primMinusNatS (Succ vuz391) (Succ vuz392)) (Succ (Succ vuz392))",fontsize=16,color="magenta"];6378 -> 6380[label="",style="dashed", color="magenta", weight=3]; 6378 -> 6381[label="",style="dashed", color="magenta", weight=3]; 6379[label="Succ (Succ vuz391)",fontsize=16,color="green",shape="box"];6380[label="Succ vuz392",fontsize=16,color="green",shape="box"];6381 -> 5743[label="",style="dashed", color="red", weight=0]; 6381[label="primMinusNatS (Succ vuz391) (Succ vuz392)",fontsize=16,color="magenta"];6381 -> 6382[label="",style="dashed", color="magenta", weight=3]; 6381 -> 6383[label="",style="dashed", color="magenta", weight=3]; 6382[label="Succ vuz392",fontsize=16,color="green",shape="box"];6383[label="Succ vuz391",fontsize=16,color="green",shape="box"];} ---------------------------------------- (435) TRUE